Answer: The final pressure inside the bottle is 49.527 atm
Explanation:
To calculate the pressure of the gas, we use the equation given by ideal gas equation:
PV = nRT
Or,
[tex]PV=\frac{w}{M}RT[/tex]
where,
P = Pressure of the gas = ?
V = Volume of the gas = 0.500 L
w = Weight of carbon dioxide gas = 17.0 g
M = Molar mass of carbon dioxide gas = 44 g/mol
R = Gas constant = [tex]0.0820\text{ L atm }mol^{-1}K^{-1}[/tex]
T = Temperature of the gas = [tex]492.7^oC=[492.7+273]K=765.7K[/tex]
Putting values in above equation, we get:
[tex]P\times 0.500L=\frac{17.0}{44g/mol}\times 0.0821\text{ L. atm }mol^{-1}K^{-1}\times 765.7K\\\\P=\frac{17\times 0.0821\times 765.7}{0.500\times 44}=48.58atm[/tex]
We are given:
Pressure of the bottle = 0.947 atm
SO, total pressure inside the bottle = Pressure exerted by carbon dioxide + Pressure of the bottle = [48.58 + 0.947] = 49.527 atm
Hence, the final pressure inside the bottle is 49.527 atm
