80.0 mL of water is initially at room temperature (22degrees C). A chilled steel rod at 2 degrees C is placed in the water. If the final temperature of the system is 21.2 degrees C, what is the mass of the steel bar?
Specific heat of water = 4.18J/g(degreesC)
Specific heat of steel = 0.452J/g(degrees C)
PART B
The specific heat of water is 4.18 J/g(degrees C). Calculate the molar heat capacity of water.
38.9 for the first one.
75.2 for the 2nd one.
To solve this problem, we can use the concept of heat transfer and the equation:
Q = mcΔT
where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
PART A
We need to find the mass of the steel bar. Here's how we can proceed:
1. Calculate the heat gained by the water and the heat lost by the steel rod:
Qwater = mwater × cwater × ΔTwater
Qsteel = msteel × csteel × ΔTsteel
2. Since the water and steel are in thermal equilibrium (same final temperature), the heat gained by the water is equal to the heat lost by the steel:
Qwater = -Qsteel (negative sign indicates heat loss)
3. Set up the equation:
mwater × cwater × ΔTwater = -msteel × csteel × ΔTsteel
4. Plug in the given values:
(80.0 g) × (4.18 J/g°C) × (21.2°C - 22°C) = -(msteel) × (0.452 J/g°C) × (21.2°C - 2°C)
5. Solve for msteel:
msteel = (80.0 g) × (4.18 J/g°C) × (21.2 - 22) / (0.452 J/g°C) × (21.2 - 2)
Calculate the right side of the equation and solve to find msteel.
PART B
The molar heat capacity of water (C) is the amount of heat required to raise the temperature of 1 mole of a substance by 1 degree Celsius. It can be calculated using the equation:
C = q / (n × ΔT)
where C is the molar heat capacity, q is the heat transferred, n is the number of moles, and ΔT is the change in temperature.
1. Convert the mass of water to moles using its molar mass. The molar mass of water is approximately 18.015 g/mol.
moles = mass / molar mass
2. Calculate the heat transferred using the equation Q = mcΔT. In this case, the heat transferred is the same as the required heat capacity for 1 mole of water.
q = m × c × ΔT
3. Plug in the values and calculate the molar heat capacity:
C = q / (n × ΔT)
Using the given values of specific heat and the molecular weight of water, calculate the molar heat capacity of water.