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A sealed 1-liter bottle of air weighs just 1.2 grams. Fill that exact same bottle with liquid water and it weighs 1,000 grams — fill it with solid iron and it weighs nearly 8,000 grams.

Why do identical volumes of solids, liquids, and gases have such wildly different masses? The secret lies in how their particles are spaced, arranged, and bonded.

**Density** ($ho$) is the mass of a substance contained within a unit volume, defined by the formula $ho = rac{m}{V}$ (where $ho$ is density in $	ext{kg/m}^3$, $m$ is mass in $	ext{kg}$, and $V$ is volume in $	ext{m}^3$).

Because mass depends directly on the number of particles present, packing more particles into the same fixed volume directly increases density.

<!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>Particle Arrangements and Density</title>
<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;
    padding: 8px;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    min-height: 100%;
  }

  .main-grid {
    display: grid;
    grid-template-columns: repeat(3, 1fr);
    gap: 10px;
    width: 100%;
    max-width: 600px;
  }

  .state-col {
    display: flex;
    flex-direction: column;
    align-items: center;
    background: #ffffff;
    border-radius: 12px;
    padding: 10px 6px 12px;
    box-shadow: 0 2px 8px rgba(0,0,0,0.05);
    border: 2px solid transparent;
    transition: border-color 0.2s ease, transform 0.2s ease;
    cursor: pointer;
  }

  .state-col.active {
    border-color: #22b7ff;
  }

  .state-title {
    font-weight: 700;
    font-size: 15px;
    margin-bottom: 8px;
    color: #1e2945;
  }

  .canvas-wrapper {
    width: 100%;
    aspect-ratio: 1;
    position: relative;
    border: 2px solid #e2e8f0;
    border-radius: 8px;
    background: #f8fafc;
    overflow: hidden;
  }

  canvas {
    width: 100%;
    height: 100%;
    display: block;
  }

  .density-section {
    width: 100%;
    margin-top: 10px;
    display: flex;
    flex-direction: column;
    align-items: center;
    gap: 4px;
  }

  .density-label {
    font-size: 13px;
    font-weight: 600;
    color: #64748b;
  }

  .density-bar-bg {
    width: 80%;
    height: 8px;
    background: #e2e8f0;
    border-radius: 4px;
    overflow: hidden;
  }

  .density-bar-fill {
    height: 100%;
    border-radius: 4px;
    background: #22b7ff;
    transition: width 0.3s ease;
  }

  .density-val {
    font-size: 13px;
    font-weight: 700;
  }

  .solid .density-val { color: #0284c7; }
  .liquid .density-val { color: #0ea5e9; }
  .gas .density-val { color: #94a3b8; }
</style>
</head>
<body>

<div class="main-grid">
  
  <div class="state-col solid active" id="col-solid">
    <div class="state-title">Solid</div>
    <div class="canvas-wrapper">
      <canvas id="cvs-solid" width="160" height="160"></canvas>
    </div>
    <div class="density-section">
      <div class="density-label">Density</div>
      <div class="density-bar-bg">
        <div class="density-bar-fill" style="width: 100%;"></div>
      </div>
      <div class="density-val">High</div>
    </div>
  </div>

  
  <div class="state-col liquid" id="col-liquid">
    <div class="state-title">Liquid</div>
    <div class="canvas-wrapper">
      <canvas id="cvs-liquid" width="160" height="160"></canvas>
    </div>
    <div class="density-section">
      <div class="density-label">Density</div>
      <div class="density-bar-bg">
        <div class="density-bar-fill" style="width: 80%;"></div>
      </div>
      <div class="density-val">Medium</div>
    </div>
  </div>

  
  <div class="state-col gas" id="col-gas">
    <div class="state-title">Gas</div>
    <div class="canvas-wrapper">
      <canvas id="cvs-gas" width="160" height="160"></canvas>
    </div>
    <div class="density-section">
      <div class="density-label">Density</div>
      <div class="density-bar-bg">
        <div class="density-bar-fill" style="width: 15%;"></div>
      </div>
      <div class="density-val">Low</div>
    </div>
  </div>
</div>

