Advanced

Tutor model

i62 💰:9.4

i52 💰:7.9

🏆 i67 💰:62.5

i70 💰:125.0

i68 💰:125.0

🏆 i66 💰:75.0

i65 💰:125.0

i63 💰:62.5

i61 💰:75.0

i60 💰:9.4

i60 💰:37.5

i58 💰:62.5

i57 💰:22.5

i57 💰:37.5

i56 💰:45.0

⚡ i55 💰:11.25

i55 💰:37.5

i54 💰:62.5

i52 💰:35.0

i51 💰:37.5

i49 💰:15.0

i49 💰:62.5

i48 💰:11.3

i47 💰:7.5

i44 💰:25.0

i43 💰:37.5

i42 💰:187.5

i40 💰:5.0

i39 💰:100.0

i38 💰:37.5

i37 💰:11.0

i36 💰:187.5

i34 💰:12.5

i33 💰:37.5

i30 💰:1.0

i29 💰:1.5

i28 💰:150.0

i23 💰:20.0

i20 💰:4.0

i18 💰:1.0

i16 💰:25.0

i13 💰:1.5

Keep session private

What would you like to learn?

Override for the tutor's lesson content generation calls. Auto uses the system default (Claude Sonnet 5 for lesson text, Opus 5 for diagrams).

Lesson generation model

System default

i58 💰:18.8

i31 💰:11.0

i25 💰:31.3

Tutoring abilities

A bike rusting in the rain takes months to corrode, while the gunpowder inside a firework reacts in milliseconds.

The **rate of reaction** is a measure of how quickly reactants are converted into products during a chemical change.

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="aspect-ratio" content="4:3">
<style>
  * { box-sizing: border-box; margin: 0; padding: 0; }
  body {
    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
    background: transparent;
    color: #1e2945;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    min-height: 100%;
    padding: 8px;
    user-select: none;
    -webkit-user-select: none;
  }

  .main-grid {
    display: grid;
    grid-template-columns: 1fr 1.3fr;
    gap: 12px;
    width: 100%;
    max-width: 580px;
    align-items: center;
  }

  @media (max-width: 460px) {
    .main-grid {
      grid-template-columns: 1fr;
      gap: 8px;
    }
  }

  .panel {
    background: #ffffff;
    border: 1px solid #e6e6e6;
    border-radius: 12px;
    padding: 10px;
    box-shadow: 0 2px 6px rgba(0,0,0,0.03);
    display: flex;
    flex-direction: column;
    align-items: center;
  }

  /* Chamber */
  .chamber {
    width: 100%;
    height: 140px;
    background: #f8f9fa;
    border: 2px solid #cbd5e1;
    border-radius: 8px;
    position: relative;
    overflow: hidden;
    display: flex;
    flex-wrap: wrap;
    align-content: center;
    justify-content: center;
    gap: 8px;
    padding: 10px;
  }

  .particle {
    width: 16px;
    height: 16px;
    border-radius: 50%;
    transition: background-color 0.4s ease, transform 0.4s ease;
  }

  .particle.reactant {
    background: #6366f1;
  }

  .particle.product {
    background: #10b981;
    border-radius: 3px;
    transform: rotate(45deg);
  }

  .legend-row {
    display: flex;
    justify-content: space-around;
    width: 100%;
    margin-top: 8px;
    font-size: 13px;
    font-weight: 600;
  }

  .legend-item {
    display: flex;
    align-items: center;
    gap: 5px;
  }

  .dot-r { width: 10px; height: 10px; border-radius: 50%; background: #6366f1; }
  .dot-p { width: 9px; height: 9px; border-radius: 2px; background: #10b981; transform: rotate(45deg); }

  /* Graph */
  .graph-container {
    width: 100%;
    height: 170px;
    position: relative;
  }

  svg {
    width: 100%;
    height: 100%;
    overflow: visible;
  }

  /* Controls */
  .controls {
    display: flex;
    gap: 6px;
    margin-top: 10px;
    width: 100%;
    max-width: 580px;
    justify-content: center;
  }

  .btn {
    background: #f1f5f9;
    border: 1px solid #cbd5e1;
    border-radius: 8px;
    padding: 6px 14px;
    font-size: 13px;
    font-weight: 600;
    color: #475569;
    cursor: pointer;
    transition: all 0.2s ease;
    flex: 1;
    text-align: center;
    max-width: 100px;
  }

  .btn.active {
    background: #22b7ff;
    border-color: #22b7ff;
    color: #ffffff;
    box-shadow: 0 2px 4px rgba(34, 183, 255, 0.3);
  }

  .play-btn {
    max-width: 44px;
    background: #ffffff;
    color: #1e2945;
  }

  .rate-badge {
    margin-top: 6px;
    font-size: 12px;
    font-weight: 700;
    color: #64748b;
    letter-spacing: 0.5px;
    text-transform: uppercase;
  }
  .rate-val {
    color: #22b7ff;
  }
</style>
</head>
<body>

<div class="main-grid">
  
  <div class="panel">
    <div class="chamber" id="chamber"></div>
    <div class="legend-row">
      <div class="legend-item"><span class="dot-r"></span> Reactants</div>
      <div class="legend-item"><span class="dot-p"></span> Products</div>
    </div>
    <div class="rate-badge">Rate: <span id="rateLabel" class="rate-val">Fast</span></div>
  </div>

  
  <div class="panel">
    <div class="graph-container">
      <svg viewBox="0 0 240 150">
        
