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 single drop of water contains more individual molecules than there are stars in the observable universe. How do chemists count these invisible particles when weighing a sample on a digital scale?

To connect the submicroscopic world of atoms to grams in the lab, chemists use a counting unit called the **mole**.

One mole of any substance contains exactly $6.022 \times 10^{23}$ particles, a value known as **Avogadro's constant** ($N_A$). In 1811, Italian scientist Amedeo Avogadro hypothesized that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, laying the groundwork for this universal constant.

The **relative formula mass** ($M_r$) is the sum of the relative atomic masses ($A_r$) of all atoms shown in a chemical formula. When you measure out the $M_r$ of a substance in grams, you have exactly one mole of that substance.

<!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>The Mole Bridge</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
    }

    body {
      background: transparent;
      color: #1e2945;
      padding: 10px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }

    .diagram-content {
      width: 100%;
      max-width: 600px;
      display: flex;
      flex-direction: column;
      gap: 12px;
    }

    /* Path selector tabs */
    .tabs {
      display: flex;
      flex-wrap: wrap;
      gap: 6px;
      justify-content: center;
    }

    .tab-btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 20px;
      padding: 5px 12px;
      font-size: 12px;
      font-weight: 600;
      color: #475569;
      cursor: pointer;
      transition: all 0.2s ease;
      white-space: nowrap;
    }

    .tab-btn:hover {
      background: #e2e8f0;
      color: #1e2945;
    }

    .tab-btn.active {
      background: #0284c7;
      border-color: #0284c7;
      color: #ffffff;
      box-shadow: 0 2px 6px rgba(2, 132, 199, 0.35);
    }

    /* Main Grid Map */
    .map-grid {
      display: grid;
      grid-template-columns: 1fr auto 1.1fr auto 1fr;
      align-items: center;
      gap: 4px;
      background: #f8fafc;
      border-radius: 12px;
      padding: 14px 10px;
      position: relative;
    }

    @media (max-width: 480px) {
      .map-grid {
        grid-template-columns: 1fr;
        gap: 8px;
        padding: 10px 8px;
      }
    }

    /* Node Cards */
    .node {
      background: #ffffff;
      border: 2px solid #e2e8f0;
      border-radius: 10px;
      padding: 10px 6px;
      text-align: center;
      transition: all 0.25s ease;
      cursor: pointer;
      user-select: none;
    }

    .node:hover {
      border-color: #93c5fd;
      box-shadow: 0 2px 8px rgba(147, 197, 253, 0.4);
    }

    .node.active-node {
      border-color: #0284c7;
      background: #f0f9ff;
      box-shadow: 0 0 0 3px rgba(2, 132, 199, 0.2);
    }

    .node-title {
      font-size: 13px;
      font-weight: 700;
      color: #1e2945;
      line-height: 1.2;
    }

    .node-sym {
      font-size: 11px;
      font-weight: 600;
      color: #0284c7;
      margin-top: 2px;
    }

    .node-unit {
      font-size: 10px;
      color: #64748b;
      margin-top: 1px;
    }

    /* Bridge / Conversion Connectors */
    .bridge {
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      gap: 4px;
      padding: 0 2px;
    }

    @media (max-width: 480px) {
      .bridge {
        flex-direction: row;
        justify-content: space-around;
        padding: 4px 0;
      }
    }

    .op-tag {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      padding: 3px 6px;
      font-size: 10px;
      font-weight: 700;
      color: #334155;
      display: flex;
      align-items: center;
      gap: 3px;
      white-space: nowrap;
      transition: all 0.2s ease;
    }

    .op-tag.active-op {
      background: #0284c7;
      border-color: #0284c7;
      color: #ffffff;
      box-shadow: 0 2px 6px rgba(2, 132, 199, 0.35);
    }

    /* Lower Stoichiometry Section */
    .ratio-section {
      background: #ffffff;
      border: 1px dashed #cbd5e1;
      border-radius: 10px;
      padding: 10px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 8px;
    }

