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2. 50 g of a substance contains [tex]24.68 \, \text{g} \, \text{K}, 10.13 \, \text{g} \, \text{S}[/tex] and [tex]15.19 \, \text{g} \, \text{O}[/tex]. Calculate the empirical formula of the substance.

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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].
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