Practice problem using idle gas law

Answer 1

A gas occupies a volume of 2.0 L at a pressure of 3.0 atm and a temperature of 25 degrees Celsius. If the temperature is increased to 50 degrees Celsius while keeping the pressure constant, what will be the new volume of the gas?

To solve this problem, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure (3.0 atm)
V = volume (2.0 L)
n = number of moles of gas (we can assume it is constant)
R = gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin

First, we need to convert the temperatures from Celsius to Kelvin:
Initial temperature (T1) = 25 degrees Celsius + 273 = 298 K
Final temperature (T2) = 50 degrees Celsius + 273 = 323 K

Now we can substitute the initial conditions into the ideal gas law equation:
(3.0 atm) * (2.0 L) = n * (0.0821 L.atm/mol.K) * (298 K)

Solving for the number of moles:
n = (3.0 atm * 2.0 L) / (0.0821 L.atm/mol.K * 298 K)
n ≈ 0.25 mol

Now we can use the new temperature to find the new volume:
(3.0 atm) * V2 = (0.25 mol) * (0.0821 L.atm/mol.K) * (323 K)

Solving for V2:
V2 = (0.25 mol * 0.0821 L.atm/mol.K * 323 K) / 3.0 atm
V2 ≈ 6.68 L

Therefore, the new volume of the gas at a temperature of 50 degrees Celsius while keeping the pressure constant will be approximately 6.68 L.