How many grams of ice at -26.5\, ^\circ C can be completely converted to liquid at 15.0\, ^\circ C if the available heat for this process is 4.50×103 kJ?
For ice, use a specific heat of 2.01J/(g\cdot{ ^\circ C}) and H2 = 6.01 kJ/mol.
I word to the wise should be sufficient; i.e., you would do well not to try to type in the special symbols. The ones displayed on my screen look like Sanskrit and they are not readable.
For your problem, assuming I have translated the Sanskrit correctly, is
4.50E6 J = mass ice x heat fusion + [mass water x specific heat water x (Tfnal-Tinitial)]
You have one unknown, mass ice and mass water (same unknown).
To solve this problem, we need to use the concept of heat transfer and the equations related to it. I'll explain step by step how to approach this problem.
1. Determine the amount of heat required to raise the temperature of the ice from -26.5°C to 0°C (the melting point of ice). This can be calculated using the equation:
Q = m * c * ΔT
where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Substituting the known values:
Q1 = m * 2.01 J/(g·°C) * (0°C - (-26.5°C))
2. Determine the amount of heat required to melt the ice at 0°C. This can be calculated using the equation:
Q2 = m * ΔHf
where Q2 is the heat energy, m is the mass, and ΔHf is the heat of fusion.
Substituting the known values:
Q2 = m * 6.01 kJ/mol
3. Determine the amount of heat required to raise the temperature of the liquid water from 0°C to 15°C. This can be calculated using the equation:
Q3 = m * c * ΔT
where Q3 is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Substituting the known values:
Q3 = m * 4.18 J/(g·°C) * (15°C - 0°C)
4. Add up the heat energies from steps 1, 2, and 3 to get the total amount of heat required for the process:
Q_total = Q1 + Q2 + Q3
5. Finally, calculate the mass of ice that can be completely converted to liquid using the available heat (4.50×10^3 kJ):
m = Q_total / Heat_available
Substitute the known values and solve the equation to find the mass of ice.
Please note that in this explanation, I used the specific heat of liquid water (4.18 J/(g·°C)) instead of the specific heat of ice because the ice is being converted to liquid water.