Answer to Question #142820 in General Chemistry for Dave

Question

Calculate how much bigger a 2.5mL fish lung will get if it’s brought up from 2000m deep where the pressure is 200 atm. Pressure at the surface is 1 atm.

Answer 1

$\begin{aligned} V_1(\textsf{ Volume of fish lung 2000m deep}) = 2.5mL\\ \end{aligned}$ $\begin{aligned} P_1 &= 200atm \end{aligned}$

$\begin{aligned} V_2(\textsf{ Volume of fish lung at surface} = ? \end{aligned}$ $P_2 = 1atm$

From Boyle's Law,

$P_1V_1 = P_2V_2\\ 200× 2.5 = 1 × V_2\\ V_2 = 500mL$

$\begin{aligned} \triangle V &= V_2-V_1 = 500mL -2.5mL \\ &= 475.5mL \end{aligned}$

$\therefore$ The fish lung will get 475.5mL bigger if it is brought up to the surface from 2000m deep underground.