Questions: The gram-formula mass of (NH4)2CO3 is (A) 96.0 g / mol (B) 78.0 g / mol (C) 64 g / mol (D) 46 g / mol

Transcript text: The gram-formula mass of $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}$ is (A) $96.0 \mathrm{~g} / \mathrm{mol}$ (B) $78.0 \mathrm{~g} / \mathrm{mol}$ (C) $64 \mathrm{~g} / \mathrm{mol}$ (D) $46 \mathrm{~g} / \mathrm{mol}^{\circ}$

Solution

Solution Steps

Step 1: Identify the Chemical Formula Components

The chemical formula for ammonium carbonate is $(\mathrm{NH}_4)_2\mathrm{CO}_3$ . This compound consists of:

2 ammonium ions $(\mathrm{NH}_4)^+$
1 carbonate ion $(\mathrm{CO}_3)^{2-}$

Step 2: Calculate the Molar Mass of Each Component

Ammonium Ion $(\mathrm{NH}_4)^+$ :
- Nitrogen (N): 1 atom × 14.01 g/mol = 14.01 g/mol
- Hydrogen (H): 4 atoms × 1.008 g/mol = 4.032 g/mol
- Total for one $(\mathrm{NH}_4)^+$ : 14.01 + 4.032 = 18.042 g/mol
Carbonate Ion $(\mathrm{CO}_3)^{2-}$ :
- Carbon (C): 1 atom × 12.01 g/mol = 12.01 g/mol
- Oxygen (O): 3 atoms × 16.00 g/mol = 48.00 g/mol
- Total for $(\mathrm{CO}_3)^{2-}$ : 12.01 + 48.00 = 60.01 g/mol

Step 3: Calculate the Total Gram-Formula Mass

Total mass of 2 ammonium ions: $2 \times 18.042 = 36.084$ g/mol
Total mass of 1 carbonate ion: $60.01$ g/mol
Total gram-formula mass of $(\mathrm{NH}_4)_2\mathrm{CO}_3$ : $36.084 + 60.01 = 96.094 \, \text{g/mol}$