Question

Calculate:
(1) The number of moles in 12g of oxygen gas.
(2) The weight of ${10}^{22}$atoms of carbon. [C = 12, Avagadro’s No. = $6\times {10}^{23}$]
(3) Molecular formula of a compound is $C_6{H}_{18}{O}_3$. Find its empirical formula.

Answer 1

Hint: (1) The concept mole is a convenient way of expressing the amount of any substance, and like any measurement, a mole can also be broken into two parts- the numerical magnitude and unit as ‘mol’.
(2) One mole of any molecule or element is equal to the molecular or molar weight of that compound. To be more precise, one mole of any elementary entity will have $6.022\times {10}^{23}$ atoms or molecules or ions.
(3) The chemical formula which shows the simplest ratio of atoms of each element. The empirical formula gives the formula in which the atoms in a compound are present in the lowest whole number ratio.

Complete step by step solution:
-A mole is defined as the amount of a substance that contains exactly $6.02214076\times {10}^{23}$ elementary entities such as atoms, molecules, monatomic/polyatomic ions, and other particles in a given substance.
-The word mole was introduced by the German chemist Wilhelm Ostwald in the year 1896 who derived the term from a Latin word meaning a ‘heap’ or ‘pile’.
-(1) The number of moles of a substance in a given pure sample can be calculated using the formula-
Number of moles $={\displaystyle \frac{\text{Given mass (n)}}{\text{Molar mass(M)}}}$
Given mass = 12g
The molecular weight of oxygen $(O_2)=16\times 2=32g$
From the formula of calculating moles,
Number of moles $={\displaystyle \frac{12}{32}}=0.375mole$
Alternatively, we can also use the unitary method
We know that 32g of oxygen gas = 1 mole
Therefore, 12g of oxygen gas will have $={\displaystyle \frac{1}{32}}\times 12=0.375moles$
Hence, 12 g of oxygen will have 0.375 moles.
(2) We know that from the above knowledge that,
$6.022\times {10}^{23}$ atoms of carbon weigh = 12 gm
Therefore, ${10}^{22}$ atoms will weigh $={\displaystyle \frac{12\times {10}^{22}}{6.022\times {10}^{23}}}=2\times {10}^{-1}=0.2g$
Hence, ${10}^{22}$atoms of carbon will weigh 0.2 grams.
(3) Molecular formula of the compound = $C_6{H}_{18}{O}_3$
Molecular formula $={(\text{Empirical formula)}}_n$ where n is the common multiple.
Take the common multiple from the molecular formula $={(C_2{H}_{6}O)}_3$
Therefore, the empirical formula $C_2{H}_{6}O$.

Note: You must remember without confusion some relatable formula related to the mole concept which is given below-
(i) The number of moles in a given sample of an element/compound can be calculated by the formula-
Number of moles $={\displaystyle \frac{\text{Given mass}}{\text{Molar mass}}}$
(ii) The total number of atoms/molecules in a sample can be calculated by the formula-
Number of atoms or molecules $=\text{Number of moles}\times (6.022\times {10}^{23})$
(iii) The relationship between the atomic mass unit (amu) and the gram is given as-
1 amu = ${\displaystyle \frac{1\text{ gram}}{6.022\times {10}^{23}}}=1.66\times {10}^{-24}grams$