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

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) $46 \mathrm{~g} / \mathrm{mol}^{\circ}$
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Solution

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Solution Steps

Step 1: Identify the Chemical Formula Components

The chemical formula for ammonium carbonate is (NH4)2CO3(\mathrm{NH}_4)_2\mathrm{CO}_3. This compound consists of:

  • 2 ammonium ions (NH4)+(\mathrm{NH}_4)^+
  • 1 carbonate ion (CO3)2(\mathrm{CO}_3)^{2-}
Step 2: Calculate the Molar Mass of Each Component
  1. Ammonium Ion (NH4)+(\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 (NH4)+(\mathrm{NH}_4)^+: 14.01 + 4.032 = 18.042 g/mol
  2. Carbonate Ion (CO3)2(\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 (CO3)2(\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: 2×18.042=36.0842 \times 18.042 = 36.084 g/mol
  • Total mass of 1 carbonate ion: 60.0160.01 g/mol
  • Total gram-formula mass of (NH4)2CO3(\mathrm{NH}_4)_2\mathrm{CO}_3: 36.084+60.01=96.094g/mol 36.084 + 60.01 = 96.094 \, \text{g/mol}

Final Answer

The gram-formula mass of (NH4)2CO3(\mathrm{NH}_4)_2\mathrm{CO}_3 is 96.0g/mol\boxed{96.0 \, \text{g/mol}}.

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