Answer
\[\underline{18.2\text{ atm}}\]
Work Step by Step
The area of the face mask is \[125\text{ c}{{\text{m}}^{2}}\].
\[1\text{ c}{{\text{m}}^{2}}={{10}^{-4}}\text{ }{{\text{m}}^{2}}\]
Thus, the area of the face mask in meters is \[125\times {{10}^{-4}}\text{ }{{\text{m}}^{2}}\].
The relation between pressure and force is as follows:
\[P=\frac{F}{A}\]
Here, P is pressure, F is force applied, and A is area.
Thus, pressure is calculated as follows:
\[\begin{align}
& P=\frac{2.31\times {{10}^{4}}\text{ N}}{125\times {{10}^{-4}}\text{ }{{\text{m}}^{2}}} \\
& =1.85\times {{10}^{6}}\text{ N/}{{\text{m}}^{2}}
\end{align}\]
Now,
\[1\text{ Pa}=1\text{ N/}{{\text{m}}^{2}}\]
and
\[1\text{ atm}=101,325\text{ Pa}\]
So,
\[\begin{align}
& P=\left( 1.85\times {{10}^{6}}\text{ N/}{{\text{m}}^{2}} \right)\left( \frac{1\text{ atm}}{101325\text{ N/}{{\text{m}}^{2}}} \right) \\
& =18.2\text{ atm}
\end{align}\]
The pressure on the face mask is \[\underline{18.2\text{ atm}}\].
