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

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BogoKoYawaNgaNN @BogoKoYawaNgaNN

August 2022 1 3 Report

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?

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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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