Question

A small bubble rises from the bottom of a lake where the temperature and pressure are 4.0 C and 3.0 atm, to the water’s surface, where the temperature is 25 C and the pressure is 0.95 atm. Calculate the final volume of the bubble if the initial volume was 2.1 mL.

Answer 1

Answer:

The final volume of the bubble is 7.13 mL.

Explanation:

The combined gas equation is,

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

where,

$P_1$ = initial pressure of gas = 3 atm

$P_2$ = final pressure of gas = 0.95 atm

$V_1$ = initial volume of gas = $2.1 mL=0.0021 L$

$V_2$ = final volume of gas = ?

$T_1$ = initial temperature of gas = $4^oC=273.15+4K=277.15 K$

$T_2$ = final temperature of gas = $25^oC=273.15+25 k=298 .15 K$

Now put all the given values in the above equation, we get:

$\frac{3 atm\times 0.0021 L}{277.15 K}=\frac{0.95 atm\times V_2}{298.15 K}$

$V_2=\frac{3 atm\times 0.0021 L\times 298.15 K}{277.15 K\times 0.95 atm}=0.00713 L = 7.13 mL$

The final volume of the bubble is 7.13 mL.