calculate the van dar waals coorectionj terms to pressure and volume for Cl2 at STP. The values of the van der waals constant a and b are 6.49L2-atm/mol2 and 0.056L/mol, respectively, for Cl2. At STP, which is the major cause of deviation from ideal behavior, the volume of the Cl2 molecules or the attrractive forces betweem them? Why?
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To calculate the van der Waals correction terms for pressure and volume for Cl2 at STP (Standard Temperature and Pressure), we need to use the van der Waals equation:
(P + a(n/V)^2)(V - nb) = nRT
Where:
P is the pressure,
V is the volume,
n is the number of moles,
R is the ideal gas constant, and
T is the temperature.
Given:
a = 6.49 L^2-atm/mol^2
b = 0.056 L/mol
At STP:
P = 1 atm
T = 273 K
First, we need to calculate the values for n/V and (n/V)^2:
n/V = n / (V / 1 mol) = n / 22.4 L/mol (since 1 mole of any gas at STP occupies 22.4 L)
(n/V)^2 = (n / 22.4 L/mol)^2
Next, we plug these values into the van der Waals equation and solve for (P + a(n/V)^2) and (V - nb):
(P + a(n/V)^2) = nRT / (V - nb)
(P + a(n / 22.4 L/mol)^2) = (1 mol)(0.0821 L-atm/mol-K)(273 K) / (V - (0.056 L/mol)(n))
Now, we can substitute the given values of a and b into the equation:
(P + 6.49 L^2-atm/mol^2[(n / 22.4 L/mol)^2]) = (0.0821 L-atm/mol-K)(273 K) / (V - 0.056 L/mol(n))
Finally, we can simplify and solve for the van der Waals correction terms:
(P + 6.49 L^2-atm/mol^2[(n / 22.4 L/mol)^2]) = 22.2 / (V - 0.056 L/mol(n))
Now, let's address the major cause of deviation from ideal behavior at STP for Cl2.
In the van der Waals equation, the term (V - nb) accounts for the volume occupied by the gas molecules, while the term a(n/V)^2 represents the attractive forces between the gas molecules. Attractive forces tend to cause the inward condensation of gas particles, resulting in a smaller apparent volume.
In the case of Cl2, which is a diatomic gas, the dominant factor causing the deviation from ideal behavior at STP is the attractive forces between the molecules. This is because the attractive forces between Cl2 molecules are relatively stronger compared to the volume that the molecules occupy. Therefore, the attractive forces cause Cl2 to deviate from ideal gas behavior more significantly than the effect of molecular volume.
To summarize, in Cl2 at STP, the major cause of deviation from ideal behavior is the attractive forces between the molecules rather than the volume occupied by the molecules.