Question

What is the mass of carbon dioxide which contains the same number of molecules as are contained in $40\mathrm{g}$ of oxygen?

• A. $40\mathrm{g}$
• B. $55\mathrm{g}$
• C. $32\mathrm{g}$
• D. $44\mathrm{g}$

Answer 1

The correct option is B

$55\mathrm{g}$

Explanation for the correct option

$\mathbf{\left(}\mathbf{B}\mathbf{\right)}\mathbf{}\mathbf{55}\mathbf{}\mathbf{g}$

Step 1: Given,

• $\mathrm{Mass}\mathrm{of}\mathrm{oxygen}\left({\mathrm{O}}_2\right)=40\mathrm{g}$

Step 2: To determine the molar mass of ${\mathbf{O}}_{\mathbf{2}}$ and ${\mathbf{CO}}_{\mathbf{2}}$.

• $\begin{array}{rcl}\mathrm{Molar}\mathrm{mass}\mathrm{of}{\mathrm{O}}_2& =& 2\times \mathrm{Atomic}\mathrm{mass}\mathrm{of}\mathrm{oxygen}\\ & =& 2\times 16\mathrm{g}{\mathrm{mol}}^{-1}\\ & =& 32\mathrm{g}{\mathrm{mol}}^{-1}\end{array}$
• $\begin{array}{rcl}\mathrm{Molar}\mathrm{mass}\mathrm{of}{\mathrm{CO}}_2& =& \mathrm{Atomic}\mathrm{mass}\mathrm{of}\mathrm{carbon}+(2\times \mathrm{Atomic}\mathrm{mass}\mathrm{of}\mathrm{oxygen})\\ & =& 12+(2\times 16)\\ & =& 44\mathrm{g}{\mathrm{mol}}^{-1}\end{array}$

Step 3: To determine the number of molecules of ${\mathbf{O}}_{\mathbf{2}}$.

• $1\mathrm{mole}$ of a substance contains $6.022\times {10}^{23}$ molecules.
• As of ${\mathrm{O}}_2$ contains the number of molecules $=6.022\times {10}^{23}$
• So, $40\mathrm{g}$ of ${\mathrm{O}}_2$ contains number of molecules $=\frac{40\mathrm{g}}{32\mathrm{g}}\times 6.022\times {10}^{23}=7.5275\times {10}^{23}$

Step 4: To determine the mass of carbon dioxide ${\mathbf{CO}}_{\mathbf{2}}$.

• As, the mass of $6.022\times {10}^{23}$ molecules of ${\mathrm{CO}}_2=44\mathrm{g}$
• So, the mass of $7.5275\times {10}^{23}$ molecules of carbon dioxide is as follows:

$\begin{array}{rcl}\mathrm{Mass}& =& \frac{7.5275\times {10}^{23}}{6.022\times {10}^{23}}\times 44\mathrm{g}\\ & =& 55\mathrm{g}\end{array}$

Explanation for incorrect options:

• The mass of Carbon dioxide is $55\mathrm{g}$.
• Hence, all the other options $\mathbf{\left(}\mathbf{A}\mathbf{\right)}\mathbf{,}\mathbf{}\mathbf{\left(}\mathbf{C}\mathbf{\right)}$ and $\mathbf{\left(}\mathbf{D}\mathbf{\right)}$ are incorrect.

Therefore, the correct option is $\mathbf{\left(}\mathbf{B}\mathbf{\right)}\mathbf{}\mathbf{55}\mathbf{}\mathbf{g}$.