Substance A has a normal fusion point of ‑10.0 oC, an enthalpy of fusion = 150.0 J g^-1; specific heats for the solid and the liquid are 3.00 and 6.20 J g^-1 oC^-1, respectively. How much heat, in J, is required to change 150 grams of A from a solid at –40.0 oC to a liquid at +70.0 oC?
There are two formula to use and you can progress from the solid, liquid, gas.
When you change the phase, you go with q = mass x heat fusion (at the melting point) or q = mass x heat vap at the boiling point.
When the phase is not changing, you go with q = mass x specific heat x (Tfinal-Tinitial).
This applies in the solid phase, the liquid phase, and the gaseous phase.
Then total q = sum of the individual qs. Post your work if you get stuck.
To calculate the heat required to change a substance from a solid to a liquid, you need to consider two main processes: heating the substance from its initial temperature to its fusion point, and then melting the substance at its fusion point.
1. Calculating the heat required to heat the substance from -40.0 oC to its fusion point (-10.0 oC):
This can be calculated using the formula Q = m * Cp * ΔT, where Q is the heat, m is the mass of the substance, Cp is the specific heat capacity, and ΔT is the change in temperature.
So, the heat required to heat the substance from -40.0 oC to -10.0 oC is:
Q1 = 150 g * 3.00 J g^-1 oC^-1 * ( -10.0 oC - ( -40.0 oC ))
= 150 g * 3.00 J g^-1 oC^-1 * 30.0 oC
2. Calculating the heat required to melt the substance at its fusion point (-10.0 oC):
This can be calculated using the formula Q = m * ΔHf, where Q is the heat, m is the mass of the substance, and ΔHf is the enthalpy of fusion.
So, the heat required to melt the substance is:
Q2 = 150 g * 150.0 J g^-1
3. Calculating the heat required to heat the substance from its fusion point (-10.0 oC) to its final temperature (70.0 oC):
Similarly, this can be calculated using the formula Q = m * Cp * ΔT.
So, the heat required to heat the substance from -10.0 oC to 70.0 oC is:
Q3 = 150 g * 6.20 J g^-1 oC^-1 * (70.0 oC - (-10.0 oC))
Now, to obtain the total heat required to change the substance from a solid at -40.0 oC to a liquid at 70.0 oC, you can simply add all three calculated quantities:
Total heat required = Q1 + Q2 + Q3
Calculating this will give you the final answer in joules (J).