Your spaceship has docked at a space station above Mars. The temperature inside the space station is a carefully controlled 26 ∘C at a pressure of 755 mmHg . A balloon with a volume of 455 mL drifts into the airlock where the temperature is -87 ∘C and the pressure is 0.115 atm . What is the final volume, in milliliters, of the balloon if n remains constant and the balloon is very elastic?

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davidlcastiblanco davidlcastiblanco · Answer 1 · 2019-11-19T15:29:59+01:00

Answer:

[tex]V_2=32.7mL[/tex]

Explanation:

Given

[tex]T_1=26+273=299K[/tex], [tex]T_2=-87+273=186K[/tex]

[tex]P_1=0.115atm*\frac{760mmHg}{1atm}=87.4 mmHg[/tex],[tex]P_2=755mmHg[/tex]

[tex]V_1=455mL[/tex]

Using the Law of gases to solve the final volume in milliliters

[tex]\frac{P_1*V_1}{T_1}= \frac{P_2*V_2}{T_2}[/tex]

Solve to V2

[tex]V_2=\frac{T_2*P_1*V_1}{T_1*P_2}[/tex]

[tex]V_2=\frac{186K*87.4mmHg*455mL}{299K*755mmHg}[/tex]

[tex]V_2=32.7mL[/tex]