Answer:
The pressure required for the gas to expand to 5.00 L if the temperature cooled in the process to 300 K is 0.84 atm.
Step-by-step explanation:
To solve this problem, we can use the ideal gas law:
PV = nRT
where:
P is the pressure in atm
V is the volume in L
n is the number of moles of gas
R is the gas constant (0.08206 L atm / mol K)
T is the temperature in K
Since we are dealing with the same sample of gas, the number of moles of gas remains constant. Therefore, we can write the ideal gas law as follows:
P1V1 = P2V2
where:
P1 is the initial pressure (1 atm)
V1 is the initial volume (4.20 L)
P2 is the final pressure (unknown)
V2 is the final volume (5.00 L)
Substituting the given values into the equation, we get:
1 atm * 4.20 L = P2 * 5.00 L
P2 = 0.84 atm
Therefore, the pressure required for the gas to expand to 5.00 L if the temperature cooled in the process to 300 K is 0.84 atm.