Question

What is the mass of potassium chloride produced when $12.25\ \mathrm{g}$ potassium chlorate undergoes decomposition? (Atomic masses: $\mathrm{K} = 39$, $\mathrm{Cl} = 35.5$, $\mathrm{O} = 16$)

• A. $16.0\ \mathrm{g}$
• B. $14.9\ \mathrm{g}$
• C. $7.45\ \mathrm{g}$
• D. $4.25\ \mathrm{g}$

Hint:

Notice how clean the numbers are! The given mass ($12.25\ \mathrm{g}$) is exactly one-tenth of the molar mass of $\mathrm{KClO}_3$ ($122.5\ \mathrm{g}$). Since the molar ratio is $1:1$, the answer must simply be one-tenth of the molar mass of $\mathrm{KCl}$ ($74.5\ \mathrm{g}$), which gives $7.45\ \mathrm{g}$ with zero heavy calculations.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the mass of potassium chloride ($\mathrm{KCl}$) produced from the complete thermal decomposition of $12.25\ \mathrm{g}$ of potassium chlorate ($\mathrm{KClO}_3$).

Step 2: Key Formula or Approach:
Write down the balanced chemical equation representing the decomposition of potassium chlorate: $$2\mathrm{KClO}_3(s) \xrightarrow{\Delta} 2\mathrm{KCl}(s) + 3\mathrm{O}_2(g)$$ This balanced equation shows a $2:2$ stoichiometric ratio, meaning exactly $1\text{ mole}$ of $\mathrm{KClO}_3$ yields $1\text{ mole}$ of $\mathrm{KCl}$ upon decomposing. We can use the standard relation: $$\text{Number of moles } (n) = \frac{\text{Given Mass}}{\text{Molar Mass}}$$

Step 3: Detailed Explanation:
1. Compute the molar mass of potassium chlorate ($\mathrm{KClO}_3$): $$M_{\mathrm{KClO}_3} = 39 + 35.5 + (3 \times 16) = 74.5 + 48 = 122.5\ \mathrm{g/mol}$$ 2. Find the number of moles in $12.25\ \mathrm{g}$ of $\mathrm{KClO}_3$: $$n_{\mathrm{KClO}_3} = \frac{12.25\ \mathrm{g}}{122.5\ \mathrm{g/mol}} = 0.1\ \mathrm{mol}$$ 3. Since the stoichiometric ratio between $\mathrm{KClO}_3$ and $\mathrm{KCl}$ is $1:1$, the number of moles of $\mathrm{KCl}$ produced is also exactly $0.1\ \mathrm{mol}$.
4. Compute the molar mass of potassium chloride ($\mathrm{KCl}$): $$M_{\mathrm{KCl}} = 39 + 35.5 = 74.5\ \mathrm{g/mol}$$ 5. Convert the moles of $\mathrm{KCl}$ back into mass: $$\text{Mass of KCl} = \text{moles} \times M_{\mathrm{KCl}} = 0.1\ \mathrm{mol} \times 74.5\ \mathrm{g/mol} = 7.45\ \mathrm{g}$$

Step 4: Final Answer:
The net mass of potassium chloride produced is $7.45\ \mathrm{g}$, which matches option (C).