0.11 mol of argon gas is admitted to an evacuated 50cm^3 container at 10 degree C. The gas then undergoes an isothermal expansion to a volume of 200cm^3.
What is the final pressure of the gas?
In isothermal expansions, the product
P*V = a constant. Therefore
P2/P1 = V1/V2 = 50/200 = 1/4
Since you were not told the initial pressure P1, you will have to use the perfect gas law and the information given.
0.11 moles at STP (1 atm and 273K) occupies 0.11*22.4 = 2.46 liters. At 10C (283K) it would occupy 2.55 liters. Since the initial volume is only 50 cm^3 = 0.05 l, the initial pressure must be
P1 = 2.55/0.05 = 51 atm.
The final pressure is 1/4 of that.
You could also have used P = nRT/V to get the initial pressure. Personally I find it easier to remember that 1 mole is 22.4 liters at STP. There are too many values of R, with different units, to try to remember.
To find the final pressure of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant
T = temperature of the gas in Kelvin
First, let's convert the given temperature from degrees Celsius to Kelvin.
T(K) = T(°C) + 273.15
T(K) = 10°C + 273.15
T(K) = 283.15 K
Now, let's rearrange the ideal gas law equation to solve for the final pressure:
P = (n * R * T) / V
Substituting the given values into the equation:
P = (0.11 mol * (0.0821 L·atm/mol·K) * 283.15 K) / 0.050 L
P = (0.11 * 0.0821 * 283.15) / 0.050
P ≈ 1.0943 atm
So, the final pressure of the gas is approximately 1.0943 atm.
To find the final pressure of the gas after the isothermal expansion, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature of the gas in Kelvin
Given:
n = 0.11 mol
V1 = 50 cm^3
V2 = 200 cm^3
T = 10°C
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T = 10°C + 273.15 = 283.15 K
Now, let's calculate the initial pressure (P1) using the ideal gas law:
P1 * V1 = n * R * T
P1 = (n * R * T) / V1
Plugging in the values:
P1 = (0.11 mol * 0.0821 L·atm/(mol·K) * 283.15 K) / (50 cm^3) ≈ 0.616 atm
Since the gas undergoes an isothermal expansion, the final pressure (P2) can be found using the following equation, using the initial pressure and volume:
P1 * V1 = P2 * V2
Rearranging the equation to solve for P2:
P2 = (P1 * V1) / V2
Plugging in the values:
P2 = (0.616 atm * 50 cm^3) / 200 cm^3
P2 = 0.154 atm
Therefore, the final pressure of the gas is approximately 0.154 atm.