Question

Saccharin is the active ingredient in many sweeteners used today. It is made up of carbon, hydrogen, oxygen, sulfur, and nitrogen. When \(7.500 \mathrm{~g}\) of saccharin are burned in oxygen, \(12.6 \mathrm{~g} \mathrm{CO}_{2}, 1.84 \mathrm{~g} \mathrm{H}_{2} \mathrm{O},\) and \(2.62 \mathrm{~g} \mathrm{SO}_{2}\) are ob- tained. Another experiment using the same mass of sample \((7.500 \mathrm{~g})\) shows that saccharin has \(7.65 \% \mathrm{~N}\). What is the simplest formula for saccharin?

Short answer

Answer: The simplest formula for saccharin is C7H5SON.

Step-by-step solution

Calculate moles of carbon from CO2

We know that 12.6 g of CO2 is produced when 7.500 g of saccharin is burned. We can convert the mass of CO2 to moles using the molar mass: \(mol \mathrm{CO}_{2} = \frac{12.6 \mathrm{~g}}{44.01 \mathrm{~g/mol}} = 0.286 \mathrm{~mol}\). Since there is 1 mole of carbon in 1 mole of CO2, we have 0.286 mol of carbon.

Calculate moles of hydrogen from H2O

We know that 1.84 g of H2O is produced in the reaction. We can convert the mass of H2O to moles using the molar mass: \(mol \mathrm{H}_{2} \mathrm{O} = \frac{1.84 \mathrm{~g}}{18.02 \mathrm{~g/mol}} = 0.102 \mathrm{~mol}\). Since there are 2 moles of hydrogen in 1 mole of H2O, we have 0.204 mol of hydrogen.

Calculate moles of sulfur from SO2

We know that 2.62 g of SO2 is produced in the reaction. We can convert the mass of SO2 to moles using the molar mass: \(mol \mathrm{SO}_{2} = \frac{2.62 \mathrm{~g}}{64.07 \mathrm{~g/mol}} = 0.0409 \mathrm{~mol}\). Since there is 1 mole of sulfur in 1 mole of SO2, we have 0.0409 mol of sulfur.

Calculate moles of nitrogen from the given percentage

Saccharin has 7.65% nitrogen content. So, in the 7.500 g sample, we have \(7.500\mathrm{~g} \cdot 0.0765 = 0.57375 \mathrm{~g}\) of nitrogen. We can convert the mass of nitrogen to moles using the molar mass: \(mol \mathrm{N} = \frac{0.57375 \mathrm{~g}}{14.01 \mathrm{~g/mol}} = 0.0410 \mathrm{~mol}\).

Calculate the empirical formula using moles of C, H, O, S, N

Divide each mole amount by the smallest mole value: C = \(\frac{0.286}{0.0409} = 7.00\); H = \(\frac{0.204}{0.0409} = 4.99\); S = \(\frac{0.0409}{0.0409} = 1\); N = \(\frac{0.0410}{0.0409} = 1\). The smallest whole number multiples for these ratios are 7:5:1:1. So, the empirical formula of saccharin is \(\mathrm{C}_{7}\mathrm{H}_{5}\mathrm{SO}_{1}\mathrm{N}_{1}\), or simply \(\mathrm{C}_{7}\mathrm{H}_{5}\mathrm{SON}\).