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