A sample of Xe gas in a 20.00 liter container at 1.45 atm and 85 degree Celsius . It is compresses to a new value of 0.250 liter at 350 degree Celsius. What is the pressure the Van der Waals equation.
help please!
To find the pressure using the Van der Waals equation, we need to know the values for the Van der Waals constants a and b. The Van der Waals equation is given as:
(P + a(n/V)^2)(V - nb) = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin
a and b = Van der Waals constants
In this case, we are given the initial and final volume, the initial and final temperature, and we are assuming that the number of moles is constant.
Step 1: Convert the given temperatures to Kelvin.
The temperature given is in degrees Celsius, so we need to convert it to Kelvin. To convert from Celsius to Kelvin, we use the following formula:
T(K) = T(°C) + 273.15
Given initial temperature = 85 °C
Initial temperature in Kelvin: T1 = 85 + 273.15 = 358.15 K
Given final temperature = 350 °C
Final temperature in Kelvin: T2 = 350 + 273.15 = 623.15 K
Step 2: Calculate the constant b.
The constant b is calculated using the formula:
b = (V / n)
Given initial volume = 20.00 L
Given final volume = 0.250 L
Since the number of moles is constant, we can use either the initial or final volume value to calculate b. Let's use the initial volume:
b = (20.00 L / n)
Step 3: Calculate the constant a.
The equation to calculate a is:
a = (27/64) * (R^2) * (Tc^2 / Pc)
Where R is the gas constant, Tc is the critical temperature, and Pc is the critical pressure.
The critical temperature (Tc) and critical pressure (Pc) values for Xenon gas are known:
Tc = 289.75 K
Pc = 58.4 atm
Plugging in the values:
a = (27/64) * (0.0821 L·atm/mol·K)^2 * (289.75 K)^2 / 58.4 atm
Step 4: Use the Van der Waals equation to calculate the pressure.
The Van der Waals equation becomes:
(P + a(n/V)^2)(V - nb) = nRT
Plugging in the given values:
(P + a(n/V)^2)(V - nb) = nRT
Let's rearrange the equation to solve for P:
P = (nRT/(V - nb)) - a(n/V)^2
Now, simply plug in the values we calculated into the equation and solve for P:
P1 = (n * R * T1 / (V1 - n * b)) - a(n / V1)^2
P2 = (n * R * T2 / (V2 - n * b)) - a(n / V2)^2
Note: We need to know the number of moles (n) of Xenon gas to complete the calculation.