Calculating Hydrogen Content
Methane vs Ammonia

Understanding the Concept

To determine which substance contains a greater number of hydrogen atoms, we must follow these systematic steps:

1. Determine the molar mass of each compound.
2. Calculate the number of moles for the given mass of each substance.
3. Identify the number of hydrogen atoms per molecule of the compound.
4. Calculate the total number of moles of hydrogen atoms in the given sample.

Step-by-Step Calculation

1. For 9 g of Methane ($CH_4$)

• Molar Mass of $CH_4$: $12.01 + (4 \times 1.008) \approx 16 \text{ g/mol}$
• Moles of $CH_4$: $\frac{9 \text{ g}}{16 \text{ g/mol}} = 0.5625 \text{ moles}$
• Hydrogen atoms per molecule: There are 4 hydrogen atoms in one $CH_4$ molecule.
• Total moles of H: $0.5625 \times 4 = 2.25 \text{ moles of H atoms}$

2. For 10 g of Ammonia ($NH_3$)

• Molar Mass of $NH_3$: $14.01 + (3 \times 1.008) \approx 17 \text{ g/mol}$
• Moles of $NH_3$: $\frac{10 \text{ g}}{17 \text{ g/mol}} \approx 0.588 \text{ moles}$
• Hydrogen atoms per molecule: There are 3 hydrogen atoms in one $NH_3$ molecule.
• Total moles of H: $0.588 \times 3 \approx 1.764 \text{ moles of H atoms}$

Conclusion

Comparing the two results:

• $CH_4$ contains $2.25$ moles of hydrogen atoms.
• $NH_3$ contains $\approx 1.764$ moles of hydrogen atoms.

Since $2.25 > 1.764$, 9 g of $CH_4$ contains a greater number of hydrogen atoms than 10 g of $NH_3$.