    .ratio-title {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
    }

    .ratio-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      width: 100%;
    }

    .sub-box {
      flex: 1;
      max-width: 150px;
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 6px;
      text-align: center;
      transition: all 0.25s ease;
    }

    .sub-box.active-sub {
      border-color: #2563eb;
      background: #eff6ff;
      box-shadow: 0 0 0 2px rgba(37, 99, 235, 0.2);
    }

    .sub-name {
      font-size: 12px;
      font-weight: 700;
      color: #1e2945;
    }

    .sub-sub {
      font-size: 10px;
      color: #64748b;
    }

    .ratio-connector {
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 2px;
    }

    .ratio-badge {
      background: #0284c7;
      color: #ffffff;
      font-size: 10px;
      font-weight: 700;
      padding: 3px 8px;
      border-radius: 12px;
      white-space: nowrap;
    }

    /* Formula Banner */
    .formula-banner {
      background: #f0f9ff;
      border: 1px solid #bae6fd;
      border-radius: 8px;
      padding: 8px 12px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
      font-size: 12px;
      color: #0369a1;
      font-weight: 600;
    }

    .formula-math {
      font-family: "Courier New", Courier, monospace;
      font-size: 13px;
      font-weight: 700;
      color: #0c4a6e;
    }
  </style>
</head>
<body>

  <div class="diagram-content">
    
    <div class="tabs">
      <button class="tab-btn active" onclick="setPath('all')">View All</button>
      <button class="tab-btn" onclick="setPath('mass-to-mole')">Mass ➔ Moles</button>
      <button class="tab-btn" onclick="setPath('mole-to-mass')">Moles ➔ Mass</button>
      <button class="tab-btn" onclick="setPath('mole-to-part')">Moles ➔ Particles</button>
      <button class="tab-btn" onclick="setPath('ratio')">Substance A ➔ B</button>
    </div>

    
    <div class="map-grid">
      
      <div class="node" id="node-mass" onclick="setPath('mass-to-mole')">
        <div class="node-title">Mass</div>
        <div class="node-sym">(m)</div>
        <div class="node-unit">grams (g)</div>
      </div>

      
      <div class="bridge">
        <div class="op-tag" id="op-m-to-n">÷ M<sub>r</sub> ➔</div>
        <div class="op-tag" id="op-n-to-m">⬅ × M<sub>r</sub></div>
      </div>

      
      <div class="node" id="node-moles" onclick="setPath('all')">
        <div class="node-title">Moles</div>
        <div class="node-sym">(n)</div>
        <div class="node-unit">Central Hub</div>
      </div>

      
      <div class="bridge">
        <div class="op-tag" id="op-n-to-p">× N<sub>A</sub> ➔</div>
        <div class="op-tag" id="op-p-to-n">⬅ ÷ N<sub>A</sub></div>
      </div>

      
      <div class="node" id="node-particles" onclick="setPath('mole-to-part')">
        <div class="node-title">Particles</div>
        <div class="node-sym">(N)</div>
        <div class="node-unit">atoms / molecules</div>
      </div>
    </div>

    
    <div class="ratio-section">
      <div class="ratio-title">Mole-to-Mole Stoichiometry</div>
      <div class="ratio-row">
        <div class="sub-box" id="box-sub-a">
          <div class="sub-name">Substance A</div>
          <div class="sub-sub">Moles (n<sub>A</sub>)</div>
        </div>

        <div class="ratio-connector">
          <div class="ratio-badge" id="badge-ratio">Balanced Ratio (A : B)</div>
          <span style="font-size: 13px; color: #64748b;">⇄</span>
        </div>

        <div class="sub-box" id="box-sub-b">
          <div class="sub-name">Substance B</div>
          <div class="sub-sub">Moles (n<sub>B</sub>)</div>
        </div>
      </div>
    </div>

    
    <div class="formula-banner">
      <span id="formula-label">Mole Hub Formula:</span>
      <span class="formula-math" id="formula-display">n = m ÷ M<sub>r</sub> &nbsp;|&nbsp; N = n × 6.022×10²³</span>
    </div>
  </div>

