A 1.6-mole sample of an ideal gas is gently cooled at constant temperature 280 K. It contracts from initial volume 37 L to final volume V2. A total of 1.9 kJ of heat is removed from the gas during the contraction process. What is V2? Let the ideal-gas constant R = 8.314 J/(mol • K).

32 L

22 L

29 L

17 L

To find the final volume (V2), we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure (assuming it remains constant)
V = volume
n = number of moles
R = ideal gas constant
T = temperature

Since the temperature (T) remains constant, we can rewrite the equation as:

P1V1 = P2V2

Where:
P1 and V1 are the initial pressure and volume.
P2 and V2 are the final pressure and volume.

Given:
n = 1.6 moles
V1 = 37 L
T = 280 K
R = 8.314 J/(mol • K)

We need to find V2. We are also given that 1.9 kJ (or 1900 J) of heat is removed from the gas during the contraction process. This heat can be written as Q = -1900 J because it is removed from the gas.

Since the process is gentle and at constant temperature, there is no change in the internal energy (ΔU) of the gas. Therefore, we can say that ΔU = Q + W, where ΔU is the change in internal energy, Q is heat, and W is work done by the gas.

In this case, since the heat (Q) is negative (removal of heat), the work done by the gas (W) will also be negative. Therefore, W = -1900 J.

The work done by the gas can be calculated using the equation:

W = -PΔV

Where ΔV = V2 - V1 is the change in volume.

Combining these equations, we have:

-1900 J = -P(ΔV)

Now we can substitute the values known:
P1 = P2 (since pressure remains constant)
V1 = 37 L
V2 = unknown
W = -1900 J

Plugging in these values, we get:

-1900 J = -P(V2 - V1)

Since P = P1 = P2, the pressure drops out of the equation:

-1900 J = -(V2 - 37 L)

Simplifying, we have:

-1900 J = -V2 + 37 L

Rearranging the equation, we get:

-V2 = -1900 J + 37 L

Multiplying both sides by -1, we get:

V2 = 1900 J - 37 L

Simplifying further, we get:

V2 = 1863 J

Converting J to L, we divide by 8.314 J/(mol • K), which is the ideal gas constant R:

V2 ≈ 1863 J / (8.314 J/(mol • K))

V2 ≈ 224 moles • K

V2 ≈ 26.95 L

Therefore, the final volume V2 is approximately 27 L.