Question

a gas made up of atoms escapes through a pinhole 1.40 times as fast as ar 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 Ar (argon) be gas 2 (\( r_2 \)). Given \( \frac{r_1}{r_2} = 1.40 \), and \( M_{Ar}=39.95\space g/mol \).

Step2: Solve for \( M_1 \)

Substitute the values into Graham's Law: \( 1.40=\sqrt{\frac{39.95}{M_1}} \). Square both sides: \( 1.40^2=\frac{39.95}{M_1} \), so \( M_1=\frac{39.95}{1.40^2} \). Calculate \( 1.40^2 = 1.96 \), then \( M_1=\frac{39.95}{1.96}\approx20.4\space g/mol \).

Step3: Identify the gas

Looking at the molar masses of noble - gas atoms (since the gas is made up of atoms), Ne (neon) has a molar mass \( M_{Ne} = 20.18\space g/mol\approx20.4\space g/mol \) (considering rounding in the calculation).

Answer:

\(\text{Ne}\)