Assume that 0.10 mol of argon gas is admitted to an evacuated 50 cm3
container at 20° C. The gas then undergoes isobaric heating to a temperature of 300° C. What is the final pressure of the gas? What is the final volume?
Use PV=nRT to find the pressure of the gas in the container at 20 deg.C. All the variables except for P are given to you in the problem.
The heating process is isobaric -so, the pressure would not change. But its volume would increase which you can find by using the equation: P1V1/T1 = P2V2/T2
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin
First, we need to convert the temperature to Kelvin:
20°C + 273 = 293 K (initial temperature)
300°C + 273 = 573 K (final temperature)
Given:
n = 0.10 mol
V = 50 cm3 = 50/1000 = 0.05 L
R = 0.0821 L·atm/mol·K (constant, no need to convert)
T₁ = 293 K (initial temperature)
T₂ = 573 K (final temperature)
Now we can calculate the initial pressure (P₁) using the ideal gas law:
P₁V = nRT₁
P₁ = (nRT₁) / V
P₁ = (0.10 mol * 0.0821 L·atm/mol·K * 293 K) / 0.05 L
P₁ ≈ 48.32 atm
Since the heating is isobaric (constant pressure) and we are looking for the final pressure, the final pressure will also be 48.32 atm.
Finally, we can calculate the final volume (V₂) using the ideal gas law:
P₂V₂ = nRT₂
V₂ = (nRT₂) / P₂
V₂ = (0.10 mol * 0.0821 L·atm/mol·K * 573 K) / 48.32 atm
V₂ ≈ 1.19 L
So, the final pressure of the gas will be approximately 48.32 atm, and the final volume will be approximately 1.19 L.
To find the final pressure and final volume 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 gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature of the gas in Kelvin
First, let's convert the given temperatures to Kelvin:
Initial temperature (20 °C) = 20 + 273 = 293 K
Final temperature (300 °C) = 300 + 273 = 573 K
Next, we can substitute the given values into the equation:
P1V1 = nRT1
Here, P1 = unknown (final pressure)
V1 = 50 cm^3 (given volume)
n = 0.10 mol (given number of moles)
R = 0.0821 L·atm/mol·K (ideal gas constant)
T1 = 293 K (initial temperature)
Now, let's solve for P1 (final pressure):
P1 = (nRT1) / V1
P1 = (0.10 mol * 0.0821 L·atm/mol·K * 293 K) / 50 cm^3
Simplifying the units:
P1 = (0.01003 L·atm) / 50 cm^3
To convert cm^3 to liters, we divide by 1000:
P1 = 0.01003 L·atm / 50 / 1000 L
P1 = 0.0002006 atm
So, the final pressure of the gas is approximately 0.0002006 atm.
To find the final volume of the gas, we can use the same equation:
P2V2 = nRT2
Here, P2 = unknown (final pressure)
V2 = unknown (final volume)
n = 0.10 mol (given number of moles)
R = 0.0821 L·atm/mol·K (ideal gas constant)
T2 = 573 K (final temperature)
Now, let's solve for V2 (final volume):
V2 = (nRT2) / P2
V2 = (0.10 mol * 0.0821 L·atm/mol·K * 573 K) / 0.0002006 atm
Simplifying the units:
V2 = (4.72913 L·atm) / 0.0002006 atm
V2 = 23573.03 L
So, the final volume of the gas is approximately 23573.03 L.