To find the empirical formula of the substance, we need to determine the simplest whole number ratio of the elements present. Here's a step-by-step guide to solving this problem:
1. Determine the mass of each element in the substance:
- Potassium ([tex]$K$[/tex]): 24.68 grams
- Sulfur ([tex]$S$[/tex]): 10.13 grams
- Oxygen ([tex]$O$[/tex]): 15.19 grams
2. Find the molar mass of each element:
- Potassium, [tex]$K$[/tex]: 39.10 g/mol
- Sulfur, [tex]$S$[/tex]: 32.06 g/mol
- Oxygen, [tex]$O$[/tex]: 16.00 g/mol
3. Calculate the number of moles of each element:
- Moles of [tex]$K = \frac{24.68 \text{ g}}{39.10 \text{ g/mol}} = 0.6312 \text{ moles}$[/tex]
- Moles of [tex]$S = \frac{10.13 \text{ g}}{32.06 \text{ g/mol}} = 0.3160 \text{ moles}$[/tex]
- Moles of [tex]$O = \frac{15.19 \text{ g}}{16.00 \text{ g/mol}} = 0.9494 \text{ moles}$[/tex]
4. Find the ratio of the moles of each element by dividing by the smallest number of moles:
- The smallest number of moles among [tex]$K$[/tex], [tex]$S$[/tex], and [tex]$O$[/tex] is [tex]$0.3160$[/tex] moles (moles of S).
- Ratio of [tex]$K$[/tex]:
[tex]\[
\frac{0.6312}{0.3160} = 2
\][/tex]
- Ratio of [tex]$S$[/tex]:
[tex]\[
\frac{0.3160}{0.3160} = 1
\][/tex]
- Ratio of [tex]$O$[/tex]:
[tex]\[
\frac{0.9494}{0.3160} = 3
\][/tex]
5. The simplest whole number ratio gives us the empirical formula:
Thus, the empirical formula is [tex]\( \text{K}_2 \text{S}_1 \text{O}_3 \)[/tex], typically represented as [tex]\( \text{K}_2 \text{SO}_3 \)[/tex].