<script>
  // Selection handling
  const cols = document.querySelectorAll('.state-col');
  cols.forEach(col => {
    col.addEventListener('click', () => {
      cols.forEach(c => c.classList.remove('active'));
      col.classList.add('active');
    });
  });

  const R = 7;
  const PARTICLE_COLOR = '#0284c7';
  const PARTICLE_STROKE = '#0369a1';

  // --- SOLID ---
  const cvsSolid = document.getElementById('cvs-solid');
  const ctxSolid = cvsSolid.getContext('2d');
  const solidGrid = [];
  const rows = 6, colsCount = 6;
  const spacingX = 160 / (colsCount + 1);
  const spacingY = 160 / (rows + 1);

  for (let r = 1; r <= rows; r++) {
    for (let c = 1; c <= colsCount; c++) {
      solidGrid.push({
        baseX: c * spacingX,
        baseY: r * spacingY,
        phase: Math.random() * Math.PI * 2
      });
    }
  }

  // --- LIQUID ---
  const cvsLiquid = document.getElementById('cvs-liquid');
  const ctxLiquid = cvsLiquid.getContext('2d');
  const liquidParticles = [];
  const liquidCount = 28;

  for (let i = 0; i < liquidCount; i++) {
    liquidParticles.push({
      x: 15 + Math.random() * 130,
      y: 35 + Math.random() * 110,
      vx: (Math.random() - 0.5) * 0.6,
      vy: (Math.random() - 0.5) * 0.6
    });
  }

  // --- GAS ---
  const cvsGas = document.getElementById('cvs-gas');
  const ctxGas = cvsGas.getContext('2d');
  const gasParticles = [];
  const gasCount = 5;

  for (let i = 0; i < gasCount; i++) {
    const angle = Math.random() * Math.PI * 2;
    const speed = 1.8 + Math.random() * 0.6;
    gasParticles.push({
      x: 20 + Math.random() * 120,
      y: 20 + Math.random() * 120,
      vx: Math.cos(angle) * speed,
      vy: Math.sin(angle) * speed
    });
  }

  function drawParticle(ctx, x, y) {
    ctx.beginPath();
    ctx.arc(x, y, R, 0, Math.PI * 2);
    ctx.fillStyle = PARTICLE_COLOR;
    ctx.fill();
    ctx.strokeStyle = PARTICLE_STROKE;
    ctx.lineWidth = 1.5;
    ctx.stroke();
  }

  let t = 0;
  function animate() {
    t += 0.05;

    // 1. Solid Render
    ctxSolid.clearRect(0, 0, 160, 160);
    solidGrid.forEach(p => {
      const jx = Math.sin(t * 8 + p.phase) * 1.2;
      const jy = Math.cos(t * 8 + p.phase) * 1.2;
      drawParticle(ctxSolid, p.baseX + jx, p.baseY + jy);
    });

    // 2. Liquid Render
    ctxLiquid.clearRect(0, 0, 160, 160);
    liquidParticles.forEach(p => {
      p.x += p.vx;
      p.y += p.vy;

      if (p.x < R + 2 || p.x > 158 - R) p.vx *= -1;
      if (p.y < 30 || p.y > 158 - R) p.vy *= -1;

      // Soft wander
      p.vx += (Math.random() - 0.5) * 0.1;
      p.vy += (Math.random() - 0.5) * 0.1;
      p.vx = Math.max(-0.8, Math.min(0.8, p.vx));
      p.vy = Math.max(-0.8, Math.min(0.8, p.vy));

      drawParticle(ctxLiquid, p.x, p.y);
    });

    // 3. Gas Render
    ctxGas.clearRect(0, 0, 160, 160);
    gasParticles.forEach(p => {
      p.x += p.vx;
      p.y += p.vy;

      if (p.x <= R + 2) { p.x = R + 2; p.vx *= -1; }
      if (p.x >= 158 - R) { p.x = 158 - R; p.vx *= -1; }
      if (p.y <= R + 2) { p.y = R + 2; p.vy *= -1; }
      if (p.y >= 158 - R) { p.y = 158 - R; p.vy *= -1; }

      drawParticle(ctxGas, p.x, p.y);
    });

    requestAnimationFrame(animate);
  }

  animate();
</script>

</body>
</html>

Why does particle spacing change so dramatically across the three states of matter? Let's look at the forces holding them together.

