Question

The following question may have more than one correct options:
$1.5{\text{ g}}$ of oxygen is produced by heating ${\text{KCl}}{{\text{O}}_{\text{3}}}$ . How much ${\text{KCl}}$ is produced in the reaction?
(A) $4.15 \times {10^{ - 2}}{\text{ mol}}$
(B) $4.33{\text{ g}}$
(C) $3.125 \times {10^{ - 2}}{\text{ mol}}$
(D) $2.33{\text{ g}}$

Answer 1

Mole is the basic unit for the measurement of the amount of a substance in the International System of units, commonly known as the SI Units. One mole of a substance is defined as the amount of the substance that contains particles equal to the Avogadro’s number. To answer this question, you must recall the formula for calculating the number of moles of a substance. From the reaction equation, we shall calculate the number of moles formed in the reactant and product side and then use the mole concept to calculate the moles of oxygen used.

Formula used: $n = \dfrac{w}{M}$
Where, $n$ represents the number of moles of the given substance
$w$ represents the given mass of the substance
And, $M$ represents the molar mass of the given substance.

Complete step by step solution
The decomposition reaction of ${\text{KCl}}{{\text{O}}_{\text{3}}}$ to give potassium chloride and oxygen is given by:
${\text{2KCl}}{{\text{O}}_{\text{3}}} \to 2{\text{KCl}} + 3{{\text{O}}_2}$
We are given that $1.5{\text{ g}}$ of oxygen is produced. So the number of moles of oxygen produced will be
${{\text{n}}_{{{\text{O}}_{\text{2}}}}} = \dfrac{{1.5}}{{32}} = 4.68 \times {10^{ - 2}}{\text{ mol}}$
From the chemical equation of the reaction, we can see that the decomposition of 2 moles of potassium chlorate will give two moles of potassium chloride and three moles of oxygen. Or we can say that 2 moles of potassium chloride are produced every three moles of oxygen gas.
So the number of moles of potassium chloride produced with one mole of oxygen is $= \dfrac{2}{3} \times {{\text{n}}_{{{\text{O}}_2}}}$
$\Rightarrow {{\text{n}}_{{\text{KCl}}}} = \dfrac{2}{3} \times 4.68 \times {10^{ - 2}}$
$\Rightarrow {{\text{n}}_{{\text{KCl}}}} = 3.12 \times {10^{ - 2}}{\text{ mol}}$
So, the mass of potassium chloride produced will be given by the product of the number of moles and the molar mass of the compound.
${\text{m}} = {\text{n}} \times {\text{M}}$
${\text{m}} = 2.324{\text{ grams}}$
The correct answers are C and D.

Note
The Avogadro’s number represented by ${{\text{N}}_{\text{A}}}$ is given by the value $6.022 \times {10^{23}}$ . Thus, we can say that one mole of a substance contains $6.022 \times {10^{23}}$ particles (atoms, molecules or ions depending on the substance).