  <script>
    function clearHighlights() {
      document.querySelectorAll('.node').forEach(el => el.classList.remove('active-node'));
      document.querySelectorAll('.op-tag').forEach(el => el.classList.remove('active-op'));
      document.querySelectorAll('.sub-box').forEach(el => el.classList.remove('active-sub'));
      document.querySelectorAll('.tab-btn').forEach(el => el.classList.remove('active-active', 'active'));
    }

    function setPath(type) {
      clearHighlights();

      const label = document.getElementById('formula-label');
      const display = document.getElementById('formula-display');

      if (type === 'mass-to-mole') {
        document.getElementById('node-mass').classList.add('active-node');
        document.getElementById('node-moles').classList.add('active-node');
        document.getElementById('op-m-to-n').classList.add('active-op');
        event && event.target && event.target.classList.add('active');
        label.textContent = "Mass to Moles:";
        display.innerHTML = "n = mass ÷ M<sub>r</sub>";
      } else if (type === 'mole-to-mass') {
        document.getElementById('node-moles').classList.add('active-node');
        document.getElementById('node-mass').classList.add('active-node');
        document.getElementById('op-n-to-m').classList.add('active-op');
        event && event.target && event.target.classList.add('active');
        label.textContent = "Moles to Mass:";
        display.innerHTML = "mass = n × M<sub>r</sub>";
      } else if (type === 'mole-to-part') {
        document.getElementById('node-moles').classList.add('active-node');
        document.getElementById('node-particles').classList.add('active-node');
        document.getElementById('op-n-to-p').classList.add('active-op');
        event && event.target && event.target.classList.add('active');
        label.textContent = "Moles to Particles:";
        display.innerHTML = "N = n × 6.022 × 10²³";
      } else if (type === 'ratio') {
        document.getElementById('box-sub-a').classList.add('active-sub');
        document.getElementById('box-sub-b').classList.add('active-sub');
        event && event.target && event.target.classList.add('active');
        label.textContent = "Stoichiometric Ratio:";
        display.innerHTML = "n<sub>B</sub> = n<sub>A</sub> × (coeff B ÷ coeff A)";
      } else {
        document.getElementById('node-moles').classList.add('active-node');
        const defaultBtn = document.querySelector('.tab-btn');
        if (defaultBtn) defaultBtn.classList.add('active');
        label.textContent = "Key Relations:";
        display.innerHTML = "n = m ÷ M<sub>r</sub> &nbsp;|&nbsp; N = n × N<sub>A</sub>";
      }
    }
  </script>
</body>
</html>

What happens when an exam asks you not just for the number of molecules, but for the specific number of individual ions or atoms inside a sample?

To find the number of individual ions or atoms in a given mass, calculate the moles of compound first, then multiply by the number of specific atoms per formula unit before using Avogadro's constant.

Let's solve a classic Grade 8/9 question: **Calculate the total number of oxide ions ($\text{O}^{2-}$)** present in $10.20\text{ g}$ of aluminum oxide, $\text{Al}_2\text{O}_3$ ($A_r: \text{Al} = 27.0, \text{O} = 16.0$).

First, determine the relative formula mass: $$M_r(\text{Al}_2\text{O}_3) = (2 \times 27.0) + (3 \times 16.0) = 102.0\text{ g/mol}$$

Next, find the moles of $\text{Al}_2\text{O}_3$: $$n = \frac{\text{mass}}{M_r} = \frac{10.20\text{ g}}{102.0\text{ g/mol}} = 0.100\text{ mol}$$

Because each formula unit of $\text{Al}_2\text{O}_3$ contains $3$ oxide ions, $0.100\text{ mol}$ of $\text{Al}_2\text{O}_3$ delivers $0.300\text{ mol}$ of $\text{O}^{2-}$ ions.

