0.490 mol of argon gas is admitted to an evacuated 50.0 cm^3 container at 60.0 C. The gas then undergoes an isochoric heating to a temperature of 400 C. What is the pressure?
To find the pressure of the gas after isochoric heating, 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
Given values:
n = 0.490 mol
V = 50.0 cm^3
T1 = 60.0 C = 333.15 K (temperature before heating)
T2 = 400 C = 673.15 K (temperature after heating)
First, we need to calculate the initial pressure of the gas before heating.
Substituting the given values into the ideal gas law equation:
P1 * V = n * R * T1
Rearranging the equation to solve for P1:
P1 = (n * R * T1) / V
Plugging in the values:
P1 = (0.490 mol * 8.314 J/(mol*K) * 333.15 K) / 50.0 cm^3
Converting cm^3 to m^3:
P1 = (0.490 mol * 8.314 J/(mol*K) * 333.15 K) / 0.00005 m^3
Calculating P1:
P1 = 8697.05 Pa
Now, to find the pressure after isochoric heating, we can use the same equation with the final temperature:
P2 * V = n * R * T2
Rearranging the equation to solve for P2:
P2 = (n * R * T2) / V
Plugging in the values:
P2 = (0.490 mol * 8.314 J/(mol*K) * 673.15 K) / 0.00005 m^3
Calculating P2:
P2 = 357416.84 Pa
Therefore, the pressure of the argon gas after isochoric heating is approximately 357416.84 Pa.
To determine the final pressure in the container, we need to apply the ideal gas law, which states:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles of gas
R is the ideal gas constant
T is the temperature in Kelvin
Let's break down the problem step by step:
Step 1: Convert the initial temperature to Kelvin.
Given: Initial temperature (Ti) = 60.0 °C
To convert to Kelvin, we use the equation: Tk = Tc + 273.15
Ti (Kelvin) = 60.0 + 273.15 = 333.15 K
Step 2: Convert the final temperature to Kelvin.
Given: Final temperature (Tf) = 400 °C
Tf (Kelvin) = 400 + 273.15 = 673.15 K
Step 3: Convert the initial volume to liters.
Given: Initial volume (Vi) = 50.0 cm^3
To convert to liters, we divide by 1000.
Vi (liters) = 50.0 / 1000 = 0.05 L
Step 4: Convert the number of moles to the final volume.
Given: Number of moles (n) = 0.490 mol
Since the gas undergoes an isochoric (constant volume) heating, the final volume (Vf) will be the same as the initial volume (Vi).
Step 5: Apply the ideal gas law to calculate the final pressure.
Using the ideal gas law equation: PV = nRT
Pf * Vf = n * R * Tf
Since Vi = Vf, we can rewrite the equation:
Pf * Vi = n * R * Tf
Solving for Pf:
Pf = (n * R * Tf) / Vi
Now, substitute the known values:
Pf = (0.490 * 0.0821 * 673.15) / 0.05
Calculating:
Pf = 5.787 atm
Therefore, the final pressure in the container, after the isochoric heating, is approximately 5.787 atm.