What is the percent by mass sulfur in (NH4)2SO3

What is the percent by mass sulfur in (NH4)2SO3?

A. 58.0%

B. 13.8%

C. 3.00%

D. 27.6%

E. 43.0%

The correct answer and explanation is:

To calculate the percent by mass of sulfur in (NH4)2SO3(NH_4)_2SO_3, we follow these steps:

1. Find the molar mass of the compound:
   The formula for ammonium sulfite is (NH4)2SO3(NH_4)_2SO_3, which consists of ammonium ions and sulfite ions. We need to calculate the molar mass by adding the atomic masses of all the elements involved:
   • Nitrogen (N) has an atomic mass of approximately 14.01 g/mol.
   • Hydrogen (H) has an atomic mass of approximately 1.008 g/mol.
   • Sulfur (S) has an atomic mass of approximately 32.07 g/mol.
   • Oxygen (O) has an atomic mass of approximately 16.00 g/mol.
   The molar mass of (NH4)2SO3(NH_4)_2SO_3 is calculated as follows:
   • Ammonium ions: There are two ammonium ions, each containing one nitrogen atom and four hydrogen atoms. So, the mass contribution from nitrogen and hydrogen is: 2×(14.01 g/mol+4×1.008 g/mol)=2×(14.01 g/mol+4.032 g/mol)=2×18.042 g/mol=36.084 g/mol2 \times (14.01 \, \text{g/mol} + 4 \times 1.008 \, \text{g/mol}) = 2 \times (14.01 \, \text{g/mol} + 4.032 \, \text{g/mol}) = 2 \times 18.042 \, \text{g/mol} = 36.084 \, \text{g/mol}
   • Sulfur: There is one sulfur atom in the compound, contributing: 32.07 g/mol32.07 \, \text{g/mol}
   • Oxygen: There are three oxygen atoms in the sulfite ion, contributing: 3×16.00 g/mol=48.00 g/mol3 \times 16.00 \, \text{g/mol} = 48.00 \, \text{g/mol}
   Now, add up the masses: 36.084 g/mol+32.07 g/mol+48.00 g/mol=116.154 g/mol36.084 \, \text{g/mol} + 32.07 \, \text{g/mol} + 48.00 \, \text{g/mol} = 116.154 \, \text{g/mol}
2. Find the percent by mass of sulfur:
   The percent by mass of sulfur is calculated by dividing the mass of sulfur by the molar mass of the entire compound and then multiplying by 100 to convert to a percentage: 32.07 g/mol116.154 g/mol×100=27.6%\frac{32.07 \, \text{g/mol}}{116.154 \, \text{g/mol}} \times 100 = 27.6\%

Thus, the correct answer is D. 27.6%.

This calculation shows how to break down the compound into its atomic masses, compute the total molar mass, and then determine the contribution of sulfur to the overall mass of the compound.