Which of the following sample(s) must have an average molar mass greater than that of a mixture of ${\mathrm{N}}_2$ and ${\mathrm{CO}}_2$?

The correct option is D

Mixture of ${\mathrm{CH}}_4$ and ${\mathrm{SO}}_3$

The explanation for the correct options:

(D) Mixture of ${\mathrm{CH}}_4$ and ${\mathrm{SO}}_3$

Step 1: Molar mass of ${\mathrm{CH}}_4$

• Atomic mass of Carbon ($\mathrm{C}$) $=$ $12$
• Atomic mass of Hydrogen ($\mathrm{H}$) $=$ $1$
• Molar mass of Methane (${\mathrm{CH}}_4$) $=$ $12+(4\times 1)$

$=$$16$

Step 2: Molar mass of ${\mathrm{SO}}_3$

• Atomic mass of Sulphur ($\mathrm{S}$) $=$ $32$
• Atomic mass of Oxygen ($\mathrm{O}$) $=$$16$
• Molar mass of Sulphur Trioxide (${\mathrm{SO}}_3$) $=$ $32+(3\times 16)$

$=$ $80$

Step 3: Molar mass of the mixture of ${\mathrm{CH}}_4$ and ${\mathrm{SO}}_3$

• Molar mass of the mixture $=$$16+80$

$=$ $96$

• Therefore, the molar mass of the mixture of ${\mathrm{CH}}_4$ and ${\mathrm{SO}}_3$is $96$ which is greater than that of a mixture of ${\mathrm{N}}_2$ and ${\mathrm{CO}}_2$ which is $58$.

(C) Mixture of ${\mathrm{SO}}_2$ and ${\mathrm{SO}}_3$

Step 1: Molar mass of ${\mathrm{SO}}_2$

• Atomic mass of Sulphur ($\mathrm{S}$) $=$ $32$
• Atomic mass of Oxygen ($\mathrm{O}$) $=$$16$
• Molar mass of Sulphur dioxide (${\mathrm{SO}}_2$) $=32+(2\times 16)$

$=64$

Step 2: Molar mass of ${\mathrm{SO}}_3$

• Atomic mass of Sulphur ($\mathrm{S}$) $=$ $32$
• Atomic mass of Oxygen ($\mathrm{O}$) $=$$16$
• Molar mass of Sulphur Trioxide (${\mathrm{SO}}_3$) $=$ $32+(3\times 16)$

$=$ $80$

Step 3: Molar mass of the mixture of ${\mathrm{SO}}_2$ and ${\mathrm{SO}}_3$

• Molar mass mixture of ${\mathrm{SO}}_2$ and ${\mathrm{SO}}_3$ $=64+80$

$=144$

• Therefore, the molar mass of the mixture of ${\mathrm{SO}}_2$ and ${\mathrm{SO}}_3$is $144$ which is greater than that of a mixture of ${\mathrm{N}}_2$ and ${\mathrm{CO}}_2$ which is $58$

The explanation for the incorrect option:

(A) Pure ${\mathrm{O}}_3$

• Molar mass of pure ${\mathrm{O}}_3$ $=$ $3\times 16$

$=$ $48$

• It is an incorrect option because the molar mass of pure ${\mathrm{O}}_3$ is $48$ which is less than that of a mixture of ${\mathrm{N}}_2$ and ${\mathrm{CO}}_2$ which is $58$.

(B) Pure $\mathrm{Ne}$

• Molar mass of $\mathrm{Ne}$ $=20$
• It is an incorrect option because molar mass of pure $\mathrm{Ne}$ is $20$ which is less than that of a mixture of ${\mathrm{N}}_2$ and ${\mathrm{CO}}_2$ which is $58$.

Hence the correct options are (D) Mixture of ${\mathrm{CH}}_4$ and ${\mathrm{SO}}_3$ and (C) Mixture of ${\mathrm{SO}}_2$ and ${\mathrm{SO}}_3$.