PCHEM Workshop 1 Notes

First workshop with Dineli for Physical Chemistry (CHEM 3321) with Dr. Nielsen at UT Dallas!

To anyone reviewing my notes: Please feel free to reach out if you need any clarification on anything I wrote! I know the cursive can get a bit sloppy at times, especially when I’m trying to write quickly!

If you want to contact me for more information/ any clarification/ to start a study group/ need talk to someone… please comment below, DM me on Instagram, or send an email by clicking this link, the icon in the top right corner, or manually typing out breealbright@gmail.com.

FIRST WORKSHOP WITH DINELI | August 27, 2019

Be sure to check Dineli’s page as she mentioned that she would upload some of her notes online. These are not the complete answers for the problem set. Make sure you plug and chug to get the individual answers!

SIG FIGS, UNITS, OTHER FUNDAMENTALS

Dineli already had this information written down/ prepared. She said that she would be posting it online for us to review. I tried to write as much as I could here, but she breezed through it to get to the actual homework for the week!

PROBLEM 1 – IDEAL GAS LAW

1 a) What mass of helium is contained in a 25.0 L flask at 25.0 ◦C under 5.00 atm pressure? Please follow the accepted rules for significant figures.

1 b) What is the density, in g/L, of methane at 5.0 atm and 50.0 ◦C?

1 c) What is the volume, in mL, occupied by a mixture of 4.50 g of O2 and 7.00 g of CO2 at a temperature of 22.0 ◦C and a (total) pressure of 48.2 atm?

PROBLEM 2VAN DER WAALS EQUATION OF STATE

Repeat problem 1 using the van der Waals equation of state. You will need to use Table 16.3 in your textbook. Also, since the equations are more complicated, I recommend you use a simple online math program to help, for example WolframAlpha, www.wolframalpha.com. For part (c) you may assume Dalton’s Law of Partial Pressures.

2 a) What mass of helium is contained in a 25.0 L flask at 25.0 ◦C under 5.00 atm pressure? Please follow the accepted rules for significant figures.

Here’s the WolframAlpha link to the factored equation needed for this problem!

2 b) What is the density, in g/L, of methane at 5.0 atm and 50.0 ◦C?

Note: I wrote a couple of things wrong while trying to keep up in the workshop. 1) The boxed equation that I have labelled as equation (1) should follow the standard form of V^3 – V^2 + V – n = 0. I mistakenly wrote a positive sign after V^3, but that should be negative. 2) The units for a and b are incorrect. (a = dm^6 atm mol^-2 and b = dm^3 mol^-1)

Here is the WolframAlpha link to the factored equation needed for this problem!

2 c) What is the volume, in mL, occupied by a mixture of 4.50 g of O2 and 7.00 g of CO2 at a temperature of 22.0 ◦C and a (total) pressure of 48.2 atm?

Note: wrong units again ~ the units for b of O2 is incorrect. (b = dm^3 mol^-1)

I’d like to note – I ended up with slightly different numbers from what’s on Dineli’s website, as I rounded differently… but here’s the Wolfram Alpha link that I used to solve this problem! When you are selecting which of the factors to use for your answer, keep in mind that the answer to this problem will be close to the answer to (1 c), so pick the number closer to 15 mL! The exact value you get will vary depending on how you rounded throughout the problem, so just plug your equation into WolframAlpha and see what your answer is. Don’t forget to change from L to mL!

PROBLEM 3 – IDEAL GAS PROPERTIES

3 a) The coefficient of thermal expansion α is defined as:

Calculate α for an ideal gas. Show that your expression simplifies to α = 1/T.

Note on equation A: This could be left simply as (V bar = RT/P). I think I included (V bar = V/n) because I was anticipating solving for a value as Dineli was reviewing this problem in the workshop. While this is not incorrect information, it is excess information so it is unnecessary to include in your notes/ write up!

3 b) The isothermal compressibility κ is defined as:

Calculate κ for an ideal gas. Show that your expression simplifies to κ = 1/P.

PROBLEM 4 – VAN DER WAALS EQUATION OF STATE PROPERTIES

Repeat problem 3 using the van der Waals equation of state. (You will not be able to simplify the resulting expressions.)

4 a) The coefficient of thermal expansion α is defined as:

Calculate α for an ideal gas. Show that your expression simplifies to α = 1/T.

4 b) The isothermal compressibility κ is defined as:

Calculate κ for an ideal gas. Show that your expression simplifies to κ = 1/P.

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