Construct a cooling curve (looks the same as a heating curve) for a substance with a molar mass of 200 that has a gas phase specific heat capacity of 2.9J/g K, a boiling point of 525 K,a liquid phase specific heat capacity of 3.24 J/g K, a freezing point of 352 K, a solid phase specific heat capacity of 3.3 J/g K and molar enthalpies of fusion and condensation of -14.3 kJ/mol and -46.4 kJ/mol.
I know that a diagram of the cooling curve cannot be posted on this forum, but here is what I got on the diagram:
x-axis: Heat Removed --->
y-axis: Temperature (K)
The curve starts with a negative slope line (gas) and then stays constant
(boiling point) and then the line goes goes down with a negative slope ( liquid) and then stays constant (freezing point) and then goes down with a negative slope (solid) and finally stays constant.
The heat required to condense 200 g of a substance is -9,280 kJ ( is this correct?).
The heat required to melt 200 g of a substance is -2,860 kJ (is this correct?).
The heat required to change a 200 g substance to a liquid phase with a liquid phase specific heat capacity of 3.24 J/g K from 525 K to 352 K is 112 KJ (is this correct?).
I do not know if I am supposed to find the q for the gas phase and the solid. If so, how do I find it. I know that I have to use the q= m cs delta T but I don't know what is the final temperature of the gas phase and the initial temperature of the solid phase.
Thank you.
To construct a cooling curve for the substance with the given properties, you need to determine the heat transferred at different temperature ranges during the cooling process. Let's break down the different phases and calculate the heat transferred for each one.
1. Gas phase:
Since the specific heat capacity of the gas is given as 2.9 J/g K, you can use the equation q = m * c * ΔT to calculate the heat transferred. The mass of the substance is 200 g, and the initial temperature is not given. However, if you consider the start of the cooling process as the boiling point (525 K), you can assume that the initial temperature of the gas phase is also 525 K. To find the final temperature of the gas phase, you need more information about the cooling process.
2. Boiling point:
At the boiling point (525 K), the substance undergoes a phase change from the gas phase to the liquid phase. The molar enthalpy of condensation is given as -46.4 kJ/mol. To calculate the heat transferred during this phase change, you can use the equation q = n * ΔH, where n is the number of moles of the substance. Since the molar mass is given as 200 g/mol, you can calculate the number of moles (n) as 200 g / 200 g/mol = 1 mol. Therefore, the heat required to condense 200 g of the substance is -46.4 kJ.
3. Liquid phase:
During the cooling from the boiling point (525 K) to the freezing point (352 K), the substance remains in the liquid phase. The specific heat capacity of the liquid is given as 3.24 J/g K. You can use the equation q = m * c * ΔT to calculate the heat transferred. The mass of the substance is 200 g, and you need to calculate the change in temperature (ΔT = 525 K - 352 K = 173 K). Therefore, the heat required to change the substance to the liquid phase is 200 g * 3.24 J/g K * 173 K = 112,896 J or 112.9 kJ.
4. Freezing point:
At the freezing point (352 K), the substance undergoes a phase change from the liquid phase to the solid phase. The molar enthalpy of fusion is given as -14.3 kJ/mol. Again, using the equation q = n * ΔH, you can calculate the heat transferred during this phase change. Since you have 1 mole of the substance (200 g / 200 g/mol = 1 mol), the heat required to melt 200 g of the substance is -14.3 kJ.
5. Solid phase:
During the cooling from the freezing point (352 K), the substance remains in the solid phase. The specific heat capacity of the solid is given as 3.3 J/g K. Using the equation q = m * c * ΔT, you can calculate the heat transferred. The mass of the substance is 200 g, and you need to calculate the change in temperature (ΔT = 352 K - final temperature of the gas). Unfortunately, the final temperature of the gas phase is not provided, so you cannot calculate the heat transferred in this phase without that information.
To summarize, you have correctly calculated the heat required for the phase changes (condensation and fusion) and for the liquid phase. However, you are missing the heat transferred in the gas and solid phases due to the lack of final temperature information for the gas phase and the solid phase.