In a **solid**, strong **intermolecular forces** hold particles tightly in a fixed, regular lattice. Because particles can only vibrate around fixed points, they pack tightly with minimal empty space, producing the highest density.

In a **liquid**, particles have enough kinetic energy to partially overcome these attractive forces. They remain touching in a random, irregular arrangement but can slide past one another, leading to a density only slightly lower than a solid.

In a **gas**, particles have completely overcome attractive forces. They move rapidly in random directions, separated by vast distances of empty space, making gases roughly 1,000 times less dense than solids and liquids.

<!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>Particle Arrangements and Density</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
      background-color: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 12px 8px;
    }
    .states-grid {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 8px;
      width: 100%;
      max-width: 600px;
    }
    .state-card {
      background: #ffffff;
      border: 1px solid #e6e6e6;
      border-radius: 12px;
      padding: 8px 6px 10px;
      display: flex;
      flex-direction: column;
      align-items: center;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.04);
    }
    .state-title {
      font-size: 15px;
      font-weight: 700;
      color: #1e2945;
      margin-bottom: 6px;
    }
    .canvas-container {
      width: 100%;
      aspect-ratio: 1;
      max-width: 160px;
      background: #f1f5f9;
      border: 1.5px solid #cbd5e1;
      border-radius: 8px;
      overflow: hidden;
      position: relative;
    }
    canvas {
      display: block;
      width: 100%;
      height: 100%;
    }
    .density-meter {
      width: 100%;
      max-width: 160px;
      margin-top: 8px;
      display: flex;
      flex-direction: column;
      gap: 3px;
    }
    .density-track {
      width: 100%;
      height: 7px;
      background: #e2e8f0;
      border-radius: 4px;
      overflow: hidden;
    }
    .density-fill {
      height: 100%;
      border-radius: 4px;
      background: #22b7ff;
    }
    .density-label {
      font-size: 11px;
      font-weight: 600;
      color: #64748b;
      text-align: center;
    }
    .solid .density-fill {
      width: 100%;
      background: #0284c7;
    }
    .liquid .density-fill {
      width: 92%;
      background: #38bdf8;
    }
    .gas .density-fill {
      width: 8%;
      background: #94a3b8;
    }
  </style>
</head>
<body>

  <div class="states-grid">
    
    <div class="state-card solid">
      <div class="state-title">Solid</div>
      <div class="canvas-container">
        <canvas id="solidCanvas"></canvas>
      </div>
      <div class="density-meter">
        <div class="density-track">
          <div class="density-fill"></div>
        </div>
        <div class="density-label">High density</div>
      </div>
    </div>

    
    <div class="state-card liquid">
      <div class="state-title">Liquid</div>
      <div class="canvas-container">
        <canvas id="liquidCanvas"></canvas>
      </div>
      <div class="density-meter">
        <div class="density-track">
          <div class="density-fill"></div>
        </div>
        <div class="density-label">High density</div>
      </div>
    </div>

    
    <div class="state-card gas">
      <div class="state-title">Gas</div>
      <div class="canvas-container">
        <canvas id="gasCanvas"></canvas>
      </div>
      <div class="density-meter">
        <div class="density-track">
          <div class="density-fill"></div>
        </div>
        <div class="density-label">Low density</div>
      </div>
    </div>
  </div>