Finally, multiply the moles of oxide ions by Avogadro's constant: $$N = 0.300\text{ mol} \times (6.022 \times 10^{23}\text{ ions/mol}) = 1.807 \times 10^{23}\text{ oxide ions}$$

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Stoichiometry Conversion Pipeline</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    }
    body {
      background: transparent;
      color: #0f172a;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100vh;
    }
    .pipeline-container {
      width: 100%;
      max-width: 680px;
      display: flex;
      flex-direction: column;
      gap: 12px;
    }
    .formula-banner {
      background: #f8fafc;
      border: 1.5px solid #cbd5e1;
      border-radius: 10px;
      padding: 10px 14px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      flex-wrap: wrap;
      gap: 8px;
    }
    .formula-display {
      font-size: 18px;
      font-weight: 800;
      letter-spacing: 0.5px;
      color: #0f172a;
    }
    .formula-sub {
      color: #c2410c;
      background: #ffedd5;
      padding: 2px 6px;
      border-radius: 6px;
      border: 1px solid #fdba74;
    }
    .status-text {
      font-size: 13px;
      font-weight: 700;
      color: #1e293b;
    }
    .steps-grid {
      display: grid;
      grid-template-columns: repeat(4, 1fr);
      gap: 8px;
      position: relative;
    }
    @media (max-width: 540px) {
      .steps-grid {
        grid-template-columns: repeat(2, 1fr);
        gap: 8px;
      }
    }
    @media (max-width: 340px) {
      .steps-grid {
        grid-template-columns: 1fr;
      }
    }
    .step-card {
      background: #f8fafc;
      border: 2px solid #cbd5e1;
      border-radius: 10px;
      padding: 10px 6px;
      display: flex;
      flex-direction: column;
      align-items: center;
      text-align: center;
      position: relative;
      cursor: pointer;
      transition: border-color 0.2s ease, background-color 0.2s ease, box-shadow 0.2s ease;
      opacity: 0.88;
    }
    .step-card.active {
      background: #ffffff;
      border-color: #0284c7;
      box-shadow: 0 3px 10px rgba(2, 132, 199, 0.2);
      opacity: 1;
    }
    .step-num {
      font-size: 11px;
      font-weight: 800;
      color: #475569;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      margin-bottom: 4px;
    }
    .step-card.active .step-num {
      color: #0284c7;
    }
    .step-value-box {
      min-height: 48px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      margin-bottom: 6px;
    }
    .step-value {
      font-size: 13px;
      font-weight: 800;
      color: #0f172a;
      line-height: 1.25;
      white-space: nowrap;
    }
    .step-card.active .step-value {
      color: #0369a1;
    }
    .step-species {
      font-size: 12px;
      font-weight: 600;
      color: #334155;
      margin-top: 2px;
      white-space: nowrap;
    }
    .op-badge {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      font-size: 11px;
      font-weight: 700;
      padding: 4px 6px;
      border-radius: 6px;
      background: #e2e8f0;
      color: #1e293b;
      border: 1px solid #cbd5e1;
      width: 100%;
      white-space: nowrap;
    }
    .op-badge.highlight-orange {
      background: #ffedd5;
      color: #9a3412;
      border: 1px solid #fb923c;
      font-weight: 800;
    }
    .step-card.active .op-badge:not(.highlight-orange) {
      background: #e0f2fe;
      color: #0369a1;
      border-color: #7dd3fc;
    }
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 10px;
      margin-top: 4px;
    }
    .ctrl-btn {
      background: #ffffff;
      border: 1.5px solid #94a3b8;
      border-radius: 8px;
      padding: 6px 14px;
      font-size: 13px;
      font-weight: 700;
      color: #1e293b;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 4px;
      transition: background-color 0.15s ease;
    }
    .ctrl-btn:hover {
      background: #f1f5f9;
      border-color: #64748b;
    }
    .ctrl-btn:active {
      background: #e2e8f0;
    }
    .dots {
      display: flex;
      gap: 6px;
      align-items: center;
      margin-left: 4px;
    }
    .dot {
      width: 12px;
      height: 12px;
      border-radius: 50%;
      background: #cbd5e1;
      cursor: pointer;
      border: none;
      padding: 0;
      transition: background-color 0.2s ease;
    }
    .dot.active {
      background: #0284c7;
    }
    sup, sub {
      font-size: 0.75em;
      line-height: 0;
      position: relative;
      vertical-align: baseline;
    }
    sup {
      top: -0.5em;
    }
    sub {
      bottom: -0.25em;
    }
  </style>
</head>
<body>
  <div class="pipeline-container">
    <div class="formula-banner">
      <div class="formula-display">
        Al<sub>2</sub><span class="formula-sub">O<sub>3</sub></span>
      </div>
      <div class="status-text" id="stepDesc">Step 1: Starting mass of sample</div>
    </div>

