Question

How many moles of compound are there in 4.5 kg $Ca{{(OH)}_{2}}$?

Answer 1

Hint: Find out the molar mass of the compound, and then use the formula $no\,of\,mole=\dfrac{given\,mass}{molar\,mass}$; remember to convert kilograms into grams.

Complete answer:
In order to answer the question, we need to know about moles and molar mass. Now, matter is made up of atoms, and as matter has mass, then the atoms should have an individual mass. Molar mass of an element or compound is the mass which houses $6\times {{10}^{23}}$ particles. For, example, the hydrogen molecule has a molar mass of 2 grams. This means 2 grams of hydrogen contains $6\times {{10}^{23}}$atoms, and this number is also called the Avogadro’s number.
Number of moles of an element or a compound is the ratio of its given mass taken by the user, to its molar mass. More is the number of moles, more is the concentration of the substance. Now, let us come to the question. First, we convert 4.5 kilograms to grams which comes out to be 4500 grams.
Now, 1 mole of $Ca{{(OH)}_{2}}$ contains $6\times {{10}^{23}}$ molecules.
And the molar mass of $Ca{{(OH)}_{2}}$ is 74 grams. In order to find out the number of moles of calcium hydroxide, we divide the given mass with the molar mass, as the number of moles of a compound is given by $n=\dfrac{given\,mass}{molar\,mass}$. On calculating, we get:
\[mol{{e}_{Ca{{(OH)}_{2}}}}=4500\times \dfrac{1\,mol\,Ca{{(OH)}_{2}}}{74g\,Ca{{(OH)}_{2}}}=61\,mol\]
So, 4.5kg $Ca{{(OH)}_{2}}$ contains 61 mol of the compound.

Note:
It is to be noted that in case of a molecule, to find out the molar mass, the masses of individual elements are added up. For example, ${{H}_{2}}O$ molar mass is $(2\times 1)+16$ which comes out as 18 grams.