We can solve the problem by using the ideal gas law, which states:
[tex]pV=nRT[/tex]
where
p is the gas pressure
V is the volume
n is the number of moles
R is the gas constant
T is the absolute temperature
The initial conditions of the gas in the problem are:
[tex]p=1.45 atm =1.47 \cdot 10^5 Pa[/tex]
[tex]V=85 cm^3 = 85 \cdot 10^{-6} m^3[/tex]
[tex]T=310 K[/tex]
So we can use the previous equation to find the number of moles of the gas:
[tex]n= \frac{pV}{RT}= \frac{(1.47 \cdot 10^5 Pa)(85 \cdot 10^{-6} m^3)}{(8.31 J/mol K)(310 K)} =4.9 \cdot 10^{-3} mol [/tex]
The final conditions of the gas are:
[tex]V=180 cm^3 = 180 \cdot 10^{-6} m^3[/tex]
[tex]T=280 K[/tex]
and since the number of moles didn't change, we can find the final pressure by using again the ideal gas law:
[tex]p= \frac{nRT}{V}= \frac{(4.9 \cdot 10^{-3} mol)(8.31 J/mol K)(280 K)}{180 \cdot 10^{-6} m^3}=0.63 \cdot 10^5 Pa [/tex]