    <div class="steps-grid">
      
      <div class="step-card active" id="card-0" onclick="goToStep(0)">
        <span class="step-num">Step 1</span>
        <div class="step-value-box">
          <div class="step-value">10.20 g</div>
          <div class="step-species">Al<sub>2</sub>O<sub>3</sub></div>
        </div>
        <span class="op-badge">Given mass</span>
      </div>

      
      <div class="step-card" id="card-1" onclick="goToStep(1)">
        <span class="step-num">Step 2</span>
        <div class="step-value-box">
          <div class="step-value">0.100 mol</div>
          <div class="step-species">Al<sub>2</sub>O<sub>3</sub></div>
        </div>
        <span class="op-badge">÷ 102 (M<sub>r</sub>)</span>
      </div>

      
      <div class="step-card" id="card-2" onclick="goToStep(2)">
        <span class="step-num">Step 3</span>
        <div class="step-value-box">
          <div class="step-value">0.300 mol</div>
          <div class="step-species">O<sup>2−</sup> ions</div>
        </div>
        <span class="op-badge highlight-orange">× 3 (subscript)</span>
      </div>

      
      <div class="step-card" id="card-3" onclick="goToStep(3)">
        <span class="step-num">Step 4</span>
        <div class="step-value-box">
          <div class="step-value">1.807 × 10<sup>23</sup></div>
          <div class="step-species">O<sup>2−</sup> ions</div>
        </div>
        <span class="op-badge">× 6.022 × 10<sup>23</sup></span>
      </div>
    </div>

    <div class="controls">
      <button class="ctrl-btn" onclick="prevStep()" aria-label="Previous step">◀</button>
      <button class="ctrl-btn" id="playBtn" onclick="togglePlay()">⏸ Pause</button>
      <button class="ctrl-btn" onclick="nextStep()" aria-label="Next step">▶</button>
      <div class="dots">
        <button class="dot active" onclick="goToStep(0)" aria-label="Go to Step 1"></button>
        <button class="dot" onclick="goToStep(1)" aria-label="Go to Step 2"></button>
        <button class="dot" onclick="goToStep(2)" aria-label="Go to Step 3"></button>
        <button class="dot" onclick="goToStep(3)" aria-label="Go to Step 4"></button>
      </div>
    </div>
  </div>

  <script>
    let currentStep = 0;
    let isPlaying = true;
    let timer = null;

    const descriptions = [
      "Step 1: Starting mass = 10.20 g Al₂O₃",
      "Step 2: Divide by Mr (102 g/mol) → 0.100 mol Al₂O₃",
      "Step 3: Multiply by 3 (subscript) → 0.300 mol O²⁻ ions",
      "Step 4: Multiply by Avogadro constant → 1.807 × 10²³ O²⁻ ions"
    ];

    function updateView() {
      for (let i = 0; i < 4; i++) {
        const card = document.getElementById(`card-${i}`);
        const dot = document.querySelectorAll('.dot')[i];
        if (i <= currentStep) {
          card.classList.add('active');
        } else {
          card.classList.remove('active');
        }
        dot.classList.toggle('active', i === currentStep);
      }
      document.getElementById('stepDesc').textContent = descriptions[currentStep];
    }

