Question

A 2.10-mole sample of an ideal gas is allowed to expand at a constant temperature of 278 K. The initial volume is 14.5 L and the gas performs 945 J of work. What is the final volume of the container? Let the ideal-gas constant R = 8.314 J/(mol • K).

Answers:
22.3 L
19.5 L
17.6 L
28.4 L

Answer 1

Step-by-step explanation:

Given that,

Number of mole

n = 2.1mole

Temperature

T = 278 K

Initial volume

V1 = 14.5L

Work done

W = 945J

R = 8.314 J/mol•K

Work done is given as at constant temperature is

W = -P1•V1 In(V2/V1)

Now, let know the pressure using is ideal gas law

PV = nRT

P = nRT/V

P = 2.1 × 8.314 ×278 / 14.5

P = 334.74 N/L

Then,

W = -P1•V1 In(V1/V2)

945 = -334.74×14.5 In(V1/V2)

-945/(334.74×14.5) = In(V1/V2)

In(V1/V2) = -0.1947

Take exponential of both sides

V1/V2 = exp(-0.1947)

14.5/V2 = 0.823

14.5 = 0.823V2

V2 = 14.5/0.823

V2 = 17.62 L

The third option is correct