  <script>
    function setupCanvas(canvas) {
      const rect = canvas.parentElement.getBoundingClientRect();
      const dpr = window.devicePixelRatio || 1;
      const size = Math.floor(rect.width);
      canvas.width = size * dpr;
      canvas.height = size * dpr;
      const ctx = canvas.getContext('2d');
      ctx.scale(dpr, dpr);
      return { ctx, size };
    }

    // --- 1. SOLID: Regular tight lattice vibrating in place ---
    const solidCanvas = document.getElementById('solidCanvas');
    let solidCtx, solidSize;

    const solidRows = 5;
    const solidCols = 5;
    const solidParticles = [];

    function initSolid() {
      const res = setupCanvas(solidCanvas);
      solidCtx = res.ctx;
      solidSize = res.size;
      solidParticles.length = 0;

      const pad = solidSize * 0.16;
      const spacing = (solidSize - pad * 2) / (solidRows - 1);
      const r = spacing * 0.38;

      for (let rIdx = 0; rIdx < solidRows; rIdx++) {
        for (let cIdx = 0; cIdx < solidCols; cIdx++) {
          solidParticles.push({
            baseX: pad + cIdx * spacing,
            baseY: pad + rIdx * spacing,
            radius: r,
            phaseX: Math.random() * Math.PI * 2,
            phaseY: Math.random() * Math.PI * 2,
            speed: 0.12 + Math.random() * 0.06
          });
        }
      }
    }

    // --- 2. LIQUID: Closely packed, sliding past each other ---
    const liquidCanvas = document.getElementById('liquidCanvas');
    let liquidCtx, liquidSize;
    const liquidParticles = [];

    function initLiquid() {
      const res = setupCanvas(liquidCanvas);
      liquidCtx = res.ctx;
      liquidSize = res.size;
      liquidParticles.length = 0;

      const count = 22;
      const r = solidSize ? (solidSize * 0.16) * 0.38 : 9;

      for (let i = 0; i < count; i++) {
        liquidParticles.push({
          x: r + Math.random() * (liquidSize - 2 * r),
          y: liquidSize * 0.2 + Math.random() * (liquidSize * 0.75),
          vx: (Math.random() - 0.5) * 0.6,
          vy: (Math.random() - 0.5) * 0.6,
          radius: r
        });
      }
    }

    // --- 3. GAS: Few particles, high speed, large empty spaces ---
    const gasCanvas = document.getElementById('gasCanvas');
    let gasCtx, gasSize;
    const gasParticles = [];

    function initGas() {
      const res = setupCanvas(gasCanvas);
      gasCtx = res.ctx;
      gasSize = res.size;
      gasParticles.length = 0;

      const count = 3;
      const r = solidSize ? (solidSize * 0.16) * 0.38 : 9;

      for (let i = 0; i < count; i++) {
        const angle = Math.random() * Math.PI * 2;
        const speed = 2.2;
        gasParticles.push({
          x: r + 10 + Math.random() * (gasSize - 2 * r - 20),
          y: r + 10 + Math.random() * (gasSize - 2 * r - 20),
          vx: Math.cos(angle) * speed,
          vy: Math.sin(angle) * speed,
          radius: r,
          trail: []
        });
      }
    }

    function initAll() {
      initSolid();
      initLiquid();
      initGas();
    }

    window.addEventListener('resize', initAll);
    initAll();

    function drawParticle(ctx, x, y, r, color, highlight) {
      ctx.save();
      ctx.beginPath();
      ctx.arc(x, y, r, 0, Math.PI * 2);
      ctx.fillStyle = color;
      ctx.fill();

      // Subtle 3D shine
      ctx.beginPath();
      ctx.arc(x - r * 0.3, y - r * 0.3, r * 0.32, 0, Math.PI * 2);
      ctx.fillStyle = highlight || 'rgba(255, 255, 255, 0.45)';
      ctx.fill();
      ctx.restore();
    }

    let t = 0;
    function animate() {
      t += 1;

