Respuesta :
Answer: Pressure of the gas is 0.129375 atm when the volume of the vessel increased by a factor of 16.00.
Explanation:
The formula for ideal gas equation is as follows.
[tex]PV = Nk_{b}T[/tex]
where,
[tex]k_{b}[/tex] = Boltzmann constant
N = number of moles
That can also be written as:
[tex]\frac{PV}{T} = constant[/tex]
As pressure and volume are inversely proportional to each other. So, if one of the state variable is increased then the other one will decrease or vice-versa.
So, if volume of the vessel increased by a factor of 16.00 then it means pressure is decreased by a factor of 16.00
Therefore, final volume is as follows.
[tex]65.8 L \times 16.00\\= 1052.8 L[/tex]
Now, final pressure is as follows.
[tex]\frac{2.07}{16.00}\\= 0.129375 atm[/tex]
Initially the product of pressure and volume is as follows.
[tex]PV = 2.07 \times 65.8\\= 136.206[/tex]
Hence, if volume of the vessel increased by a factor of 16.00 and pressure is decreased by a factor of 16.00 then its product is as follows.
[tex]PV = 0.129375 \times 1052.8\\= 136.206[/tex]
Here, product of pressure and volume remains the same.
Thus, we can conclude that pressure of the gas is 0.129375 atm when the volume of the vessel increased by a factor of 16.00.
