Question

How many grams of oxygen can be produced from the decomposition of $200$ grams of potassium permanganate?

Answer 1

To solve this question, first we need to find the number of moles of potassium permanganate. After that, we will find the number of moles of oxygen by looking at the stoichiometric coefficients at the reactants and product side. We will get our final result by calculating the given mass of oxygen with the help of the simple formula stated below.

Formula Used
We will use the following formula to find the solution to this equation
$n = \dfrac{{{\text{ W }}}}{{{\text{ }}{{\text{W}}_m}{\text{ }}}}$
where, $n$ is the number of moles
${\text{W}}$ is the mass of the substance
${{\text{W}}_m}$ is the molar mass of the substance.

Complete Step-by-Step solution
Let us first write the chemical equation of the decomposition of potassium permanganate
$2KMn{O_4} \to {K_2}Mn{O_4} + Mn{O_2} + {O_2}$
Now, we need to calculate the number of moles of potassium permanganate
We will use our formula to find the number of moles
According to the question, the following information is provided to us
The mass of potassium permanganate is $200$ grams
Also, the molecular weight of potassium permanganate is $158 {\text{g mo}}{{\text{l}}^{{\text{ - 1}}}}$
So, the number of moles will be
$\dfrac{{200 {\text{g}}}}{{158 {\text{g mo}}{{\text{l}}^{{\text{ - 1}}}}}} = 1.265 \;{\text{mol}}$
We can observe that the stoichiometric coefficients of the reactant and oxygen is in the ratio $2:1$ .
So, the number of moles of oxygen produced will be given by
$\dfrac{{1.265}}{2} = 0.6325\;{\text{mol}}$
Now we can rearrange the provided formula to find the mass of oxygen produced
$W = n \times {W_m}$
Let us substitute the values in this formula to get our final answer.
$W = 0.6325 {\text{mol}} \times 32 {\text{g mo}}{{\text{l}}^{{\text{ - 1}}}}$
Upon solving, we get
$\therefore W = 20.24{\text{ g}}$
Hence, $20.24$ grams of oxygen can be produced from the decomposition of $200$ grams of potassium permanganate.

Note:
Molar mass of each element is different, it is dependent on the number of protons and neutrons present in the nucleus of that element.