Question

The ratio of active masses of $22\mathrm{g}$ of ${\mathrm{CO}}_2$, $3\mathrm{g}$ of ${\mathrm{H}}_2$ and $7\mathrm{g}$ of ${\mathrm{N}}_2$ in a gaseous mixture:

• A. $22:3:7$
• B. $0.5:3:7$
• C. $1:3:1$
• D. $1:3:0.5$

Answer 1

The correct option is D

$1:3:0.5$

Explanation for correct option:

(D) $1:3:0.5$

Step 1: Given information:

• Active masses of ${\mathrm{CO}}_2$ is $22\mathrm{g}$, ${\mathrm{H}}_2$ is $3\mathrm{g}$and ${\mathrm{N}}_2$ is $7\mathrm{g}$.

Step 2: Calculation for the mole for ${\mathbf{CO}}_{\mathbf{2}}\mathbf{,}{\mathbf{H}}_{\mathbf{2}}\mathbf{,}{\mathbf{N}}_{\mathbf{2}}$:

• Mole is defined as the ratio of given mass over molar mass.
• It can be expressed as:

$\mathrm{Mole}=\frac{\mathrm{Mass}}{\mathrm{Molar}\mathrm{Mass}}$

a) $22\mathrm{g}$ of ${\mathrm{CO}}_2$

Molar mass of ${\mathrm{CO}}_2$is $44\mathrm{g}{\mathrm{mol}}^{-1}$.

$\mathrm{Mole}=\frac{22\mathrm{g}}{44\mathrm{g}{\mathrm{mol}}^{-1}}$

Moles of ${\mathrm{CO}}_2$ is $0.5\mathrm{mol}$.

b) $3\mathrm{g}$ of ${\mathrm{H}}_2$

Molar mass of ${\mathrm{H}}_2$is $2.016\mathrm{g}{\mathrm{mol}}^{-1}$.

$\mathrm{Mole}=\frac{3\mathrm{g}}{2.016\mathrm{g}{\mathrm{mol}}^{-1}}$

Moles of ${\mathrm{H}}_2$is $1.5\mathrm{mol}$.

c) $7\mathrm{g}$ of ${\mathrm{N}}_2$

Molar mass of ${\mathrm{N}}_2$is $28\mathrm{g}{\mathrm{mol}}^{-1}$.

$\mathrm{Mole}=\frac{7\mathrm{g}}{28\mathrm{g}{\mathrm{mol}}^{-1}}$

Moles of ${\mathrm{N}}_2$ is $0.25\mathrm{mol}$.

Step 3: Calculation for the total moles:

• The total number of moles is the sum of each mole.
• $\mathrm{Total}\mathrm{moles}=0.5+1.5+0.25=2.25\mathrm{mol}$

Step 4: Calculation of the ratio:

The ratio of active masses of ${\mathrm{CO}}_2,{\mathrm{H}}_2,{\mathrm{N}}_2$ $$\begin{gathered} =\frac{0.5}{{\mathrm{V}}_{\mathrm{s}}}:\frac{1.5}{{\mathrm{V}}_{\mathrm{s}}}:\frac{0.25}{{\mathrm{V}}_{\mathrm{s}}} \\ =1:3:0.5 \end{gathered}$$

Therefore, the ratio of active masses of ${\mathrm{CO}}_2$ is $22\mathrm{g}$, ${\mathrm{H}}_2$ is $3\mathrm{g}$and ${\mathrm{N}}_2$ is $7\mathrm{g}$ in a gaseous mixture is $1:3:0.5$.

Explanation for incorrect options:

The ratio of active masses of ${\mathrm{CO}}_2$ is $22\mathrm{g}$, ${\mathrm{H}}_2$ is $3\mathrm{g}$and ${\mathrm{N}}_2$ is $7\mathrm{g}$ in a gaseous mixture is $1:3:0.5$. Thus, options A, B, and C are incorrect.

Hence, the correct option is D is $1:3:0.5$.