For chlorine gas, the van der Waals constants are: a = 0.658 J·m3/mol2, and b = 5.62 × 10-5 m3/mol. A 3.0-L tank contains 10.0 moles of chlorine gas at a temperature of 625 K. What is

the pressure in the container?
A) 15.0 MPa
B) 17.3 MPa
C) 13.5 MPa
D) 18.2 MPa
E) 11.0 MPa

18.2

The pressure in the container can be calculated using the van der Waals equation:

(P + a n2/V2) (V - n b) = n R T

where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, T is the temperature, and a and b are the van der Waals constants.

First, we need to calculate the volume of the gas in the container since it is given as 3.0 L. The volume occupied by the gas molecules themselves (i.e. the "dead space" which is not available for molecule motion) is given by nb, where n is the number of moles and b is the van der Waals constant. Thus, the actual volume of the gas is V = 3.0 L + n b = 3.0 L + 10.0 mol x 5.62 x 10^-5 m^3/mol = 3.00056 L.

Now we can substitute the given values into the van der Waals equation and solve for P:

(P + a n^2/V^2) (V - n b) = n R T

(P + 0.658 x 10^2/ (3.00056 x 10^-3)^2) (3.00056 x 10^-3 - 10.0 x 5.62 x 10^-5) = 10.0 x 8.314 x 625

(P + 2.550) (0.0299944) = 52018.5

P = (52018.5/0.0299944) - 2.550

P = 1730798.2 Pa

Converting to MPa: P = 17.3 MPa

Therefore, the pressure in the container is option (B) 17.3 MPa.

To determine the pressure in the container, we can use the van der Waals equation:

P = (nRT) / (V - nb) - a(n^2 / V^2)

Where:
P = pressure
n = number of moles
R = gas constant (8.314 J/(mol·K))
T = temperature
V = volume
a, b = van der Waals constants

Given:
a = 0.658 J·m3/mol2
b = 5.62 × 10-5 m3/mol
n = 10.0 moles
T = 625 K
V = 3.0 L (convert to cubic meters: 1 L = 0.001 m^3)

First, convert the volume from liters to cubic meters:
V = 3.0 L x 0.001 m^3/L = 0.003 m^3

Next, substitute the given values into the van der Waals equation:

P = (10.0 mol x 8.314 J/(mol·K) x 625 K) / (0.003 m^3 - (10.0 mol x 5.62 × 10^-5 m^3/mol)) - (0.658 J·m^3/mol^2 x (10.0 mol)^2) / (0.003 m^3)^2

Simplifying the equation:

P = (5237.5 J) / (0.003 m^3 - 5.62 × 10^-4 m^3) - (0.658 J·m^3/mol^2 x 100 mol) / (0.003 m^3)^2

P = (5237.5 J) / (0.00244 m^3) - (0.658 J·m^3/mol^2 x 100 mol) / (9 × 10^-6 m^6)

P = 2146475.4 J/m^3 - 7288.9 J/m^3

P = 2139186.5 J/m^3

Now, we need to convert the pressure from J/m^3 to MPa (megapascals) by dividing by 10^6:

P = 2139186.5 J/m^3 / 10^6 = 2.1391865 MPa

Rounding to the nearest tenth:

P ≈ 2.1 MPa

Therefore, the pressure in the container is approximately 2.1 MPa. Since none of the answer choices match exactly, it seems there may be a mistake in the given values or the question options.