      // 1. Draw Solid
      if (solidCtx && solidSize) {
        solidCtx.clearRect(0, 0, solidSize, solidSize);
        solidParticles.forEach(p => {
          const vibAmp = 1.3;
          const x = p.baseX + Math.sin(t * p.speed + p.phaseX) * vibAmp;
          const y = p.baseY + Math.cos(t * p.speed + p.phaseY) * vibAmp;
          drawParticle(solidCtx, x, y, p.radius, '#0284c7');
        });
      }

      // 2. Draw Liquid
      if (liquidCtx && liquidSize) {
        liquidCtx.clearRect(0, 0, liquidSize, liquidSize);

        for (let i = 0; i < liquidParticles.length; i++) {
          const p = liquidParticles[i];

          // Gravity pull down, soft wander
          p.vy += 0.015;
          p.vx += (Math.random() - 0.5) * 0.12;
          p.vy += (Math.random() - 0.5) * 0.12;

          // Drag / damping
          p.vx *= 0.98;
          p.vy *= 0.98;

          p.x += p.vx;
          p.y += p.vy;

          // Wall bounds
          if (p.x < p.radius) { p.x = p.radius; p.vx *= -0.5; }
          if (p.x > liquidSize - p.radius) { p.x = liquidSize - p.radius; p.vx *= -0.5; }
          if (p.y < liquidSize * 0.12) { p.y = liquidSize * 0.12; p.vy *= -0.5; }
          if (p.y > liquidSize - p.radius) { p.y = liquidSize - p.radius; p.vy *= -0.5; }

          // Particle-particle soft collision
          for (let j = i + 1; j < liquidParticles.length; j++) {
            const p2 = liquidParticles[j];
            const dx = p2.x - p.x;
            const dy = p2.y - p.y;
            const dist = Math.hypot(dx, dy);
            const minDist = p.radius + p2.radius;

            if (dist < minDist && dist > 0) {
              const overlap = (minDist - dist) * 0.5;
              const nx = dx / dist;
              const ny = dy / dist;
              p.x -= nx * overlap;
              p.y -= ny * overlap;
              p2.x += nx * overlap;
              p2.y += ny * overlap;

              const kx = p.vx - p2.vx;
              const ky = p.vy - p2.vy;
              const pFactor = 2 * (nx * kx + ny * ky) / 2;
              p.vx -= pFactor * nx * 0.3;
              p.vy -= pFactor * ny * 0.3;
              p2.vx += pFactor * nx * 0.3;
              p2.vy += pFactor * ny * 0.3;
            }
          }
        }

        liquidParticles.forEach(p => {
          drawParticle(liquidCtx, p.x, p.y, p.radius, '#38bdf8');
        });
      }

      // 3. Draw Gas
      if (gasCtx && gasSize) {
        gasCtx.clearRect(0, 0, gasSize, gasSize);

        gasParticles.forEach(p => {
          p.trail.push({ x: p.x, y: p.y });
          if (p.trail.length > 5) p.trail.shift();

          p.x += p.vx;
          p.y += p.vy;

          if (p.x < p.radius) { p.x = p.radius; p.vx *= -1; }
          if (p.x > gasSize - p.radius) { p.x = gasSize - p.radius; p.vx *= -1; }
          if (p.y < p.radius) { p.y = p.radius; p.vy *= -1; }
          if (p.y > gasSize - p.radius) { p.y = gasSize - p.radius; p.vy *= -1; }

          // Motion trail
          for (let i = 0; i < p.trail.length; i++) {
            const pt = p.trail[i];
            const alpha = ((i + 1) / p.trail.length) * 0.25;
            gasCtx.beginPath();
            gasCtx.arc(pt.x, pt.y, p.radius * 0.7, 0, Math.PI * 2);
            gasCtx.fillStyle = `rgba(148, 163, 184, ${alpha})`;
            gasCtx.fill();
          }

          drawParticle(gasCtx, p.x, p.y, p.radius, '#64748b');
        });
      }

      requestAnimationFrame(animate);
    }

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

If solids are generally denser than liquids, why does ice float on top of liquid water?

Almost all substances contract and become denser as they freeze, but water is a famous exception due to **hydrogen bonding** between its polar molecules.