    function goToStep(idx) {
      currentStep = idx;
      updateView();
    }

    function nextStep() {
      currentStep = (currentStep + 1) % 4;
      updateView();
    }

    function prevStep() {
      currentStep = (currentStep - 1 + 4) % 4;
      updateView();
    }

    function togglePlay() {
      isPlaying = !isPlaying;
      document.getElementById('playBtn').textContent = isPlaying ? "⏸ Pause" : "▶ Play";
      if (isPlaying) {
        startTimer();
      } else {
        clearInterval(timer);
      }
    }

    function startTimer() {
      clearInterval(timer);
      timer = setInterval(() => {
        if (isPlaying) {
          nextStep();
        }
      }, 3200);
    }

    updateView();
    startTimer();
  </script>
</body>
</html>

A common mistake in exams is forgetting to multiply by the subscript; students often compute total molecules instead of the requested target atom or ion.

Now, what if an exam links this particle count across a chemical equation to an entirely different product?

## Synoptic Mastery: Reactions and Particle Yield

The **stoichiometric ratio** is the mole ratio given by the balancing numbers (coefficients) in front of chemical formulas in a balanced equation.

Consider the complete reaction of iron with chlorine gas: $$2\text{Fe}\text{ (s)} + 3\text{Cl}_2\text{ (g)} \rightarrow 2\text{FeCl}_3\text{ (s)}$$ **How many chloride ions ($\text{Cl}^-$) are formed when $5.585\text{ g}$ of iron reacts completely with excess chlorine?** ($A_r: \text{Fe} = 55.85$)

Step 1: Calculate moles of iron: $$n(\text{Fe}) = \frac{5.585\text{ g}}{55.85\text{ g/mol}} = 0.100\text{ mol}$$

Step 2: Use the stoichiometric ratio from the balanced equation ($2\text{ mol Fe} : 2\text{ mol FeCl}_3$, which simplifies to $1:1$) to find that $0.100\text{ mol}$ of $\text{FeCl}_3$ is produced.

Step 3: Each formula unit of $\text{FeCl}_3$ yields $3$ chloride ions ($\text{Cl}^-$), giving: $$n(\text{Cl}^-) = 0.100\text{ mol} \times 3 = 0.300\text{ mol of } \text{Cl}^-$$

Step 4: Convert moles of ions to particle count using Avogadro's constant: $$N(\text{Cl}^-) = 0.300\text{ mol} \times (6.022 \times 10^{23}\text{ ions/mol}) = 1.807 \times 10^{23}\text{ chloride ions}$$

<!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="1:1">
  <title>Stoichiometry & Ion Count</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; font-family: system-ui, -apple-system, sans-serif; }
    body {
      background: #ffffff;
      color: #1e2945;
      padding: 10px;
      display: flex;
      flex-direction: column;
      gap: 10px;
      max-width: 600px;
      margin: 0 auto;
    }
    
    /* Chemical Header */
    .eqn-bar {
      display: flex;
      justify-content: center;
      align-items: center;
      gap: 6px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 6px 12px;
      font-size: 15px;
      font-weight: 700;
    }
    .c-fe { color: #d97706; }
    .c-cl { color: #059669; }
    .c-comp { color: #2563eb; }
    .muted-op { color: #64748b; font-weight: 600; }

    /* Panels */
    .panel {
      border: 1px solid #e2e8f0;
      background: #ffffff;
      border-radius: 10px;
      padding: 10px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }
    .panel-tag {
      font-size: 11px;
      font-weight: 800;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
    }

    /* Molar Bridge Flow */
    .flow-row {
      display: grid;
      grid-template-columns: 1fr auto 1fr auto 1fr;
      align-items: center;
      gap: 4px;
    }
    .box {
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 8px;
      padding: 6px 4px;
      text-align: center;
      transition: all 0.3s ease;
    }
    .box.active {
      border-color: #2563eb;
      background: #eff6ff;
      box-shadow: 0 0 0 2px rgba(37,99,235,0.15);
    }
    .box-val { font-size: 13px; font-weight: 700; }
    .box-sub { font-size: 11px; color: #64748b; margin-top: 2px; }
    
