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

The final volume of the bubble is 7.13 mL.

Step-by-step explanation:

The combined gas equation is,

`(P_1V_1)/(T_1)=(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:

`(3 atm* 0.0021 L)/(277.15 K)=(0.95 atm* V_2)/(298.15 K)`

`V_2=(3 atm* 0.0021 L* 298.15 K)/(277.15 K* 0.95 atm)=0.00713 L = 7.13 mL`

The final volume of the bubble is 7.13 mL.