To determine the empirical formula of the substance, we need to follow a series of steps to convert the given masses of each element to their mole ratios, and then to the simplest whole-number ratio. Here’s a detailed, step-by-step solution:
1. Determine the mass of each element in the substance:
- Potassium (K): [tex]\( 24.68 \, \text{g} \)[/tex]
- Sulfur (S): [tex]\( 10.13 \, \text{g} \)[/tex]
- Oxygen (O): [tex]\( 15.19 \, \text{g} \)[/tex]
2. Find the atomic masses of each element:
- Atomic mass of K: [tex]\( 39.10 \, \text{g/mol} \)[/tex]
- Atomic mass of S: [tex]\( 32.07 \, \text{g/mol} \)[/tex]
- Atomic mass of O: [tex]\( 16.00 \, \text{g/mol} \)[/tex]
3. Calculate the number of moles of each element:
[tex]\[
\text{Moles of K} = \frac{24.68 \, \text{g}}{39.10 \, \text{g/mol}} \approx 0.6312 \, \text{mol}
\][/tex]
[tex]\[
\text{Moles of S} = \frac{10.13 \, \text{g}}{32.07 \, \text{g/mol}} \approx 0.3159 \, \text{mol}
\][/tex]
[tex]\[
\text{Moles of O} = \frac{15.19 \, \text{g}}{16.00 \, \text{g/mol}} \approx 0.9494 \, \text{mol}
\][/tex]
4. Determine the simplest whole-number ratio of moles:
- To find the simplest ratio, divide the number of moles of each element by the smallest number of moles calculated:
[tex]\[
\text{Smallest number of moles} = 0.3159 \, \text{mol (S)}
\][/tex]
[tex]\[
\text{Ratio of K} = \frac{0.6312}{0.3159} \approx 2.00
\][/tex]
[tex]\[
\text{Ratio of S} = \frac{0.3159}{0.3159} = 1.00
\][/tex]
[tex]\[
\text{Ratio of O} = \frac{0.9494}{0.3159} \approx 3.01
\][/tex]
5. Write the empirical formula based on the simplest whole-number ratio:
- The whole-number ratio corresponds to approximately [tex]\( 2:1:3 \)[/tex] for K, S, and O respectively.
- Thus, the empirical formula of the substance is [tex]\( \text{K}_2\text{SO}_3 \)[/tex].
So, given the masses and after completing the calculations, the empirical formula of the substance is [tex]\( \text{K}_2\text{SO}_3 \)[/tex].