    .bridge-arrow {
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      font-size: 10px;
      font-weight: 700;
      color: #2563eb;
      line-height: 1.1;
      padding: 0 2px;
    }
    .arrow-glyph { font-size: 14px; }

    /* Particle Breakdown Panel */
    .breakdown-grid {
      display: grid;
      grid-template-columns: 100px auto 1fr;
      align-items: center;
      gap: 8px;
    }
    @media (max-width: 420px) {
      .breakdown-grid { grid-template-columns: 1fr; gap: 6px; }
      .flow-row { grid-template-columns: 1fr; gap: 4px; }
      .bridge-arrow { flex-direction: row; gap: 4px; }
      .arrow-glyph { transform: rotate(90deg); }
    }

    .unit-cluster {
      background: #eff6ff;
      border: 1.5px dashed #3b82f6;
      border-radius: 8px;
      padding: 6px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 4px;
    }
    .ions-wrap {
      display: flex;
      flex-wrap: wrap;
      gap: 3px;
      justify-content: center;
    }
    .ion-pill {
      font-size: 10px;
      font-weight: 800;
      padding: 2px 5px;
      border-radius: 4px;
    }
    .ion-fe { background: #fef3c7; color: #b45309; border: 1px solid #fde68a; }
    .ion-cl { background: #d1fae5; color: #047857; border: 1px solid #a7f3d0; }

    .calc-chain {
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 10px;
      display: flex;
      flex-direction: column;
      gap: 6px;
    }
    .calc-step {
      display: flex;
      align-items: center;
      justify-content: space-between;
      font-size: 12px;
      font-weight: 600;
      padding: 4px 6px;
      border-radius: 6px;
      background: #ffffff;
      border: 1px solid #e2e8f0;
    }
    .calc-step.highlight {
      border-color: #059669;
      background: #ecfdf5;
    }

    /* Controls */
    .controls {
      display: flex;
      justify-content: center;
      align-items: center;
      gap: 8px;
      margin-top: 2px;
    }
    .btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      color: #334155;
      padding: 5px 12px;
      border-radius: 6px;
      font-size: 12px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 4px;
    }
    .btn:hover { background: #e2e8f0; }
    .btn.active {
      background: #2563eb;
      color: #ffffff;
      border-color: #2563eb;
    }
  </style>
</head>
<body>

  
  <div class="eqn-bar">
    <span class="c-fe">2Fe</span>
    <span class="muted-op">+</span>
    <span class="c-cl">3Cl₂</span>
    <span class="muted-op">→</span>
    <span class="c-comp">2FeCl₃</span>
  </div>

  
  <div class="panel">
    <div class="panel-tag">Stage 1: Molar Bridge</div>
    <div class="flow-row">
      <div class="box active" id="b1">
        <div class="box-val c-fe">5.585 g</div>
        <div class="box-sub">Mass Fe</div>
      </div>
      
      <div class="bridge-arrow">
        <span>÷ 55.85</span>
        <span class="arrow-glyph">→</span>
      </div>

      <div class="box" id="b2">
        <div class="box-val c-fe">0.100 mol</div>
        <div class="box-sub">Moles Fe</div>
      </div>

      <div class="bridge-arrow">
        <span>2 : 2</span>
        <span class="arrow-glyph">→</span>
      </div>

      <div class="box" id="b3">
        <div class="box-val c-comp">0.100 mol</div>
        <div class="box-sub">Moles FeCl₃</div>
      </div>
    </div>
  </div>

  
  <div class="panel">
    <div class="panel-tag">Stage 2: Ion Breakdown (1 FeCl₃ → 1 Fe³⁺ + 3 Cl⁻)</div>
    <div class="breakdown-grid">
      
