A 5.0 L container is filled with a gas to a pressure of 4.00 atm at 0 C at what temperature will the pressure inside the container be 2.00 atm

Answer 1

To find the new temperature at which the pressure inside the container will be 2.00 atm, we will use the ideal gas law:

\(PV = nRT\)

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin

Given:
Initial pressure, P1 = 4.00 atm
Initial volume, V1 = 5.0 L
Initial temperature, T1 = 0 C = 273 K (conversion from Celsius to Kelvin)

Final pressure, P2 = 2.00 atm
Final volume, V2 = 5.0 L (volume remains constant)
Final temperature, T2 = ?

First, we need to find the number of moles of gas in the container using the initial conditions:

\(n = \frac{PV}{RT} = \frac{(4.00\ atm)(5.0\ L)}{(0.0821\ L\ atm/mol\ K)(273\ K)} \approx 0.92\ mol\)

Now, we can use the ideal gas law to find the final temperature (T2):

\(T2 = \frac{P2V2}{nR}\)

\(T2 = \frac{(2.00\ atm)(5.0\ L)}{(0.92\ mol)(0.0821\ L\ atm/mol\ K)} \approx 108.7\ K\)

Therefore, the temperature inside the container when the pressure is 2.00 atm will be 108.7 K.