s. What is the molar mass of the unknown gas? What is it? 3. What is the ratio o...

Questions

October 2022 1 3 Report

Solve and show your solution of the following problems on a separate sheet of paper. 1. On the average, CO2 travels at 410 m/s at 25⁰C. Find the average rate of Cl2 at 25⁰C. 2. At a certain temperature fluorine gas travels at 585 m/s and a noble gas travels at 394 m/s. What is the molar mass of the unknown gas? What is it? 3. What is the ratio of the rate of effusion of helium and neon?

Answers & Comments

GreatRedSpot

1. SOLUTION:

Step 1: List the given values.

$\begin{aligned} & r_{\text{CO}_2} = \text{410 m/s} \\ & MM_{\text{CO}_2} = \text{44.01 g/mol} \\ & MM_{\text{Cl}_2} = \text{70.90 g/mol} \end{aligned}$

Step 2: Use Graham's law of diffusion/effusion to calculate the rate of effusion of a gas.

$\begin{aligned} \frac{r_{\text{Cl}_2}}{r_{\text{CO}_2}} & = \sqrt{\frac{MM_{\text{CO}_2}}{MM_{\text{Cl}_2}}} \\ \frac{r_{\text{Cl}_2}}{\text{410 m/s}} & = \sqrt{\frac{\text{44.01 g/mol}}{\text{70.90 g/mol}}} \\ \frac{r_{\text{Cl}_2}}{\text{410 m/s}} & = 0.787866 \\ r_{\text{Cl}_2} & = \text{(410 m/s)(0.787866)} \\ & = \boxed{\text{323 m/s}} \end{aligned}$

Hence, the average rate of Cl₂ at 25°C is 323 m/s.

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2. SOLUTION:

Step 1: List the given values.

$\begin{aligned} & r_{\text{F}_2} = \text{585 m/s} \\ & r_{\text{noble gas}} = \text{394 m/s} \\ & MM_{\text{F}_2} = \text{38.0 g/mol} \end{aligned}$

Step 2: Use Graham's law of diffusion/effusion to calculate the molar mass of a gas.

$\begin{aligned} \sqrt{\frac{MM_{\text{noble gas}}}{MM_{\text{F}_2}}} & = \frac{r_{\text{F}_2}}{r_{\text{noble gas}}} \\ \sqrt{\frac{MM_{\text{noble gas}}}{\text{38.0 g/mol}}} & = \frac{\text{585 m/s}}{\text{394 m/s}} \\ \frac{MM_{\text{noble gas}}}{\text{38.0 g/mol}} & = \left(\frac{\text{585 m/s}}{\text{394 m/s}}\right)^2 \\ MM_{\text{noble gas}} & = (\text{38.0 g/mol})\left(\frac{\text{585 m/s}}{\text{394 m/s}}\right)^2 \\ & = \boxed{\text{83.8 g/mol}} \\ & \boxed{\text{The unknown noble gas is krypton.}} \end{aligned}$

Hence, the molar mass of the unknown gas is 83.8 g/mol. The unknown noble gas is krypton.

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3. SOLUTION:

Step 1: List the given values.

$\begin{aligned} & MM_{\text{He}} = \text{4.003 g/mol} \\ & MM_{\text{Ne}} = \text{20.18 g/mol} \end{aligned}$

Step 2: Use Graham's law of diffusion/effusion to calculate the ratio of the rates of effusion of the two gases.

$\begin{aligned} \frac{r_{\text{He}}}{r_{\text{Ne}}} & = \sqrt{\frac{MM_{\text{Ne}}}{MM_{\text{He}}}} \\ \frac{r_{\text{He}}}{r_{\text{Ne}}} & = \sqrt{\frac{\text{20.18 g/mol}}{\text{4.003 g/mol}}} \\ & = \boxed{2.25} \end{aligned}$