Question

a gas made up of homonuclear diatomic molecules escapes through a pinhole 1.62 times as fast as kr gas. write the chemical formula of the gas.

Explanation:

Step1: Apply Graham's Law of Effusion

Graham's Law is \( \frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}} \), where \( r \) is the rate of effusion and \( M \) is the molar mass. Let the unknown gas be gas 1 (\( r_1 \)) and Kr be gas 2 (\( r_2 \)). Given \( \frac{r_1}{r_2} = 1.62 \), and \( M_{Kr}=83.8\space g/mol \).
Substitute into the formula: \( 1.62=\sqrt{\frac{83.8}{M_1}} \).

Step2: Square both sides of the equation

Squaring both sides gives \( (1.62)^2=\frac{83.8}{M_1} \).
So, \( M_1=\frac{83.8}{(1.62)^2} \).
Calculate \( (1.62)^2 = 2.6244 \). Then \( M_1=\frac{83.8}{2.6244}\approx32.0\space g/mol \).

Step3: Determine the gas

Since it is a homonuclear diatomic molecule. The molar mass of \( O_2 \) is \( 2\times16.0 = 32.0\space g/mol \).

Answer:

\( O_2 \)