As water freezes below $4^\circ	ext{C}$, the molecules lock into an open hexagonal lattice that forces them further apart than in liquid water, making **ice roughly 9% less dense** than liquid water.

<!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>Particle Arrangements and Density</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      user-select: none;
      -webkit-user-select: none;
    }
    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;
      width: 100%;
      min-height: 100%;
      padding: 12px;
      gap: 10px;
    }
    .tabs {
      display: flex;
      gap: 6px;
      width: 100%;
      max-width: 480px;
      justify-content: center;
    }
    .tab-btn {
      flex: 1;
      padding: 8px 4px;
      font-size: 14px;
      font-weight: 600;
      background: #ffffff;
      color: #6b7280;
      border: 1px solid #e5e7eb;
      border-radius: 8px;
      cursor: pointer;
      text-align: center;
      transition: all 0.2s ease;
    }
    .tab-btn.active {
      background: #22b7ff;
      color: #ffffff;
      border-color: #22b7ff;
      box-shadow: 0 2px 8px rgba(34, 183, 255, 0.3);
    }
    .stage {
      display: flex;
      width: 100%;
      max-width: 540px;
      gap: 8px;
      justify-content: center;
      align-items: stretch;
      flex: 1;
    }
    .panel {
      flex: 1;
      background: #ffffff;
      border: 1px solid #e5e7eb;
      border-radius: 12px;
      padding: 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 8px;
      transition: opacity 0.3s ease, transform 0.3s ease;
    }
    .panel.dimmed {
      opacity: 0.35;
    }
    .canvas-box {
      width: 100%;
      aspect-ratio: 1 / 1;
      max-height: 160px;
      background: #f0f7ff;
      border: 2px solid #cbd5e1;
      border-radius: 8px;
      position: relative;
      overflow: hidden;
    }
    canvas {
      width: 100%;
      height: 100%;
      display: block;
    }
    .title {
      font-size: 14px;
      font-weight: 700;
      color: #1e2945;
      text-align: center;
    }
    .density-wrap {
      width: 100%;
      display: flex;
      flex-direction: column;
      gap: 4px;
      align-items: center;
    }
    .density-bar-bg {
      width: 100%;
      height: 8px;
      background: #e5e7eb;
      border-radius: 4px;
      overflow: hidden;
    }
    .density-bar {
      height: 100%;
      background: #22b7ff;
      border-radius: 4px;
      transition: width 0.4s ease;
    }
    .density-val {
      font-size: 12px;
      font-weight: 600;
      color: #6b7280;
    }
  </style>
</head>
<body>

  <div class="tabs">
    <button class="tab-btn active" data-view="all">All</button>
    <button class="tab-btn" data-view="solid">Solid</button>
    <button class="tab-btn" data-view="liquid">Liquid</button>
    <button class="tab-btn" data-view="gas">Gas</button>
  </div>

  <div class="stage">
    
    <div class="panel" id="panel-solid">
      <span class="title">Solid</span>
      <div class="canvas-box">
        <canvas id="cvs-solid"></canvas>
      </div>
      <div class="density-wrap">
        <div class="density-bar-bg">
          <div class="density-bar" style="width: 95%;"></div>
        </div>
        <span class="density-val">High Density</span>
      </div>
    </div>

    
    <div class="panel" id="panel-liquid">
      <span class="title">Liquid</span>
      <div class="canvas-box">
        <canvas id="cvs-liquid"></canvas>
      </div>
      <div class="density-wrap">
        <div class="density-bar-bg">
          <div class="density-bar" style="width: 88%;"></div>
        </div>
        <span class="density-val">Medium Density</span>
      </div>
    </div>

    
    <div class="panel" id="panel-gas">
      <span class="title">Gas</span>
      <div class="canvas-box">
        <canvas id="cvs-gas"></canvas>
      </div>
      <div class="density-wrap">
        <div class="density-bar-bg">
          <div class="density-bar" style="width: 12%;"></div>
        </div>
        <span class="density-val">Low Density</span>
      </div>
    </div>
  </div>

