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

`V_2= 38.9mL`

Step-by-step 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:

`(P_2V_2)/(T_2)= (P_1V_1)/(T_1)`

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

`V_2= (P_1V_1T_2)/(T_1P_2)`

Now, we plug in the data to obtain:

`V_2= (1.30atm*46.0mL*(2.09+273)K)/((5+273)K*1.52atm)\\\\V_2= 38.9mL`

Best regards!