Question

The number of oxygen atoms in $1.58$ g of $KMn{O_4}$ is:
A. $6.02 \times {10^{21}}$
B. $2.4 \times {10^{22}}$
C. $1.4 \times {10^{22}}$
D. $3.0 \times {10^{20}}$

Answer 1

The molecular weight of $KMn{O_4}$ is $158.034$ g/mol which can be used in finding the number of moles first and then with this, calculate the number of oxygen atoms.

Complete step by step answer:
Given that:
Mass of $KMn{O_4}$, $N = 2.4 \times {10^{22}}$
Molar mass of $KMn{O_4}$, $M = 158.034g/mol$
Number of moles:
$\Rightarrow$ $n = \dfrac{w}{M} = \dfrac{{1.58g}}{{158g/mol}}$
$\Rightarrow$ After solving, $n = 0.01mol$
Each molecule contain four O atoms,
Number of O atoms, $N = 4 \times n \times {N_A}$
$\Rightarrow$ $4 \times 0.01 \times 6.022 \times {10^{23}}$ atoms
$\Rightarrow$ $N = 2.4 \times {10^{22}}$ atoms

Hence, Option B is correct.

Additional Information:
This compound is actually water-soluble and comprises two ions which are Permanganate ion and potassium ion. It is a dark purple colour and odourless solid in its physical state.
When potassium permanganate crystals are completely dissolved in water, the solution which is formed is generally purple. It is known as a strong oxidizing agent and does not form toxic by-products. It is generally formed from other minerals such as manganese oxide.
Potassium permanganate is generally prepared by mixing a solution of potassium hydroxide and powdered manganese oxide, along with oxidizing agents such as potassium chlorate. The mixture is then boiled and evaporated and the residue is heated in iron pans until it acquires a pasty consistency.
Oxygen is a chemical element that is a substance which contains only one type of atom. Its official chemical symbol is O, and the atomic number is eight, which tells that an oxygen atom has eight protons in its nucleus. Oxygen is a gas at room temperature and colourless, no smell or no taste. Oxygen is found naturally as a molecule.

Note: Firstly the mass and molar mass should be noted down for further calculations, then number of moles should be calculated using them and then number of oxygen atoms should be calculated using all the steps.