Work: How much work is done by 3.00 mol of ideal gas when it triples its volume at a constant temperature of 127°C? The ideal gas constant is R = 8.314 J/mol ∙ K.

Question

Quizplus · Accepted Answer

The work done by a gas when it undergoes a volume change at constant pressure is given by:

W = -PΔV

where P is the pressure and ΔV is the change in volume. Since the gas is ideal, we can use the ideal gas law to relate P, V, and n (the number of moles):

PV = nRT

where T is the temperature and R is the ideal gas constant.

Since the temperature is constant, we can write:

P1V1 = P2V2

where the subscripts 1 and 2 refer to the initial and final states, respectively.

The volume of the gas triples, so V2 = 3V1. Substituting this into the equation above and solving for P2, we get:

P2 = P1/3

The amount of work done by the gas is then:

W = -PΔV = -(P1/3)(3V1 - V1) = -2/3 P1V1

We can now use the ideal gas law to express P1V1 in terms of n and T:

P1V1 = nRT

Substituting this into the equation for work, we get:

W = -2/3 nRT

We know the values of n, R, and T, so we can calculate the work:

W = -(2/3)(3 mol)(8.314 J/mol ∙ K)(400 K) = -9963.6 J

The work done is negative because the gas is expanding (ΔV is positive) and work is being done on the surroundings.

Converting to kilojoules:

W = -9.9636 kJ

Taking the absolute value, we get:

|W| = 9.9636 kJ

Therefore, the best choice is C) 11.0 kJ, which is the closest answer to 9.9636 kJ. Note that the answer is positive because we are taking the absolute value.

Work: How Much Work Is Done by 3