        <line x1="30" y1="125" x2="230" y2="125" stroke="#94a3b8" stroke-width="1.5" />
        <line x1="30" y1="15" x2="30" y2="125" stroke="#94a3b8" stroke-width="1.5" />
        
        
        <text x="230" y="140" fill="#64748b" font-size="11" font-weight="600" text-anchor="end">Time →</text>
        <text x="10" y="20" fill="#64748b" font-size="11" font-weight="600" transform="rotate(-90 15 20)">Amount</text>

        
        <path id="curveR" fill="none" stroke="#6366f1" stroke-width="2.5" stroke-linecap="round" />
        
        
        <path id="curveP" fill="none" stroke="#10b981" stroke-width="2.5" stroke-linecap="round" />

        
        <line id="timeLine" x1="30" y1="15" x2="30" y2="125" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="3,3" />

        
        <circle id="pointR" cx="30" cy="25" r="4.5" fill="#6366f1" stroke="#fff" stroke-width="1.5" />
        <circle id="pointP" cx="30" cy="125" r="4.5" fill="#10b981" stroke="#fff" stroke-width="1.5" />
      </svg>
    </div>
  </div>
</div>

<div class="controls">
  <button class="btn play-btn" id="playBtn" aria-label="Play/Pause">⏸</button>
  <button class="btn active" id="btn0">Start</button>
  <button class="btn" id="btn1">Middle</button>
  <button class="btn" id="btn2">End</button>
</div>

<script>
  const TOTAL_PARTICLES = 24;
  const chamber = document.getElementById('chamber');
  
  // Create particles
  for (let i = 0; i < TOTAL_PARTICLES; i++) {
    const p = document.createElement('div');
    p.className = 'particle reactant';
    chamber.appendChild(p);
  }

  // Precompute SVG curves accurately (k = 0.028)
  const x0 = 30, xMax = 225;
  const yBottom = 125, yTop = 25;
  const h = yBottom - yTop; // 100
  const k = 0.026;

  function getY_R(t) {
    return yTop + h * (1 - Math.exp(-k * t));
  }
  function getY_P(t) {
    return yBottom - h * (1 - Math.exp(-k * t));
  }

  const pathR = document.getElementById('curveR');
  const pathP = document.getElementById('curveP');

  let dR = `M ${x0} ${yTop}`;
  let dP = `M ${x0} ${yBottom}`;
  for (let x = x0; x <= xMax; x += 3) {
    const t = x - x0;
    dR += ` L ${x} ${getY_R(t).toFixed(1)}`;
    dP += ` L ${x} ${getY_P(t).toFixed(1)}`;
  }
  pathR.setAttribute('d', dR);
  pathP.setAttribute('d', dP);

  // Stepper logic
  const steps = [
    { t: 0, label: 'Fast' },
    { t: 45, label: 'Slowing' },
    { t: 185, label: 'Stopped' }
  ];

  let currentStep = 0;
  let isPlaying = true;
  let timer = null;

  function updateVisual(t, rateText) {
    const x = x0 + t;
    const yR = getY_R(t);
    const yP = getY_P(t);

    document.getElementById('timeLine').setAttribute('x1', x);
    document.getElementById('timeLine').setAttribute('x2', x);
    document.getElementById('pointR').setAttribute('cx', x);
    document.getElementById('pointR').setAttribute('cy', yR);
    document.getElementById('pointP').setAttribute('cx', x);
    document.getElementById('pointP').setAttribute('cy', yP);

    document.getElementById('rateLabel').textContent = rateText;

    // Update chamber particles
    const fracProduct = (yBottom - yP) / h;
    const numProducts = Math.round(fracProduct * TOTAL_PARTICLES);
    const particles = chamber.children;
    for (let i = 0; i < TOTAL_PARTICLES; i++) {
      if (i < numProducts) {
        particles[i].className = 'particle product';
      } else {
        particles[i].className = 'particle reactant';
      }
    }
  }

  function setStep(idx) {
    currentStep = idx;
    [0, 1, 2].forEach(i => {
      document.getElementById('btn' + i).classList.toggle('active', i === idx);
    });
    updateVisual(steps[idx].t, steps[idx].label);
  }

  function nextStep() {
    setStep((currentStep + 1) % 3);
  }

  function startAuto() {
    if (timer) clearInterval(timer);
    timer = setInterval(nextStep, 3200);
    isPlaying = true;
    document.getElementById('playBtn').textContent = '⏸';
  }

  function stopAuto() {
    if (timer) clearInterval(timer);
    isPlaying = false;
    document.getElementById('playBtn').textContent = '▶';
  }

  // Bind Buttons
  [0, 1, 2].forEach(i => {
    document.getElementById('btn' + i).addEventListener('click', () => {
      stopAuto();
      setStep(i);
    });
  });

  document.getElementById('playBtn').addEventListener('click', () => {
    if (isPlaying) {
      stopAuto();
    } else {
      nextStep();
      startAuto();
    }
  });

  // Init
  setStep(0);
  startAuto();
</script>

</body>
</html>

To calculate the mean rate of a reaction, you divide the amount of reactant used up—or the amount of product formed—by the time taken.

$$\text{Mean Rate} = \frac{\text{Quantity of reactant used or product formed}}{\text{Time taken}}$$

The units of rate depend on what you measure: mass in grams gives $\text{g/s}$, volume of gas in cubic centimeters gives $\text{cm}^3\text{/s}$, and chemical amount gives $\text{mol/s}$.

So how do we capture these changing quantities in a real laboratory setup?