      
      <div class="unit-cluster">
        <div style="font-size: 11px; font-weight: 800; color: #1e40af;">1 FeCl₃</div>
        <div class="ions-wrap">
          <span class="ion-pill ion-fe">Fe³⁺</span>
          <span class="ion-pill ion-cl">Cl⁻</span>
          <span class="ion-pill ion-cl">Cl⁻</span>
          <span class="ion-pill ion-cl">Cl⁻</span>
        </div>
      </div>

      <div style="text-align: center; color: #059669; font-weight: 800; font-size: 16px;">→</div>

      
      <div class="calc-chain">
        <div class="calc-step" id="s1">
          <span class="c-cl">Total Cl⁻ Moles</span>
          <span>0.100 × 3 = <b>0.300 mol</b></span>
        </div>
        <div class="calc-step highlight" id="s2">
          <span class="c-cl">Cl⁻ Ion Count</span>
          <span>0.300 × <i>N<sub>A</sub></i> = <b>1.807 × 10²³</b></span>
        </div>
      </div>

    </div>
  </div>

  
  <div class="controls">
    <button class="btn" id="btnPlay">⏸ Auto</button>
    <button class="btn active" data-step="0">1. Fe Moles</button>
    <button class="btn" data-step="1">2. FeCl₃ Moles</button>
    <button class="btn" data-step="2">3. Cl⁻ Count</button>
  </div>

  <script>
    const steps = [
      { boxes: ['b1', 'b2'], calcs: [] },
      { boxes: ['b2', 'b3'], calcs: ['s1'] },
      { boxes: ['b3'], calcs: ['s1', 's2'] }
    ];

    let current = 0;
    let playing = true;
    let timer = null;

    const stepBtns = document.querySelectorAll('[data-step]');
    const playBtn = document.getElementById('btnPlay');

    function applyState(idx) {
      current = idx;
      stepBtns.forEach((b, i) => b.classList.toggle('active', i === idx));

      ['b1', 'b2', 'b3'].forEach(id => {
        document.getElementById(id).classList.toggle('active', steps[idx].boxes.includes(id));
      });

      ['s1', 's2'].forEach(id => {
        document.getElementById(id).classList.toggle('highlight', steps[idx].calcs.includes(id));
      });
    }

    function nextStep() {
      applyState((current + 1) % steps.length);
    }

    function startAuto() {
      if (timer) clearInterval(timer);
      timer = setInterval(nextStep, 3500);
      playBtn.textContent = '⏸ Auto';
      playBtn.classList.remove('active');
    }

    function stopAuto() {
      if (timer) clearInterval(timer);
      timer = null;
      playBtn.textContent = '▶ Play';
      playBtn.classList.add('active');
    }

    stepBtns.forEach((btn, i) => {
      btn.addEventListener('click', () => {
        stopAuto();
        applyState(i);
      });
    });

    playBtn.addEventListener('click', () => {
      if (timer) {
        stopAuto();
      } else {
        startAuto();
      }
    });

    startAuto();
  </script>
</body>
</html>

Remember: never multiply the $M_r$ of a substance by the large balancing coefficient when calculating $n = m / M_r$.

Formula mass is an intrinsic property of the compound itself; balancing numbers only dictate how many moles react.

science

Exam Mastery: Relative Formula Mass and Stoichiometry. Solve synoptic exam questions integrating Avogadro's constant, formula masses, and reacting ratios.

GCSE Chemistry: Calculations in Chemistry - Moles and Reacting Masses

Quantitative Chemistry: Moles, Reacting Masses, and Stoichiometry

Practising Calculations in Chemistry: 14–16 Years (Stoichiometry and the Mole)

To achieve mastery at Key Stage 4 (GCSE Higher tier), teach stoichiometry using a consistent scaffold (the 3-step 'Mass-to-Moles-to-Moles-to-Mass' pipeline). Require students to write explicit units and state clearly whether a number represents mass, molar mass, amount in moles, or particle count. Address the major misconception of applying equation coefficients to $M_r$ by separating the calculation of formula mass from the stoichiometric ratio step.

Exam Mastery: Relative Formula Mass and Stoichiometry

The Mole and Avogadro's Constant

Counting Atoms and Ions in Compounds