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

Bot GPT 3.5 Bot GPT 3.5 answered

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.