When a reaction produces a gas, you can seal the flask with a stopper and collect the gas in a graduated **gas syringe** or an inverted measuring cylinder filled with water.

Consider the reaction between magnesium ribbon and hydrochloric acid: $\text{Mg}(s) + 2\text{HCl}(aq) \rightarrow \text{MgCl}_2(aq) + \text{H}_2(g)$.

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="aspect-ratio" content="4:3">
<title>Measuring Rate of Reaction</title>
<style>
  * { box-sizing: border-box; margin: 0; padding: 0; }
  body {
    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
    background: #ffffff;
    color: #1e2945;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: space-between;
    min-height: 100%;
    padding: 10px;
    user-select: none;
    -webkit-user-select: none;
  }

  .main-layout {
    display: grid;
    grid-template-columns: 1fr 1fr;
    gap: 12px;
    width: 100%;
    max-width: 620px;
    height: 280px;
  }

  @media (max-width: 480px) {
    .main-layout {
      grid-template-columns: 1fr;
      height: 380px;
    }
  }

  .panel {
    background: #f8f9fa;
    border: 1px solid #e6e6e6;
    border-radius: 10px;
    position: relative;
    overflow: hidden;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
  }

  svg {
    width: 100%;
    height: 100%;
    overflow: visible;
  }

  .controls {
    display: flex;
    gap: 6px;
    width: 100%;
    max-width: 620px;
    margin-top: 10px;
    flex-wrap: wrap;
    justify-content: center;
  }

  .btn {
    background: #f8f9fa;
    border: 1px solid #d1d5db;
    border-radius: 8px;
    padding: 6px 12px;
    font-size: 13px;
    font-weight: 600;
    color: #4b5563;
    cursor: pointer;
    transition: all 0.2s ease;
    display: flex;
    align-items: center;
    gap: 4px;
  }

  .btn:hover {
    background: #f3f4f6;
  }

  .btn.active {
    background: #22b7ff;
    border-color: #22b7ff;
    color: #ffffff;
  }

  .bubble {
    animation: rise 1.2s infinite ease-in;
  }

  @keyframes rise {
    0% { transform: translateY(0); opacity: 0.8; }
    100% { transform: translateY(-35px); opacity: 0; }
  }
</style>
</head>
<body>

<div class="main-layout">
  
  <div class="panel">
    <svg viewBox="0 0 280 220" id="apparatusSvg">
      
      <path d="M 95 105 L 95 60 Q 95 50 105 50 L 170 50 Q 175 50 175 55 L 175 78" 
            fill="none" stroke="#94a3b8" stroke-width="4" stroke-linecap="round"/>
      
      
      <path d="M 85 110 L 90 110 L 90 130 L 125 195 Q 130 205 115 205 L 65 205 Q 50 205 55 195 L 90 130 L 90 110 Z" 
            fill="#e0f2fe" stroke="#64748b" stroke-width="2.5" stroke-linejoin="round"/>
      
      <polygon points="84,110 96,110 94,120 86,120" fill="#78350f"/>
      
      
      <path d="M 64 185 Q 90 183 116 185 L 122 197 Q 126 203 115 203 L 65 203 Q 54 203 58 197 Z" 
            fill="#bae6fd" opacity="0.8"/>
      
      
      <rect id="mgRibbon" x="80" y="195" width="20" height="4" rx="2" fill="#9ca3af"/>
      
      
      <g id="bubbleGroup">
        <circle cx="82" cy="190" r="2" fill="#38bdf8" class="bubble" style="animation-delay: 0s;"/>
        <circle cx="90" cy="192" r="2.5" fill="#38bdf8" class="bubble" style="animation-delay: 0.4s;"/>
        <circle cx="97" cy="189" r="1.8" fill="#38bdf8" class="bubble" style="animation-delay: 0.8s;"/>
      </g>
      
      
      <text x="90" y="216" font-size="11" text-anchor="middle" fill="#64748b" font-weight="bold">Mg + HCl</text>

      
      <rect x="175" y="70" width="90" height="20" rx="2" fill="#f1f5f9" stroke="#64748b" stroke-width="2"/>
      <rect x="170" y="77" width="5" height="6" fill="#64748b"/>
      
      
      <line x1="190" y1="70" x2="190" y2="76" stroke="#94a3b8" stroke-width="1"/>
      <line x1="210" y1="70" x2="210" y2="76" stroke="#94a3b8" stroke-width="1"/>
      <line x1="230" y1="70" x2="230" y2="76" stroke="#94a3b8" stroke-width="1"/>
      <line x1="250" y1="70" x2="250" y2="76" stroke="#94a3b8" stroke-width="1"/>
      
      
      <text x="177" y="66" font-size="8" fill="#94a3b8">0</text>
      <text x="257" y="66" font-size="8" fill="#94a3b8">50</text>

      
      <g id="plunger" transform="translate(0, 0)" style="transition: transform 0.5s ease;">
        <rect x="175" y="71" width="5" height="18" fill="#0284c7"/>
        <rect x="180" y="77" width="75" height="6" fill="#cbd5e1" stroke="#64748b" stroke-width="1"/>
        <rect x="255" y="68" width="4" height="24" rx="1" fill="#475569"/>
      </g>
      
      
      <text x="220" y="105" font-size="11" text-anchor="middle" fill="#64748b" font-weight="bold">Gas Syringe</text>
      
