What mass of copper solid, initially at 25oC,should be added to 100 g of steam, initially at100oC, if we want exactly half of the steam to
condense?
The specific heat of copper
is 0.385 J g-1 oC-1.
For water, the heat of
vaporization is 2257 J g−1.
[mass Cu x specific heat Cu x (Tfinal-Tinitial)] + [mass steam x delta Hvap]=0
Substitute the numbers and solve for mass Cu which is the only unknown in the equation.
To solve this problem, we need to determine the amount of heat released by the steam as it condenses and then calculate the mass of copper needed to absorb that heat.
First, let's calculate the amount of heat released by the steam as it condenses. We know that the heat of vaporization for water is 2257 J/g. Since half of the steam will condense, we can calculate the heat released as:
Heat released = (mass of water condensed) * (heat of vaporization)
Heat released = (0.5) * (100 g) * (2257 J/g)
Heat released = 112,850 J
Next, we need to calculate the amount of heat absorbed by the copper. We can use the formula:
Heat absorbed = (mass of copper) * (specific heat of copper) * (change in temperature)
The change in temperature is the final temperature of the mixture (which we want to be the same as the initial temperature of the copper, 25°C) minus the initial temperature of the copper. Since the steam will condense to water, the final temperature will be 100°C.
Heat absorbed = (mass of copper) * (0.385 J/g°C) * (100°C - 25°C)
Heat absorbed = (mass of copper) * (0.385 J/g°C) * (75°C)
Heat absorbed = 28.875 (mass of copper) J
Now, we can set up an equation equating the heat released by the steam to the heat absorbed by the copper:
112,850 J = 28.875 (mass of copper)
mass of copper = 112,850 J / 28.875 J/g
mass of copper ≈ 3,904 g
Therefore, approximately 3,904 grams of copper solid should be added to 100 g of steam to exactly half of the steam condense.