Calculate the molar mass of ammonium carbonate.

Steps to Solve

1. Identify the elements and their counts in the formula

The chemical formula for ammonium carbonate is $(NH_4)_2CO_3$.

• There are 2 nitrogen (N) atoms.
• There are 8 hydrogen (H) atoms (4 from each of the 2 ammonium ions).
• There is 1 carbon (C) atom.
• There are 3 oxygen (O) atoms.

2. Find the atomic masses of the elements

Next, we will look up the atomic masses of each element:

• Nitrogen (N): approximately 14.01 g/mol
• Hydrogen (H): approximately 1.01 g/mol
• Carbon (C): approximately 12.01 g/mol
• Oxygen (O): approximately 16.00 g/mol

3. Calculate the total mass for each element

Now we will calculate the molar mass contributed by each element:

• For Nitrogen: $$ 2 \times 14.01 , \text{g/mol} = 28.02 , \text{g/mol} $$

• For Hydrogen: $$ 8 \times 1.01 , \text{g/mol} = 8.08 , \text{g/mol} $$

• For Carbon: $$ 1 \times 12.01 , \text{g/mol} = 12.01 , \text{g/mol} $$

• For Oxygen: $$ 3 \times 16.00 , \text{g/mol} = 48.00 , \text{g/mol} $$

4. Sum all the contributions to find the molar mass

Finally, we add all these values together to get the total molar mass of ammonium carbonate:

$$ 28.02 , \text{g/mol} + 8.08 , \text{g/mol} + 12.01 , \text{g/mol} + 48.00 , \text{g/mol} = 96.11 , \text{g/mol} $$