      
      <path d="M 130 42 L 145 42" stroke="#22b7ff" stroke-width="2" marker-end="url(#arrow)"/>
      <defs>
        <marker id="arrow" viewBox="0 0 6 6" refX="5" refY="3" markerWidth="4" markerHeight="4" orient="auto">
          <path d="M 0 0 L 6 3 L 0 6 z" fill="#22b7ff"/>
        </marker>
      </defs>
      <text x="137" y="36" font-size="11" text-anchor="middle" fill="#0284c7" font-weight="bold">H₂ (g)</text>
    </svg>
  </div>

  
  <div class="panel">
    <svg viewBox="0 0 280 220" id="graphSvg">
      
      <line x1="45" y1="180" x2="260" y2="180" stroke="#475569" stroke-width="2"/>
      <line x1="45" y1="180" x2="45" y2="25" stroke="#475569" stroke-width="2"/>
      
      
      <text x="255" y="196" font-size="11" text-anchor="end" fill="#475569" font-weight="bold">Time (s)</text>
      <text x="20" y="24" font-size="11" text-anchor="start" fill="#475569" font-weight="bold">Volume (cm³)</text>
      
      
      <line x1="45" y1="50" x2="260" y2="50" stroke="#e2e8f0" stroke-dasharray="3,3" stroke-width="1.5"/>
      <text x="38" y="54" font-size="9" text-anchor="end" fill="#94a3b8">50</text>
      <text x="38" y="184" font-size="9" text-anchor="end" fill="#94a3b8">0</text>
      
      
      <path id="curvePath" d="M 45 180 Q 80 55 250 50" fill="none" stroke="#cbd5e1" stroke-width="3" stroke-linecap="round"/>
      <path id="activePath" d="M 45 180 Q 80 55 250 50" fill="none" stroke="#22b7ff" stroke-width="3" stroke-linecap="round" stroke-dasharray="300" stroke-dashoffset="300" style="transition: stroke-dashoffset 0.5s ease;"/>
      
      
      <line id="tangentLine" x1="0" y1="0" x2="0" y2="0" stroke="#e11d48" stroke-width="2" stroke-dasharray="4,3" opacity="0" style="transition: all 0.5s ease;"/>
      
      
      <circle id="trackerDot" cx="45" cy="180" r="5" fill="#e11d48" stroke="#ffffff" stroke-width="2" style="transition: cx 0.5s ease, cy 0.5s ease;"/>
      
      
      <g id="rateTag" transform="translate(145, 140)" opacity="0" style="transition: opacity 0.3s ease;">
        <rect x="-45" y="-12" width="90" height="24" rx="6" fill="#1e2945" opacity="0.9"/>
        <text id="rateText" x="0" y="4" font-size="11" fill="#ffffff" text-anchor="middle" font-weight="bold">Fast Rate</text>
      </g>
    </svg>
  </div>
</div>

<div class="controls">
  <button class="btn active" onclick="setStep(0)">0s (Start)</button>
  <button class="btn" onclick="setStep(1)">20s (Fast)</button>
  <button class="btn" onclick="setStep(2)">50s (Slowing)</button>
  <button class="btn" onclick="setStep(3)">90s (Stopped)</button>
</div>

<script>
  const steps = [
    {
      plungerOffset: 0,
      mgWidth: 20,
      bubbles: 'visible',
      dashOffset: 300,
      dotX: 45,
      dotY: 180,
      tx1: 30, ty1: 200, tx2: 80, ty2: 120,
      showTangent: false,
      tagOpacity: 0,
      tagText: ''
    },
    {
      plungerOffset: 42,
      mgWidth: 14,
      bubbles: 'visible',
      dashOffset: 170,
      dotX: 95,
      dotY: 102,
      tx1: 65, ty1: 155, tx2: 135, ty2: 60,
      showTangent: true,
      tagOpacity: 1,
      tagText: 'Fast Rate'
    },
    {
      plungerOffset: 65,
      mgWidth: 7,
      bubbles: 'visible',
      dashOffset: 85,
      dotX: 160,
      dotY: 63,
      tx1: 110, ty1: 78, tx2: 210, ty2: 52,
      showTangent: true,
      tagOpacity: 1,
      tagText: 'Slowing Rate'
    },
    {
      plungerOffset: 75,
      mgWidth: 0,
      bubbles: 'none',
      dashOffset: 0,
      dotX: 240,
      dotY: 50,
      tx1: 180, ty1: 50, tx2: 260, ty2: 50,
      showTangent: true,
      tagOpacity: 1,
      tagText: 'Rate = 0'
    }
  ];

  let currentStep = 0;
  let timer = null;

  function setStep(index) {
    currentStep = index;
    const s = steps[index];

    // Buttons
    document.querySelectorAll('.btn').forEach((b, i) => {
      b.classList.toggle('active', i === index);
    });

    // Syringe Plunger
    document.getElementById('plunger').setAttribute('transform', `translate(${s.plungerOffset}, 0)`);
    
    // Mg Ribbon & Bubbles
    document.getElementById('mgRibbon').setAttribute('width', s.mgWidth);
    document.getElementById('bubbleGroup').style.display = s.bubbles;

    // Graph Elements
    document.getElementById('activePath').style.strokeDashoffset = s.dashOffset;
    document.getElementById('trackerDot').setAttribute('cx', s.dotX);
    document.getElementById('trackerDot').setAttribute('cy', s.dotY);

    // Tangent Line
    const tangent = document.getElementById('tangentLine');
    if (s.showTangent) {
      tangent.setAttribute('x1', s.tx1);
      tangent.setAttribute('y1', s.ty1);
      tangent.setAttribute('x2', s.tx2);
      tangent.setAttribute('y2', s.ty2);
      tangent.setAttribute('opacity', '1');
    } else {
      tangent.setAttribute('opacity', '0');
    }

