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Given the following two quantities: 0.50 mol of CH4 and 1.0 mol of HCl,
a. Which has more atoms?
b. Which has more molecules?
c. Which has the greater mass?
d. Which has the greater volume at the same temperature and pressure (both are gases)?

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Answer:

(a) HCl

(b) HCl

(c) HCl

(d) HCl

Explanation:

Given: 0.50 mol of CH₄ and 1.0 mol of HCl

Using stoichiometry we can calculate the answers to parts a, b, c, and d.

Part (a)

# of moles × Avogadro's number = # of atoms or molecules

Avogadro's number: 6.02 * 10²³

  • [tex]\displaystyle 0.50\ \text{mol CH}_4 \cdot \frac{6.02\cdot 10^2^3 \ \text{atoms CH}_4}{1 \ \text{mol CH}_4} = 3.01 \cdot 10^2^3 \ \text{atoms CH}_4[/tex]
  • [tex]\displaystyle 1.0\ \text{mol HCl} \cdot \frac{6.02\cdot 10^2^3 \ \text{atoms HCl}}{1 \ \text{mol HCl}} = 6.02 \cdot 10^2^3 \ \text{atoms HCl}[/tex]

HCl has more atoms than CH₄.

Part (b)

This is calculated the same way as Part (a); HCl has more molecules than CH₄.

Part (c)

Molar mass of CH₄ = 16.04 g/mol

Molar mass of HCl = 36.458 g/mol

  • [tex]\displaystyle 0.50\ \text{mol CH}_4 \cdot \frac{16.04 \ \text{g CH}_4}{1 \ \text{mol CH}_4} = 8.02 \ \text{g CH}_4[/tex]
  • [tex]\displaystyle 1.0\ \text{mol HCl} \cdot \frac{36.458 \ \text{g HCl}}{1 \ \text{mol HCl}} = 36.458 \ \text{g HCl}[/tex]

HCl has a greater mass than CH₄.

Part (d)

Assuming STP:

Molar volume of any gas at STP is 22.4 L/mol.

  • [tex]\displaystyle 0.50\ \text{mol CH}_4 \cdot \frac{22.4 \ \text{L CH}_4}{1 \ \text{mol CH}_4} = 11.2 \ \text{L CH}_4[/tex]
  • [tex]\displaystyle 1.0\ \text{mol HCl} \cdot \frac{22.4 \ \text{L HCl}}{1 \ \text{mol HCl}} = 22.4 \ \text{L HCl}[/tex]

HCl has a greater volume than CH₄.

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