Question

in an experiment, potassium chlorate decomposed according to the following chemical equation:

\\2\text{kclo}_3 \
ightarrow 2\text{kcl} + 3\text{o}_2\\

(molar mass of \\(\text{kclo}_3 = 122.5\text{ g/mol}\\); \\(\text{kcl} = 74.55\text{ g/mol}\\); \\(\text{o}_2 = 31.998\text{ g/mol}\\))

if the mass of potassium chlorate was 240 grams, which of the following calculations can be used to determine the mass of oxygen gas formed?

• \\((240 \times 2 \times 31.998) \div (122.5 \times 3)\text{ grams}\\)
• \\((240 \times 3 \times 31.998) \div (122.5 \times 2)\text{ grams}\\)
• \\((240 \times 2 \times 122.5) \div (31.998 \times 3)\text{ grams}\\)
• \\((240 \times 3 \times 122.5) \div (31.998 \times 2)\text{ grams}\\)

Explanation:

Set up the dimensional analysis expression

$$ \text{Mass of }\text{O}_2 = 240\text{ g }\text{KClO}_3 \times \frac{1\text{ mol }\text{KClO}_3}{122.5\text{ g }\text{KClO}_3} \times \frac{3\text{ mol }\text{O}_2}{2\text{ mol }\text{KClO}_3} \times \frac{31.998\text{ g }\text{O}_2}{1\text{ mol }\text{O}_2} $$

Simplify the expression algebraically

$$ \text{Mass of }\text{O}_2 = \frac{240 \times 3 \times 31.998}{122.5 \times 2}\text{ grams} $$

Match with the given options

$$ (240 \times 3 \times 31.998) \div (122.5 \times 2)\text{ grams} $$

Answer:

• (A) \((240 \times 2 \times 31.998) \div (122.5 \times 3)\text{ grams}\)
• (B) \((240 \times 3 \times 31.998) \div (122.5 \times 2)\text{ grams}\) (Correct answer)
• (C) \((240 \times 2 \times 122.5) \div (31.998 \times 3)\text{ grams}\)
• (D) \((240 \times 3 \times 122.5) \div (31.998 \times 2)\text{ grams}\)