How much heat energy must be removed from 250 g of oxygen at 21.0°C to liquefy it at −183°C? (The specific heat of oxygen gas is 0.218 cal/g⋅°C,and its heat of vaporization is 50.9 cal/g. )

Question

Quizplus · Accepted Answer

To liquefy oxygen, we need to cool it down from 21°C to -183°C and then condense it at constant temperature by extracting the heat of vaporization.

First, we calculate the heat required to cool 250 g of oxygen from 21°C to -183°C:

Q1 = m × C × ΔT = 250 g × 0.218 cal/g°C × (-183°C - 21°C) = -8556 cal

Note that the negative sign indicates that heat energy is being removed from the system (the oxygen).

Next, we calculate the heat required to liquefy the cooled oxygen at a constant temperature of -183°C:

Q2 = m × ΔHvap = 250 g × 50.9 cal/g = 12,725 cal

Finally, the total heat energy that must be removed from the oxygen is the sum of Q1 and Q2:

Qtotal = Q1 + Q2 = -8556 cal + 12,725 cal = 4169 cal

Since the question asks for the heat energy to be removed (which is negative), we take the absolute value to get:

|Qtotal| = 4169 cal ≈ 2.4 × 10^4 cal

Therefore, the answer is B) 2.4E+4 cal.

How Much Heat Energy Must Be Removed from 250 G