    // Rate Tag
    const tag = document.getElementById('rateTag');
    tag.setAttribute('opacity', s.tagOpacity);
    document.getElementById('rateText').textContent = s.tagText;
  }

  // Auto progression
  function startCycle() {
    timer = setInterval(() => {
      let next = (currentStep + 1) % steps.length;
      setStep(next);
    }, 3200);
  }

  // User click pauses auto progression temporarily
  document.querySelectorAll('.btn').forEach(btn => {
    btn.addEventListener('click', () => {
      clearInterval(timer);
      startCycle();
    });
  });

  setStep(0);
  startCycle();
</script>

</body>
</html>

When **measuring gas production**, the mean rate is calculated as $\text{Rate} = \frac{\Delta V}{\Delta t}$ in units of $\text{cm}^3/\text{s}$ or $\text{cm}^3/\text{min}$. If $45\text{ cm}^3$ of $\text{H}_2$ collects in $30\text{ s}$:

For instance, collecting $45\text{ cm}^3$ of hydrogen gas in $30\text{ s}$ gives: $$\text{Rate} = \frac{45\text{ cm}^3}{30\text{ s}} = 1.5\text{ cm}^3/\text{s} = 90\text{ cm}^3/\text{min}$$

Gas syringes work brilliantly, but what if the gas is too heavy or you don't have a syringe handy?

If a dense gas like carbon dioxide is released into the room, the total mass of the reaction flask decreases over time as the gas escapes.

You place the flask directly on a digital **top-pan balance** and plug the neck with a loose wad of **cotton wool** to let gas escape while preventing acid splashes.

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="aspect-ratio" content="4:3">
<title>Measuring Rate via Mass Loss</title>
<style>
  * { box-sizing: border-box; margin: 0; padding: 0; }
  body {
    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    color: #1e2945;
    background: transparent;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    min-height: 100vh;
    padding: 12px;
  }
  .app-container {
    width: 100%;
    max-width: 480px;
    display: flex;
    flex-direction: column;
    align-items: center;
    gap: 12px;
  }
  .controls {
    display: flex;
    gap: 8px;
    background: #f1f5f9;
    padding: 4px;
    border-radius: 24px;
  }
  .step-btn {
    border: none;
    background: transparent;
    padding: 6px 14px;
    border-radius: 20px;
    font-size: 14px;
    font-weight: 600;
    color: #64748b;
    cursor: pointer;
    transition: all 0.25s ease;
  }
  .step-btn.active {
    background: #ffffff;
    color: #0284c7;
    box-shadow: 0 2px 6px rgba(0,0,0,0.08);
  }
  .stage-card {
    width: 100%;
    background: #ffffff;
    border-radius: 16px;
    border: 1px solid #e2e8f0;
    box-shadow: 0 4px 12px rgba(0,0,0,0.03);
    padding: 12px 16px;
    display: flex;
    flex-direction: column;
    align-items: center;
  }
  .svg-wrap {
    width: 100%;
    max-width: 320px;
    height: 250px;
  }
  .readouts {
    display: flex;
    justify-content: space-around;
    width: 100%;
    margin-top: 8px;
    padding-top: 10px;
    border-top: 1px solid #f1f5f9;
  }
  .readout-box {
    text-align: center;
  }
  .readout-lbl {
    font-size: 12px;
    font-weight: 600;
    color: #64748b;
    text-transform: uppercase;
    letter-spacing: 0.5px;
  }
  .readout-val {
    font-family: ui-monospace, SFMono-Regular, Menlo, monospace;
    font-size: 20px;
    font-weight: 700;
    color: #0f172a;
    margin-top: 2px;
  }
  .gas-bubble {
    transition: opacity 0.4s ease;
  }
</style>
</head>
<body>

<div class="app-container">
  <div class="controls">
    <button class="step-btn active" onclick="setStep(0)">0 s</button>
    <button class="step-btn" onclick="setStep(1)">20 s</button>
    <button class="step-btn" onclick="setStep(2)">40 s</button>
    <button class="step-btn" id="playBtn" onclick="togglePlay()" aria-label="Play">▶</button>
  </div>

  <div class="stage-card">
    <div class="svg-wrap">
      <svg viewBox="0 0 320 250" width="100%" height="100%">
        
        <g id="gasGroup" opacity="0.1">
          <circle cx="160" cy="22" r="3.5" fill="#38bdf8"/>
          <circle cx="148" cy="14" r="2.5" fill="#38bdf8"/>
          <circle cx="172" cy="12" r="3" fill="#38bdf8"/>
          <path d="M 160 38 L 160 28" stroke="#38bdf8" stroke-width="2" stroke-linecap="round"/>
          <path d="M 148 40 L 144 24" stroke="#38bdf8" stroke-width="1.5" stroke-linecap="round"/>
          <path d="M 172 40 L 176 22" stroke="#38bdf8" stroke-width="1.5" stroke-linecap="round"/>
          <text x="212" y="24" font-size="12" font-weight="600" fill="#0284c7" text-anchor="start">CO₂ escapes</text>
          <path d="M 206 20 L 180 20" stroke="#0284c7" stroke-width="1" stroke-dasharray="2,2"/>
        </g>

        
        <polygon points="144,48 176,48 176,75 224,155 96,155 144,75" fill="#f8fafc" stroke="#64748b" stroke-width="2.5" stroke-linejoin="round"/>

