Question

1. Choose the correct answer from the options given below.

(i) The ratio between the number of molecules in $2\mathrm{g}$ of hydrogen and $32\mathrm{g}$ of oxygen is: [Given that $\mathrm{H}=1,\mathrm{O}=16$]

• A. $1:2$
• B. $1:0.01$
• C. $1:1$
• D. $0.01:1$

Answer 1

The correct option is C

$1:1$

Explanation for the correct option

(C) $1:1$

Mole

• It is defined as the amount of substance that constitutes the same number of elementary particles, such as ions, atoms, or molecules as the total number of atoms present in $12\mathrm{g}$ of Carbon-12 $\left({\mathrm{C}}^{12}\right)$.
• The expression for the calculation of the mole is as follows

$\mathrm{Mole}=\frac{\mathrm{Mass}\mathrm{of}\mathrm{the}\mathrm{substance}\mathrm{in}\mathrm{grams}}{\mathrm{Molecular}\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{substance}}$

• One mole of any chemical species contains $6.022\times {10}^{23}$ particles.
• On a macroscopic scale, the terminology of the mole allows putting quantitative data about what occurs in a chemical equation.

Calculation of number of molecules in $2\mathrm{g}$ of hydrogen

• The molecular mass of hydrogen $\left({\mathrm{H}}_2\right)$ is $2\mathrm{g}$.
• The number of moles of hydrogen is calculated as follows

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{moles}=\frac{\mathrm{Mass}\mathrm{of}\mathrm{hydrogen}}{\mathrm{Molecular}\mathrm{mass}\mathrm{of}\mathrm{hydrogen}\left({\mathrm{H}}_2\right)} \\ =\frac{2}{2} \\ =1\mathrm{mole} \end{gathered}$$

• 1 mole of hydrogen $\left({\mathrm{H}}_2\right)$ contains $6.022\times {10}^{23}$ molecules.

Calculation of number of molecules in $32\mathrm{g}$ of oxygen

• The molecular mass of oxygen $\left({\mathrm{O}}_2\right)$ is $32\mathrm{g}$.
• The number of moles of oxygen is calculated as follows

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{moles}=\frac{\mathrm{Mass}\mathrm{of}\mathrm{Oxygen}}{\mathrm{Molecular}\mathrm{mass}\mathrm{of}\mathrm{Oxygen}\left({\mathrm{O}}_2\right)} \\ =\frac{32}{32} \\ =1\mathrm{mole} \end{gathered}$$

• 1 mole of oxygen $\left({\mathrm{O}}_2\right)$ contains $6.022\times {10}^{23}$ molecules.

Calculation of ratio between the number of molecules in $2\mathrm{g}$ of hydrogen and $32\mathrm{g}$ of oxygen

• The ratio is calculated as follows

$$\begin{gathered} \mathrm{Ratio}=\left(\mathrm{Number}\mathrm{of}\mathrm{molecules}\mathrm{in}2\mathrm{g}\mathrm{of}\mathrm{hydrogen}\right):\left(\mathrm{Number}\mathrm{of}\mathrm{molecules}\mathrm{in}32\mathrm{g}\mathrm{of}\mathrm{oxygen}\right) \\ =6.022\times {10}^{23}:6.022\times {10}^{23} \\ =1:1 \end{gathered}$$

Explanation for incorrect options

The ratio calculated is not $1:2$, $1:0.01$, and $0.01:1$. Therefore, options (A), (B), and (D) are incorrect.

Hence, the correct option is (C) $1:1$. The ratio between the number of molecules in $2\mathrm{g}$ of hydrogen and $32\mathrm{g}$ of oxygen is $1:1$.