Answer :
ANSWER
The final volume of the balloon is 12.67L
EXPLANATION
Given that;
The initial volume of the ballon is 12dm^3
The initial temperature at STP is 273.15 degrees Celcius
The initial pressure at STP is 760 mmHg
The final temperature is 0 degrees Celcius
The final volume is 720 mmHg
Follow the steps below to find the new volume of the balloon
Step1; Write the general gas law equation
[tex]\text{ }\frac{\text{ P1 V1}}{\text{ T1}}=\text{ }\frac{\text{ P2V2}}{\text{ T2}}[/tex]Step 2; Convert the volume and temperature to liters and degrees Kelvin
[tex]\begin{gathered} \text{ 1dm}^3\text{ }=\text{ 1L} \\ \text{ Hence, 12dm}^3\text{ is equivalent to 12L} \\ \\ \text{ The final temperature is 0}\degree C \\ \text{ T = t + 273.15} \\ \text{ T = 0 + 273.15} \\ \text{ T = 273.15K} \end{gathered}[/tex]Step 3; Substitute the given data into the formula above to find the final volume
[tex]\begin{gathered} \text{ }\frac{\text{ P1V1}}{\text{ T1}}\text{ }=\text{ }\frac{\text{ P2 V2}}{\text{ T2}} \\ \\ \text{ }\frac{760\times\text{ 12}}{273.15}\text{ }=\frac{720\times V2}{273.15} \\ \text{ Cross multiply} \\ \text{ 760 }\times\text{ 12 }\times\text{ 273.15 }=\text{ 720 }\times\text{ V2 }\times\text{ 273.15} \\ \text{ Isolate V2} \\ \text{ V2 }=\text{ }\frac{760\text{ }\times\text{ 12}\times\text{ 273.15}}{720\text{ }\times\text{ 273.15}} \\ \text{ } \\ \text{ V2}=\frac{760\times12\times\cancel{273.15}}{720\times\cancel{273.15}} \\ \text{ } \\ \text{ V2 }=\text{ }\frac{9120}{720} \\ \text{ V2 = 12.67L} \end{gathered}[/tex]Hence, the final volume of the balloon is 12.67L