        
        <polygon points="106,153 214,153 194,115 126,115" fill="#e0f2fe" opacity="0.9"/>
        <line x1="124" y1="115" x2="196" y2="115" stroke="#38bdf8" stroke-width="2"/>

        
        <g id="chips">
          <rect x="135" y="142" width="10" height="8" rx="2" fill="#94a3b8"/>
          <rect x="150" y="140" width="12" height="10" rx="2" fill="#64748b"/>
          <rect x="166" y="143" width="9" height="7" rx="2" fill="#94a3b8"/>
          <rect x="144" y="146" width="11" height="6" rx="2" fill="#cbd5e1"/>
        </g>

        
        <g id="liquidBubbles" opacity="0">
          <circle cx="140" cy="132" r="2" fill="#0284c7"/>
          <circle cx="152" cy="126" r="2.5" fill="#0284c7"/>
          <circle cx="162" cy="130" r="1.5" fill="#0284c7"/>
          <circle cx="170" cy="124" r="2" fill="#0284c7"/>
          <circle cx="146" cy="120" r="2" fill="#0284c7"/>
        </g>

        
        <ellipse cx="160" cy="55" rx="14" ry="9" fill="#f1f5f9" stroke="#cbd5e1" stroke-width="1.5"/>
        <ellipse cx="155" cy="53" rx="6" ry="4" fill="#ffffff"/>
        <ellipse cx="164" cy="56" rx="5" ry="4" fill="#ffffff"/>
        <text x="215" y="58" font-size="12" font-weight="600" fill="#475569" text-anchor="start">Cotton wool</text>
        <path d="M 210 55 L 178 55" stroke="#94a3b8" stroke-width="1" stroke-dasharray="2,2"/>

        
        <rect x="75" y="156" width="170" height="8" rx="2" fill="#64748b"/>
        <path d="M 65 164 L 255 164 L 245 215 L 75 215 Z" fill="#e2e8f0" stroke="#cbd5e1" stroke-width="1.5"/>
        
        
        <rect x="110" y="174" width="100" height="30" rx="4" fill="#0f172a"/>
        <text id="scaleText" x="160" y="195" font-family="monospace" font-size="16" font-weight="700" fill="#38bdf8" text-anchor="middle">184.20 g</text>
      </svg>
    </div>

    <div class="readouts">
      <div class="readout-box">
        <div class="readout-lbl">Time</div>
        <div class="readout-val" id="timeVal">0 s</div>
      </div>
      <div class="readout-box">
        <div class="readout-lbl">Mass</div>
        <div class="readout-val" id="massVal">184.20 g</div>
      </div>
      <div class="readout-box">
        <div class="readout-lbl">Mass Lost</div>
        <div class="readout-val" id="lostVal" style="color:#0284c7;">0.00 g</div>
      </div>
    </div>
  </div>
</div>

<script>
  const data = [
    { time: '0 s', mass: '184.20 g', scale: '184.20 g', lost: '0.00 g', gas: 0.1, bubbles: 0 },
    { time: '20 s', mass: '183.76 g', scale: '183.76 g', lost: '-0.44 g', gas: 1.0, bubbles: 1 },
    { time: '40 s', mass: '183.32 g', scale: '183.32 g', lost: '-0.88 g', gas: 0.7, bubbles: 0.5 }
  ];

  let currentStep = 0;
  let timer = null;

  function setStep(idx) {
    currentStep = idx;
    const btns = document.querySelectorAll('.step-btn');
    btns.forEach((b, i) => {
      if (i < 3) b.classList.toggle('active', i === idx);
    });

    const d = data[idx];
    document.getElementById('timeVal').textContent = d.time;
    document.getElementById('massVal').textContent = d.mass;
    document.getElementById('lostVal').textContent = d.lost;
    document.getElementById('scaleText').textContent = d.scale;
    document.getElementById('gasGroup').style.opacity = d.gas;
    document.getElementById('liquidBubbles').style.opacity = d.bubbles;
  }

  function togglePlay() {
    const pBtn = document.getElementById('playBtn');
    if (timer) {
      clearInterval(timer);
      timer = null;
      pBtn.textContent = '▶';
    } else {
      pBtn.textContent = '⏸';
      timer = setInterval(() => {
        setStep((currentStep + 1) % 3);
      }, 2400);
    }
  }

  setStep(0);
</script>

</body>
</html>

When calcium carbonate reacts with acid: $\text{CaCO}_3(s) + 2\text{HCl}(aq) \rightarrow \text{CaCl}_2(aq) + \text{H}_2\text{O}(l) + \text{CO}_2(g)$, the balance reading drops from $184.20\text{ g}$ to $183.32\text{ g}$ in $40\text{ s}$.

The mass of gas lost is $184.20 - 183.32 = 0.88\text{ g}$. Dividing by $40\text{ s}$ gives a rate of $0.022\text{ g/s}$.

Note that this mass-loss method is accurate for heavy gases like $\text{CO}_2$, but not for $\text{H}_2$, which is so light that the mass loss is too small for standard classroom balances to detect reliably.

What if a reaction does not produce any gas at all, but instead forms a solid?

## Method 3: Measuring Precipitation (Disappearing Cross)

A **precipitate** is an insoluble solid that forms inside a liquid solution, making the mixture cloudy or **turbid**.

