Find the total number of H, S and O atoms in the following a) 196gmH2So4 b) 196amu h2so4 c) 5 mole h2s2o6 d) 3 molecules h2s2o6

Key Ideas You Must Know

1. Molecular (Molar) Mass
   • H₂SO₄ → $2\times1 + 32 + 4\times16 = 98\,\text{g mol}^{-1}$
   • This tells us that 1 mole (≈6.022×10²³ molecules) weighs 98 g.
2. Counting With the Mole
   • If you have mass $m$ of a substance, the moles present are $n = \frac{m}{M}$ where $M$ is molar mass.
   • One mole of molecules contains the same number (Avogadro’s number, $N_A$) of each atom as the subscript inside the formula.
3. From Molecules to Atoms
   • Each H₂SO₄ molecule has 2 H, 1 S, 4 O atoms.
   • Multiply number of molecules (or moles) by these sub-scripts to get atoms (or moles of atoms).
4. AMU vs g
   • In amu, the number itself tells you how many molecules because 1 molecule of H₂SO₄ = 98 amu.
   • So 196 amu = 2 molecules.

Logical Chain for Each Sub-part

• (a) 196 g H₂SO₄
  1. Compute moles: $\frac{196}{98}=2 \text{mol}$ of molecules.
  2. Use sub-scripts → Atoms: H = $2\,\text{mol} \times 2$, S = $2\,\text{mol} \times 1$, O = $2\,\text{mol} \times 4$.
• (b) 196 amu H₂SO₄
  1. $98\,\text{amu}$ per molecule ⇒ $\frac{196}{98}=2$ molecules.
  2. Directly multiply counts per molecule.
• (c) 5 mol H₂S₂O₆
  1. Already given molecules in moles.
  2. Atoms per molecule: H₂S₂O₆ ⇒ 2 H, 2 S, 6 O.
  3. Multiply by 5.
• (d) 3 molecules H₂S₂O₆ same as (c) but with 3 molecules.

Always remember: atoms = (molecules) × (sub-script) and molecules = (mass)/(molar mass) when mass is given.

🎈 Imagine LEGO Blocks

Think of molecules as small LEGO sets. Each color block represents a different atom:

• Red = Hydrogen (H)
• Blue = Sulfur (S)
• Green = Oxygen (O)

Your job is to count how many of each colored block you have when someone hands you:

1. A weight of LEGO sets (196 g of H₂SO₄) – like weighing candies on a scale.
2. A mass in tiny units (196 amu of H₂SO₄) – like saying “the two‐pack weighs 196 peanuts”.
3. 5 big bags each holding lots of identical LEGO sets (5 moles of H₂S₂O₆).
4. Just 3 single LEGO sets of H₂S₂O₆.

To solve, you

1. Figure out how many complete LEGO sets (molecules) you actually have.
2. Multiply by how many of each colored block is in one set.

That’s all! 😃

Step-by-Step Calculations

(a) 196 g H₂SO₄

1. Moles of molecules:
   $n = \frac{196}{98} = 2\,\text{mol}$
2. Moles of atoms:
   $n_H = 2\times2 = 4\,\text{mol}$
   $n_S = 2\times1 = 2\,\text{mol}$
   $n_O = 2\times4 = 8\,\text{mol}$
3. Number of atoms:
   $N_H = 4N_A$
   $N_S = 2N_A$
   $N_O = 8N_A$

(b) 196 amu H₂SO₄

1. Molecules present:
   $\text{Molecules} = \frac{196}{98} = 2$
2. Atoms:
   $H = 2\times2 = 4\,\text{atoms}$
   $S = 2\times1 = 2\,\text{atoms}$
   $O = 2\times4 = 8\,\text{atoms}$

(c) 5 mol H₂S₂O₆

1. Atoms in 1 mole of molecules: H = 2 mol, S = 2 mol, O = 6 mol.
2. For 5 mol:
   $n_H = 5\times2 = 10\,\text{mol}$
   $n_S = 5\times2 = 10\,\text{mol}$
   $n_O = 5\times6 = 30\,\text{mol}$
3. Number of atoms:
   $N_H = 10N_A$
   $N_S = 10N_A$
   $N_O = 30N_A$

(d) 3 molecules H₂S₂O₆

1. Atoms:
   $H = 3\times2 = 6\,\text{atoms}$
   $S = 3\times2 = 6\,\text{atoms}$
   $O = 3\times6 = 18\,\text{atoms}$