  <script>
    const cvsS = document.getElementById('cvs-solid');
    const cvsL = document.getElementById('cvs-liquid');
    const cvsG = document.getElementById('cvs-gas');
    const ctxS = cvsS.getContext('2d');
    const ctxL = cvsL.getContext('2d');
    const ctxG = cvsG.getContext('2d');

    function resizeCanvas(c, ctx) {
      const rect = c.getBoundingClientRect();
      const dpr = window.devicePixelRatio || 1;
      c.width = rect.width * dpr;
      c.height = rect.height * dpr;
      ctx.scale(dpr, dpr);
      return { w: rect.width, h: rect.height };
    }

    let dims = { w: 100, h: 100 };
    function handleResize() {
      dims = resizeCanvas(cvsS, ctxS);
      resizeCanvas(cvsL, ctxL);
      resizeCanvas(cvsG, ctxG);
      initSolid();
      initLiquid();
      initGas();
    }

    // Solid setup: 5x5 grid
    let solidNodes = [];
    function initSolid() {
      solidNodes = [];
      const cols = 5;
      const rows = 5;
      const padX = dims.w * 0.16;
      const padY = dims.h * 0.16;
      const stepX = (dims.w - 2 * padX) / (cols - 1);
      const stepY = (dims.h - 2 * padY) / (rows - 1);

      for (let r = 0; r < rows; r++) {
        for (let c = 0; c < cols; c++) {
          solidNodes.push({
            bx: padX + c * stepX,
            by: padY + r * stepY,
            phase: Math.random() * Math.PI * 2
          });
        }
      }
    }

    // Liquid setup: 22 particles in fluid motion
    let liquidNodes = [];
    function initLiquid() {
      liquidNodes = [];
      const count = 22;
      const r = dims.w * 0.055;
      for (let i = 0; i < count; i++) {
        liquidNodes.push({
          x: r + Math.random() * (dims.w - 2 * r),
          y: dims.h * 0.25 + Math.random() * (dims.h * 0.7 - r),
          vx: (Math.random() - 0.5) * 0.6,
          vy: (Math.random() - 0.5) * 0.6,
          r: r
        });
      }
    }

    // Gas setup: 4 fast particles
    let gasNodes = [];
    function initGas() {
      gasNodes = [];
      const count = 4;
      const r = dims.w * 0.06;
      for (let i = 0; i < count; i++) {
        const angle = Math.random() * Math.PI * 2;
        const speed = 1.6;
        gasNodes.push({
          x: r + Math.random() * (dims.w - 2 * r),
          y: r + Math.random() * (dims.h - 2 * r),
          vx: Math.cos(angle) * speed,
          vy: Math.sin(angle) * speed,
          r: r
        });
      }
    }

    function drawParticle(ctx, x, y, radius, color = '#22b7ff') {
      ctx.beginPath();
      ctx.arc(x, y, radius, 0, Math.PI * 2);
      ctx.fillStyle = color;
      ctx.fill();
      ctx.lineWidth = 1.5;
      ctx.strokeStyle = '#0284c7';
      ctx.stroke();

      // Soft highlight
      ctx.beginPath();
      ctx.arc(x - radius * 0.3, y - radius * 0.3, radius * 0.3, 0, Math.PI * 2);
      ctx.fillStyle = 'rgba(255, 255, 255, 0.7)';
      ctx.fill();
    }

    let t = 0;
    function render() {
      t += 0.05;

      // Render Solid
      ctxS.clearRect(0, 0, dims.w, dims.h);
      const sRadius = dims.w * 0.058;
      solidNodes.forEach(n => {
        const jx = Math.sin(t * 3 + n.phase) * 1.2;
        const jy = Math.cos(t * 3.5 + n.phase) * 1.2;
        drawParticle(ctxS, n.bx + jx, n.by + jy, sRadius);
      });