In the reaction between sodium thiosulfate and acid, an insoluble solid precipitate of **colloidal sulfur** forms: $$\text{Na}_2\text{S}_2\text{O}_3\text{(aq)} + 2\text{HCl(aq)} \rightarrow 2\text{NaCl(aq)} + \text{SO}_2\text{(g)} + \text{S(s)} + \text{H}_2\text{O(l)}$$

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Disappearing Cross Reaction</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px;
      user-select: none;
    }

    .main-view {
      display: flex;
      flex-wrap: wrap;
      align-items: center;
      justify-content: center;
      gap: 16px;
      width: 100%;
      max-width: 520px;
      margin: auto 0;
    }

    /* Flask container */
    .flask-wrapper {
      position: relative;
      width: 190px;
      height: 190px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    /* Paper under flask with printed 'X' */
    .paper-base {
      position: absolute;
      width: 170px;
      height: 170px;
      background: #ffffff;
      border: 2px solid #e2e8f0;
      border-radius: 8px;
      box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);
      display: flex;
      align-items: center;
      justify-content: center;
    }

    .cross-mark {
      font-size: 88px;
      font-weight: 900;
      line-height: 1;
      color: #0f172a;
      transition: filter 0.2s ease, opacity 0.2s ease;
    }

    /* Top-down conical flask view */
    .flask-top {
      position: absolute;
      width: 180px;
      height: 180px;
      border-radius: 50%;
      border: 4px solid rgba(148, 163, 184, 0.6);
      box-shadow: inset 0 0 16px rgba(148, 163, 184, 0.3), 0 6px 16px rgba(0, 0, 0, 0.08);
      overflow: hidden;
      display: flex;
      align-items: center;
      justify-content: center;
      background: transparent;
    }

    /* Cloudy colloidal sulfur solution layer */
    .solution-layer {
      position: absolute;
      inset: 0;
      border-radius: 50%;
      background: #fef08a;
      opacity: 0;
      transition: opacity 0.2s ease;
      backdrop-filter: blur(0px);
    }

    .flask-neck {
      position: absolute;
      width: 60px;
      height: 60px;
      border-radius: 50%;
      border: 2px dashed rgba(100, 116, 139, 0.4);
      pointer-events: none;
    }

    /* Data & Timer Panel */
    .info-panel {
      display: flex;
      flex-direction: column;
      gap: 10px;
      min-width: 150px;
      align-items: center;
    }

    .timer-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px 16px;
      text-align: center;
      width: 100%;
      box-shadow: 0 2px 8px rgba(0, 0, 0, 0.04);
    }

    .timer-val {
      font-family: ui-monospace, SFMono-Regular, Menlo, monospace;
      font-size: 26px;
      font-weight: 700;
      color: #0f172a;
    }

    .status-badge {
      font-size: 13px;
      font-weight: 600;
      padding: 4px 10px;
      border-radius: 20px;
      background: #e0f2fe;
      color: #0369a1;
      margin-top: 4px;
      display: inline-block;
      transition: background 0.3s, color 0.3s;
    }

    .status-badge.obscured {
      background: #fef2f2;
      color: #b91c1c;
    }

    .rate-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 8px 14px;
      text-align: center;
      font-size: 14px;
      font-weight: 600;
      color: #334155;
      width: 100%;
    }

    .rate-formula {
      color: #0284c7;
      font-weight: 700;
      margin-top: 2px;
    }

    /* Controls */
    .controls {
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 10px;
      width: 100%;
      max-width: 420px;
      margin-top: 8px;
    }

    .btn-group {
      display: flex;
      gap: 8px;
      width: 100%;
      justify-content: center;
    }

    .btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 8px;
      padding: 6px 12px;
      font-size: 13px;
      font-weight: 600;
      color: #334155;
      cursor: pointer;
      flex: 1;
      text-align: center;
      transition: background 0.2s, box-shadow 0.2s;
    }

    .btn.active {
      background: #22b7ff;
      border-color: #22b7ff;
      color: #ffffff;
      box-shadow: 0 2px 6px rgba(34, 183, 255, 0.4);
    }

    .slider-row {
      display: flex;
      align-items: center;
      gap: 10px;
      width: 100%;
    }

    input[type="range"] {
      flex: 1;
      accent-color: #22b7ff;
      cursor: pointer;
      height: 6px;
    }

    .play-btn {
      background: #22b7ff;
      border: none;
      color: #ffffff;
      border-radius: 50%;
      width: 32px;
      height: 32px;
      font-size: 13px;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      flex-shrink: 0;
    }
  </style>
</head>
<body>

  <div class="main-view">
    
    <div class="flask-wrapper">
      <div class="paper-base">
        <span class="cross-mark" id="cross">✕</span>
      </div>
      <div class="flask-top">
        <div class="solution-layer" id="solution"></div>
        <div class="flask-neck"></div>
      </div>
    </div>

    
    <div class="info-panel">
      <div class="timer-card">
        <div class="timer-val" id="timeDisplay">0.0 s</div>
        <div class="status-badge" id="statusBadge">Cross Visible</div>
      </div>

      <div class="rate-card">
        <div>Precipitate: <span style="color:#d97706">S(s)</span></div>
        <div class="rate-formula">Rate ∝ 1 / time</div>
      </div>
    </div>
  </div>

  
  <div class="controls">
    <div class="btn-group">
      <button class="btn active" id="btn0" onclick="setTime(0)">0s (Clear)</button>
      <button class="btn" id="btn1" onclick="setTime(15)">15s (Turbid)</button>
      <button class="btn" id="btn2" onclick="setTime(30)">30s (Obscured)</button>
    </div>

    <div class="slider-row">
      <button class="play-btn" id="playBtn" onclick="togglePlay()">▶</button>
      <input type="range" id="timeSlider" min="0" max="30" step="0.5" value="0" oninput="onSlide(this.value)">
    </div>
  </div>

