Question

A small bubble rises from the bottom of a lake, where the temperature and the pressure are $8{}^{\circ }\text{C}$ and $6.0atm$ respectively, to the water's surface, where the temperature is $25{}^{\circ }\text{C}$ and the pressure is $1.0atm$. Calculate the final volume of the bubble if its initial volume was $2mL$.

• A. $14\text{mL}$
• B. $12.72\text{mL}$
• C. $11.31\text{mL}$
• D. $15\text{mL}$

Answer 1

The correct option is B $12.72\text{mL}$

We know, $PV=nRT$

At the bottom of the lake,
$P_1{V}_1=n_{1}R{T}_1$ ... (1)

At the surface of the lake,
$P_2{V}_2=n_{2}R{T}_2$ ... (2)

The moles of gas in the bubble remains constant, so $n_1=n_2$.
Dividing (1) and (2) we get,
$\frac{P_1{V}_1}{P_2{V}_2}=\frac{T_1}{T_2}$

$\Rightarrow V_2=V_1\times \frac{P_1}{P_2}\times \frac{T_2}{T_1}$
$=2.0\text{mL}\times \frac{6.0\text{atm}}{1.0\text{atm}}\times \frac{298\text{K}}{281\text{K}}$
$=12.72\text{mL}$