I don't understand this:

For the temperature vs time graph for heat and changes of state.

The graph starts at -2.1 degrees C
The heat of fusion is at 2.0 degrees C
The heat of vaporization is on 101.0 degrees C. The graph ends at 103.0 degrees C.

So to get the heat of solid it is C(m)(Temp.) for the temp. would it be 2.0 + 2.1 = 4.1 degrees C

Then what temp would I use to find the heat of liquid? Would it be 101.0 - 2.0 = 99.0 degrees C OR 101.0 + 2.0 = 103.0 degrees?

Then what temp would I use ro find the heat of vapor would it be 103.0 - 101.0 = 2.0

I just don't know if I have to minus for add the temp to find the temp to use for the equation. Although I think that it's minus...

I'm not usre of your use of the terms heat of solid and heat of liquid.

The heat required to move the temperature of a solid from Tinitial to Tfinal, is
q = mass x specific heat solid x (Tfinal-Tinitial) and Tfinal can't be greater than the melting point.

The heat required to change the state from solid to liquid at the melting point is
q = mass solid x heat fusion

The heat required to move the temperature from the melting point to the boiling point is
q = mass liquid x specific heat liquid x (Tfinal-Tinitial) and Tfinal can't be more than the boiling point.

The heat required to change the liquid state to the vapor state is
q = mass liquid x heat vaporization.

The heat required to more the temperature of the vapor from the boiling point to some point higher is
q = mass vapor x specific heat vapor x (Tfinal-Tinitial).

Total q then is q1 + q2 + q3 etc until one has added all of the heats together that covers from the starting point of the material to the ending point of the material.

To determine the temperature at which a specific process occurs on a temperature vs. time graph, you need to consider the reference points provided.

1. Heat of solidification: This refers to the transition from a liquid to a solid state. In your case, the graph starts at -2.1 degrees C and the heat of fusion is at 2.0 degrees C. To find the temperature to use in the equation, you should take the difference between the heat of fusion (2.0 degrees C) and the starting temperature (-2.1 degrees C). So, 2.0 - (-2.1) equals 4.1 degrees C. Therefore, the temperature to use in the equation is 4.1 degrees C.

2. Heat of vaporization: This represents the transition from a liquid to a gaseous state. In your scenario, the heat of vaporization occurs at 101.0 degrees C, and the graph ends at 103.0 degrees C. To find the temperature to use in the equation, you should take the difference between the ending temperature (103.0 degrees C) and the heat of vaporization (101.0 degrees C). So, 103.0 - 101.0 equals 2.0 degrees C. Therefore, the temperature to use in the equation is 2.0 degrees C.

In both cases, you need to subtract the lower temperature from the higher temperature to find the temperature difference.