  <script>
    let currentTime = 0;
    let isPlaying = false;
    let timerId = null;

    const cross = document.getElementById('cross');
    const solution = document.getElementById('solution');
    const timeDisplay = document.getElementById('timeDisplay');
    const statusBadge = document.getElementById('statusBadge');
    const timeSlider = document.getElementById('timeSlider');
    const playBtn = document.getElementById('playBtn');

    function updateState(t) {
      currentTime = Math.min(30, Math.max(0, t));
      const fraction = currentTime / 30; // 0 to 1

      // Visual updates
      timeDisplay.textContent = currentTime.toFixed(1) + ' s';
      timeSlider.value = currentTime;

      // Solution turbidity & Cross fading
      solution.style.opacity = Math.pow(fraction, 0.8) * 0.98;
      const blurPx = fraction * 7;
      const crossOpacity = Math.max(0, 1 - Math.pow(fraction, 1.2));
      cross.style.opacity = crossOpacity;
      cross.style.filter = `blur(${blurPx}px)`;

      // Status text
      if (fraction < 0.3) {
        statusBadge.textContent = 'Cross Visible';
        statusBadge.className = 'status-badge';
      } else if (fraction < 0.95) {
        statusBadge.textContent = 'Precipitating...';
        statusBadge.className = 'status-badge';
      } else {
        statusBadge.textContent = 'Cross Obscured ✕';
        statusBadge.className = 'status-badge obscured';
      }

      // Button active states
      document.getElementById('btn0').classList.toggle('active', currentTime === 0);
      document.getElementById('btn1').classList.toggle('active', currentTime === 15);
      document.getElementById('btn2').classList.toggle('active', currentTime === 30);
    }

    function setTime(t) {
      pause();
      updateState(t);
    }

    function onSlide(val) {
      pause();
      updateState(parseFloat(val));
    }

    function togglePlay() {
      if (isPlaying) {
        pause();
      } else {
        if (currentTime >= 30) currentTime = 0;
        play();
      }
    }

    function play() {
      isPlaying = true;
      playBtn.textContent = '⏸';
      const intervalMs = 50;
      const step = (30 / (4000 / intervalMs)); // 4s total playback
      timerId = setInterval(() => {
        if (currentTime >= 30) {
          pause();
        } else {
          updateState(currentTime + step);
        }
      }, intervalMs);
    }

    function pause() {
      isPlaying = false;
      playBtn.textContent = '▶';
      if (timerId) clearInterval(timerId);
    }

    // Initialize
    updateState(0);
  </script>
</body>
</html>

In the **disappearing cross** technique, you time how long ($t$) it takes for the insoluble **colloidal sulfur precipitate** to obscure a printed black 'X' beneath the flask.

Because the same amount of precipitate is produced at the end-point, relative rate is determined using the reciprocal relationship $\text{Rate} \propto \frac{1}{t}$ (units $\text{s}^{-1}$).

If the cross disappears in $50\text{ s}$, the relative rate is $\frac{1}{50\text{ s}} = 0.02\text{ s}^{-1}$.

A common mistake is assuming that a longer time means a faster reaction—remember, shorter time means the solid formed more rapidly, giving a higher rate value.

To eliminate the human judgment of when the cross 'disappears', scientists use a **colorimeter** or light sensor to measure how light transmission decreases continuously over time.

Rigorous **mathematical analysis** of rates requires converting raw times into consistent decimals and reporting results to appropriate significant figures.

To quantitatively compare how changes in temperature or concentration alter speed, calculate the fold-increase: $$\text{Ratio} = \frac{\text{Rate}_2}{\text{Rate}_1}$$

For example, if warming a solution increases its relative rate from $0.020\text{ s}^{-1}$ to $0.080\text{ s}^{-1}$, the rate ratio is $\frac{0.080}{0.020} = 4.0$, meaning the reaction proceeds $4.0\times$ faster.

## Mathematical Analysis and Rate Comparisons

Careful **mathematical analysis** of rate data requires consistent decimal conversion of raw times and rounding results to appropriate **significant figures**.

To compare how changing conditions (like concentration or temperature) affects speed, calculate the fold-increase using a rate ratio:

$$\text{Fold Increase} = \frac{\text{Rate}_2}{\text{Rate}_1}$$

For example, if a reaction rate rises from $0.025\text{ s}^{-1}$ to $0.075\text{ s}^{-1}$, the ratio $\frac{0.075}{0.025} = 3.0$, representing a $3\text{-fold}$ rate increase.

science

Defining and Measuring Rate of Reaction. Define the rate of a chemical reaction and explain how it is measured quantitatively through mass loss, gas production, or precipitation.

Measuring Rates of Reaction - GCSE Chemistry Single & Combined Science

Evaluating Methods for Measuring the Rate of Reaction (KS4 Chemistry)

Introduction to Reaction Rates and Measuring Quantitative Change

Pedagogical focus should center on concrete apparatus selection linked to state symbols in balanced equations: $(s) \rightarrow (g)$ triggers mass loss or gas syringe methods, while $(aq) \rightarrow (s)$ triggers precipitation turbidity methods. Explicitly drill the mathematical relationship between time ($t$) and rate ($\text{Rate} \propto 1/t$) to eradicate the prevalent inverse-speed confusion, and insist on explicit unit tracking across arithmetic operations.

Defining and Measuring Rate of Reaction

Method 1: Measuring Gas Production