Question

There are $6.022 \times {10^{22}}$ moles each of ${N_2}$, ${O_2}$ , and ${H_2}$ which mixed together at $760mm$ and $273K$. The mass of total mixture in grams.
A.$6.2gm$
B.$4.12gm$
C.$3.09gm$
D.$7gm$

Answer 1

The atomic number of Nitrogen is 7 and that of Oxygen is 8. The atomic mass of nitrogen is 14 and that of oxygen is 16. The atomic mass is the sum of protons and neutrons in a molecule. For nitrogen (${N_2}$), the atomic mass is $2 \times 14 = 28$. The atomic mass of Oxygen can be calculated $16 + 16 = 32$. To find the masses of a mixture of gases, the moles and molecular mass of gases is to be known. Avogadro’s number for an element is the number of atoms present in one mole of the element. Now, one mole of an element is equal to the atomic mass of the element. So, the number of atoms in one mole of an element (for hydrogen, $1mol = 2g$) is always equal to Avogadro’s number. 1 Mole of each gas will contain $6.022 \times {10^{23}}$ molecules.

Complete step by step answer:
We have $6.022 \times {10^{22}}$ molecules of each gas. (N)
So the number of moles of each can be calculated as $\dfrac{N}{{{N_A}}}$ where ${N_A}$ is the Avogadro Number.
We are given a combined number of moles of all three gases. We know that 1 Mole of each gas will contain $6.022 \times {10^{23}}$ molecules.
So, to find the mole of each gas, divide the given moles by the Avogadro number.
So the number of moles of each gas is $\dfrac{{6.022 \times {{10}^{22}}}}{{6.022 \times {{10}^{23}}}} = 0.1mol$ of each gas is present in the mixture.
Now by using the molar formula we can calculate the mass of each gas one by one by multiplying the number of moles of that gas by the molecular mass of that gas
To calculate the mass of oxygen multiplies the number of moles by the molar mass of nitrogen.
The molar mass of ${N_2} = 28g/mol$
Mass of $0.1mol{N_2} = 0.1 \times 28 = 2.8g$
To calculate the mass of oxygen multiplies the number of moles with the molar mass of oxygen.
Molar mass of ${O_2} = 32g/mol$
Mass of $0.1mol{O_2} = 0.1 \times 32 = 3.2g$
To calculate the mass of oxygen multiplies the number of moles by the molar mass of hydrogen.
Molar mass of ${H_2} = 2g/mol$
Mass of $0.1mol{H_2} = 0.1 \times 2 = 0.2g$
Now add all the masses
$\text{Total Mass} = 2.8 + 3.2 + 0.2 = 6.2g$
Thus, the total mass obtained is 6.2g
Hence, Choice A is correct.

Note:
When dealing with moles and masses of gas, the pressure and temperature conditions are not necessary to be taken into consideration. Avogadro number is denoted as ${N_A}$. The unit of moles in $g/mol$ as molar masses are also in gram.