Question

An unopened, cold 2.00 L bottle of soda contains 46.0 mL of gas confined at a pressure of 1.30 atm at a temperature of 5.0 ℃. If the bottle is dropped into a lake and sinks to a depth at which the pressure is 1.52 atm and the temperature is 2.09 ℃, what will be the volume of the gas in the bottle? Explanation needed

Answer 1

Answer:

$V_2= 38.9mL$

Explanation:

Hello there!

In this case, since this is a problem about the combined gas law because the temperature, volume and pressure undergo a change:

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

Thus, since we need the final volume, V2, we solve for it as shown below:

$V_2= \frac{P_1V_1T_2}{T_1P_2}$

Now, we plug in the data to obtain:

$V_2= \frac{1.30atm*46.0mL*(2.09+273)K}{(5+273)K*1.52atm}\\\\V_2= 38.9mL$

Best regards!