A 25.0 g piece of copper at 90.0 C is placed in 100.0 g of water at 20.0 C. What is the temperature (in C) of the water once the system reaches equilibrium? The molar heat capacity of copper is 24.5 J/(mol·K).
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To find the final temperature of the water, we can use the principle of conservation of energy. The heat lost by the copper will be equal to the heat gained by the water.
First, let's calculate the heat lost by the copper. We can use the formula:
q = m * C * ΔT
where:
q is the heat lost
m is the mass of the copper (25.0 g)
C is the molar heat capacity of copper (24.5 J/(mol·K))
ΔT is the change in temperature of the copper
The change in temperature of the copper is the difference between its initial temperature (90.0 °C) and the final temperature (we'll call it Tf):
ΔT = Tf - 90.0 °C
To convert the mass of copper to moles, we need to divide it by the molar mass of copper. The molar mass of copper is 63.5 g/mol.
mols = m / M
where:
m is the mass of the copper (25.0 g)
M is the molar mass of copper (63.5 g/mol)
Now, let's substitute the values into the formula for heat lost by the copper:
q = (mols * C) * ΔT
Next, we'll calculate the heat gained by the water. We can use the same formula:
q = m * C * ΔT
where:
q is the heat gained
m is the mass of the water (100.0 g)
C is the specific heat capacity of water (4.18 J/(g·K))
ΔT is the change in temperature of the water
The change in temperature of the water is the difference between its final temperature and its initial temperature (20.0 °C):
ΔT = Tf - 20.0 °C
Now, let's substitute the values into the formula for heat gained by the water:
q = (m * C) * ΔT
Since the heat lost by the copper is equal to the heat gained by the water, we can set the two equations equal to each other and solve for Tf, the final temperature of the water:
(mols * C * ΔT) = (m * C * ΔT)
Simplifying the equation:
mols = (m * C)/ (mols * C)
Now, let's substitute the known values into the equation:
((25.0 g) / (63.5 g/mol)) = ((100.0 g * 4.18 J/(g·K)) / Tf)
Now, isolate Tf:
Tf = ((100.0 g * 4.18 J/(g·K)) / ((25.0 g) / (63.5 g/mol)))
Now we can solve for Tf.