How much heat energy is needed to convert 125.0g of ice from -27.0ºC to a liquid at 50.0ºC?
q1 = heat need to raise T from -27 C to zero C.
q1 = mass ice x specific heat ice x (Tfinal-Tinitial).
q2 = neat to convert ice at zero C to liquid water at zero C.
q2 = mass ice x heat fusion.
q3 = heat to raise T of liquid water from zero C to 50 C
q3 = mass x specific heat x (Tfinal-Tinitial)
Total Q = q1 + q2 + q3
19650
To find the amount of heat energy needed to convert ice from -27.0ºC to a liquid at 50.0ºC, we need to calculate the energy required for each step of the phase change.
1. Heating ice from -27.0ºC to 0ºC:
The specific heat capacity of ice is 2.09 J/g·ºC. The formula for calculating heat energy is:
q = m * c * ΔT
where:
q is the heat energy (in Joules),
m is the mass of the substance (in grams),
c is the specific heat capacity (in J/g·ºC), and
ΔT is the change in temperature (in ºC).
Calculating the heat energy required to raise the temperature of the ice from -27.0ºC to 0ºC:
q1 = 125.0g * 2.09 J/g·ºC * (0ºC - (-27.0ºC))
2. Melting the ice to liquid water at 0ºC:
The heat of fusion for ice is 334 J/g. The formula for calculating heat energy during a phase change is:
q = m * ΔHf
where ΔHf is the heat of fusion (in J/g).
Calculating the heat energy required to melt the ice:
q2 = 125.0g * 334 J/g
3. Heating the liquid water from 0ºC to 50.0ºC:
The specific heat capacity of liquid water is 4.18 J/g·ºC.
Calculating the heat energy required to raise the temperature from 0ºC to 50.0ºC:
q3 = 125.0g * 4.18 J/g·ºC * (50.0ºC - 0ºC)
To find the total heat energy, we need to sum up the energy from each step:
Total heat energy = q1 + q2 + q3
By plugging in the values and performing the calculations, you will obtain the amount of heat energy needed to convert 125.0g of ice from -27.0ºC to a liquid at 50.0ºC.