Problem

A 350-mL spherical flask contains 0.075 mol of an ideal gas at a temperature of 293 K. Wha...

A 350-mL spherical flask contains 0.075 mol of an ideal gas at a temperature of 293 K. What is the average force exerted on the walls of the flask by a single molecule?

Step-by-Step Solution

Solution 1
The average force exerted on the wall by a single molecule is given by $$ \begin{aligned} F_{\text {avg }} &=\left(\frac{p}{n}\right) A \\ &=\frac{n k_{B} T}{n V} A \\ &=\frac{k_{B} T}{V} A \\ &=\left(\frac{k_{B} T}{V}\right)\left(4 \pi r^{2}\right) \\ &=\left(\frac{k_{B} T}{V}\right)(4 \pi)\left(\frac{3}{4} \frac{V}{\pi}\right)^{2 / 3} \\ &=k_{B} T\left(\frac{36 \pi}{V}\right)^{1 / 3} \\ &=\left(1.381 \times 10^{-23} \mathrm{~J} / \mathrm{K}\right)(293 \mathrm{~K})\left(\frac{36 \pi}{350 \times 10^{-6} \mathrm{~m}^{3}}\right)^{1 / 3} \\ &=2.777 \times 10^{-19} \mathrm{~N} \\ &=2.78 \times 10^{-19} \mathrm{~N} \end{aligned} $$
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