      // Render Liquid
      ctxL.clearRect(0, 0, dims.w, dims.h);
      const lRadius = dims.w * 0.055;
      for (let i = 0; i < liquidNodes.length; i++) {
        const p = liquidNodes[i];
        p.x += p.vx;
        p.y += p.vy;

        // Flow bounce bottom half
        if (p.x < lRadius) { p.x = lRadius; p.vx *= -1; }
        if (p.x > dims.w - lRadius) { p.x = dims.w - lRadius; p.vx *= -1; }
        if (p.y < dims.h * 0.22) { p.y = dims.h * 0.22; p.vy *= -1; }
        if (p.y > dims.h - lRadius) { p.y = dims.h - lRadius; p.vy *= -1; }

        drawParticle(ctxL, p.x, p.y, lRadius);
      }

      // Render Gas
      ctxG.clearRect(0, 0, dims.w, dims.h);
      gasNodes.forEach(p => {
        p.x += p.vx;
        p.y += p.vy;

        if (p.x < p.r) { p.x = p.r; p.vx *= -1; }
        if (p.x > dims.w - p.r) { p.x = dims.w - p.r; p.vx *= -1; }
        if (p.y < p.r) { p.y = p.r; p.vy *= -1; }
        if (p.y > dims.h - p.r) { p.y = dims.h - p.r; p.vy *= -1; }

        // Trail / vector hint
        ctxG.beginPath();
        ctxG.moveTo(p.x, p.y);
        ctxG.lineTo(p.x - p.vx * 3.5, p.y - p.vy * 3.5);
        ctxG.strokeStyle = 'rgba(34, 183, 255, 0.4)';
        ctxG.lineWidth = 2;
        ctxG.stroke();

        drawParticle(ctxG, p.x, p.y, p.r);
      });

      requestAnimationFrame(render);
    }

    // Tabs logic
    const tabs = document.querySelectorAll('.tab-btn');
    const panels = {
      solid: document.getElementById('panel-solid'),
      liquid: document.getElementById('panel-liquid'),
      gas: document.getElementById('panel-gas')
    };

    tabs.forEach(btn => {
      btn.addEventListener('click', () => {
        tabs.forEach(t => t.classList.remove('active'));
        btn.classList.add('active');
        const view = btn.dataset.view;

        if (view === 'all') {
          Object.values(panels).forEach(p => p.classList.remove('dimmed'));
        } else {
          Object.keys(panels).forEach(k => {
            if (k === view) {
              panels[k].classList.remove('dimmed');
            } else {
              panels[k].classList.add('dimmed');
            }
          });
        }
      });
    });

    window.addEventListener('resize', handleResize);
    window.addEventListener('load', () => {
      handleResize();
      render();
    });
  </script>
</body>
</html>

When water boils into steam, does the mass of each individual particle decrease to make the gas lighter?

During any change of state, **particle mass is conserved** — individual particles do not change mass, size, or shape when a substance melts or boils.

Gas density is drastically lower solely because the distance between particles increases by roughly 10 times in every direction, spreading the exact same mass across nearly 1,000 times more volume.

science

Particle Arrangements and Density in Solids, Liquids, and Gases. Explain differences in density between solids, liquids, and gases in terms of the spacing, arrangement, and bonding of particles.

GCSE Physics: Density of Materials and the Particle Model

Particle Explanations of Density and Pressure (Key Stage 4)

States of Matter: Basics Simulation

Teaching density through the particle model at KS4 requires students to bridge macroscopic observations ($m$, $V$, state changes) with sub-microscopic particle dynamics (spacing, ordering, forces). A high-impact pedagogical approach is the 'Equal-Volume Box' heuristic: draw identical $1\,\text{cm}^3$ boxes on the board and ask students how many particles fit in each state to establish why density is directly proportional to particle packing density when particle mass is identical. Address the ice/water anomaly explicitly to prevent over-generalisation.

Particle Arrangements and Density in Solids, Liquids, and Gases

What Is Density?

Particle Arrangements and Forces