How much energy (in kilojoules) is needed to heat 5.45g of ice from -12.0 C to 32.0 C? The heat of fusion of water is 6.01kJ/mol, and the molar heat capacity is 36.6 J/(K x mol) for ice and 75.3 J/(k x mol) for liquid water
q1 = heat to move ice from -12 C to zero C.
q1 = mass ice x specific heat ice x (Tfinal-Tinitial). Note Tfinal = 0 and Ti = -12 so 0-(-12) = +12.
q2 = heat needed to melt ice at zero C to liquid water at zero C.
q2 = mass ice x heat fusion.
q3 = heat to move T of liquid water from zero C to 32 C,.
q3 = mass x specific heat water x (Tfinal-Tinitial).
Total q = q1 + q2 + q3.
15kj
To calculate the energy required to heat the ice, we need to consider two steps: first, raising the temperature of the ice from -12.0°C to 0.0°C, and then converting the ice at 0.0°C to liquid water at 32.0°C.
STEP 1: Heating the ice from -12.0°C to 0.0°C
The heat required to raise the temperature of a substance can be calculated using the formula:
Q = m × c × ΔT
Where:
Q is the heat energy required
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
In this case, we have ice, and the specific heat capacity is given as 36.6 J/(K x mol) or 0.0366 kJ/(K x mol).
First, we need to calculate the moles of ice:
moles = mass / molar mass
The molar mass of water is 18.015 g/mol. Thus, the moles of ice can be calculated as:
moles = 5.45 g / 18.015 g/mol
Now, let's calculate the heat energy required to raise the temperature of the ice to 0.0°C:
Q1 = moles × heat of fusion
The heat of fusion of water is given as 6.01 kJ/mol.
STEP 2: Heating the ice from 0.0°C to 32.0°C
Now, we need to calculate the heat energy required to raise the ice from 0.0°C to 32.0°C. We will use the same formula as before:
Q2 = m × c × ΔT
However, since the ice has now transformed into liquid water, we need to consider the specific heat capacity of liquid water, which is given as 75.3 J/(K x mol) or 0.0753 kJ/(K x mol).
Again, calculate the moles of water:
moles = mass / molar mass
Now, let's calculate the heat energy required to raise the temperature of the water from 0.0°C to 32.0°C:
Q3 = moles × c × ΔT
Finally, we can find the total energy required by adding up the three steps:
Total energy = Q1 + Q2 + Q3
Calculate each Q value using the formulas and values provided, and sum them up to get the final result.