Determine the change in enthalpy in Joules for 20.0 g of heptane (C7H16) as it changes from a saturated liquid at 300 K [State 1] to a temperature of 370 K and a pressure of 58.7 kPa [State 4]; you can follow the hypothetical process path in the diagram to the right. Do not use tables of thermodynamic properties, except to check your answers. (In other words, you will not get credit for the problem if you use the tables.)
First, draw the states on a P-V or T-V diagram (4 pts). Then, calculate the DH for each step in the path using what you know about the enthalpy for each step. You might want to use the Antoine Equation to estimate the heat of vaporization of heptane at 300 K. Use the average heat capacity of heptane gas over the temperature range of interest (is this assumption valid?).
Assume heptane gas is an ideal gas at the relevant temperatures and pressures.
For the analysis section, be sure to discuss how this result differs than what you would have done using just the thermodynamics data tables, as well as the validity of your assumptions (5 pts).
HINTS: The key to the first step in this HPP is the Clausius-Clapeyron Equation. Use the Antoine equation to help you estimate the latent heat of vaporization at T1. In the second step, interpolate on the Cp data from the NIST WebBook to determine Cp(T1) and Cp(T2). Then, use the average of these two Cp's to evaluate the change in enthalpy. All you need to do is think a little bit and you will see how to evaluate ΔU34.
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7 comments:
Ok. I used the Antoine equation to estimate the vapor pressure at 300 K (for the phase change from 1 to 2) and got 0.066796 bar which equals 6.6796 kPa. Now that I have this value, what do I do with it? I am stuck right here. I know I need to use the Clausius-Clapeyron equation but I dont know what values to use in the equation.
Hi Dave,
Look at the Clausius-Clapeyron eqn. You can write it so that it is written in terms of a straight line, so dHvap/R = slope. The slope from the line would be dy/dx = (ln P2*-ln P1*)/(1/T2 - 1/T1).
You need to re-apply the Antoine equation to estimate P2* and P1*. Pick small Temperature values around your Temperature (so if it is 100 C, use 99.9 and 100.1) and calculate the P* values using those Temperatures, then plug them into the equation above.
That part makes a lot more sense now. I get a number that seems to be of the right magnitude but it is negative instead of positive. I'm not sure what that means.
Dave 7:01 PM,
I think you did it right.
Slope = -(deltaHvap/R)
So it is good that your slope turned out to be negative. That yields a latent heat of vaporization that is positive and that is correct.
This all makes sense if you think about the fact that we KNOW we must add energy to boil liquids, right ? The fact that the slope is negative tells us the vapor pressure increases as 1/T decreases. Another way to say that is that vapor pressure increases as T increases. At higher temperatures, molecules exert a greater pressure in an attempt to get out of the liquid phase and into the gas or vapor phase.
That makes perfect sense! I was leaving off a the negative in the equation. Thanks.
how do you calculate Cp?
Dear Anonymous,
You can get the Cp values from the NIST webbook. If the value is not given for your temperature, try interpolating between two Temperature values.
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