## Question 8.31: a monatomic ideal gas at constant P or V

Therese Abely 3A
Posts: 21
Joined: Fri Sep 25, 2015 3:00 am

### Question 8.31: a monatomic ideal gas at constant P or V

For question 8.31, it states "calculate the heat released by 5.025 g of Kr(g) at .400 atm as it cools from 97.6 C to 25.0 C at (a) constant pressure and (b) constant volume. Assume that neon behaves as an ideal gas."

Now when I looked up the answer in the answers book, it says for part (a) Cp,m = (5/2) R, and I am very confused as to where the 5/2 came from and what that even means? Why is writing this formula even necessary? because then the answers goes on to just say q =[5.025g/(83.80 g x mol^-1)] x (25.0C-97.6C) x (20.8 J x mol^-1 x C^-1) = -90.6 J

Also, where did the 20.8 J x mol^-1 x C^-1 come from? Is this just a value I would have to look up?

Thank you!

Natalie Yakobian
Posts: 45
Joined: Fri Sep 25, 2015 3:00 am

### Re: Question 8.31: a monatomic ideal gas at constant P or V

Hi,
For Gas molecules at

Constant Pressure the Heat Capacity can be found by the formula (5/2)R

Constant Volume the Heat Capacity can be found by the formula (3/2)R

We use this to get the Cm in this problem so then we can find q = nxCmxdeltaT

Hope this helps

Bryan Nguyen 1A
Posts: 20
Joined: Fri Sep 25, 2015 3:00 am

### Re: Question 8.31: a monatomic ideal gas at constant P or V

In section 7.10 A Molecular Interlude: The Origin of the Heat Capacities of Gases (sorry, I have 5th edition),
Cv, m is (3/2)R for atoms, (5/2)R for linear molecules, and 3R for nonlinear molecules, and
Cp, m is (5/2)R for atoms, (7/2)R for linear molecules, and 4R for nonlinear molecules.
I'm not 100% sure if we need to remember these values, though.

The book has an explanation on how it got the equations and what they mean, but I'm not sure how to rephrase it in a simpler way.

You get 20.8 J x mol^-1 x K^-1 (it should be K instead of C, but you can convert the unit of delta T to K) from the (5/2)R since (5/2) x (Gas constant R = 8.314 J x mol^-1 x K^-1) = 20.8 J x mol^-1 x K^-1).

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