Answer:
[tex]P_{2}=1.8atm[/tex]
Explanation:
The question molded an ideal gas law, which state in part
"The Volume(V) of a gas is directly proportional to the absolute temperature(T) and inversely proportional to the pressure(P)"
Mathematically, this can be expressed as
[tex]V\alpha \frac{T}{P}\\V=K \frac{T}{P}\\[/tex]
where K is a constant. varying the value of k, we arrive at
[tex]\frac{P_{1} *V_{1}}{T_{1}}=\frac{P_{2} *V_{2}}{T_{2}}=...=\frac{P_{n} *V_{n}}{T_{n}}\\[/tex]
using the first two expression of the above equation, where
[tex]P_{1}= 2.5atm, V_{1}=3.2L, T_{1}= 350K \\P_{1}= X,V_{2}= 9.1atm,T_{2}= 600K\\[/tex]
Note, we have to convert the volume to [tex]m^{3} \\[/tex]
since [tex]1L=10^{-3}m \\[/tex]
Now [tex]V_{1}=3.2*10^{-3}=\\V_{2}=9.1*10^{-3}=0.0091m^{3} \\[/tex]
also we convert the pressure from atm to pascal(pa) [tex]1atm=1.013*10^{5} pa\\[/tex]
[tex]P_{1}=2.5*1.013*10^{5}=2.53*10^{5}\\[/tex]
[tex]P_{2}=\frac{2.53*10^{5}pa*0.0032m^{3}*600}{0.0091*350}\\[/tex]
[tex]P_{2}=\frac{4.858*10^{5}}{2.73} =1.78*10^{5}\\[/tex]
convert back to atm
[tex]P_{2}=\frac{1.788*10^{5}}{1.013*10^{5}}=1.76atm[/tex]
Hence the value of he final pressure is
1.8atm
