## Ch 8 #31 (8.31)

$\Delta U=q+w$

Yuchien Ma 2L
Posts: 46
Joined: Wed Sep 21, 2016 2:58 pm

### Ch 8 #31 (8.31)

Calculate the heat released by 5.025 g of K (g) at 0.400 atm as it cools from 97.6o C to 25.0o at (a) a constant pressure and (b) constant volume. Assume that krypton behaves as an ideal gas.

Can anyone explain how to solve this?
Thanks.

janavi_patel_2K
Posts: 20
Joined: Wed Sep 21, 2016 2:59 pm

### Re: Ch 8 #31 (8.31)

The formula to calculate the heat released is q = m*C*change in temperature. To calculate the heat capacity, C, for a constant pressure, the formula is 5/2R, which gives a value of 20.8 (J/mol)/(degree C). m is for the mass of the substance so you have to get the mass in grams. To do so, you do 5.025 g of Kr divided by the molar mass of Kr, which is 83.80 g/mol, which gives a value of 0.06 g. Now, you just plug in all the values to the equation: q = (0.06 g)(20.8 J/mol * degree C ^-1)(25.0 degrees C - 97.6 degrees C) = -90.6 J.
You would do the same for part B, except the formula to calculate to heat capacity at a constant volume is 3/2 *R.

Trisha Agarwal 1O
Posts: 11
Joined: Wed Sep 21, 2016 2:56 pm

### Re: Ch 8 #31 (8.31)

To add to this, the reason why Cv is 3/2R is because if you add heat to a container filled with gas with a constant volume, the gas particles start to bounce around and store heat in their movement. They can move up and down, side to side, and essentially in the x, y, and z directions. We need to somehow incorporate this stored heat in our equation when finding heat released. As a result, we alter C by saying that Cv=Cx+Cy+Cz. Since we can flip the axes, Cx=Cy=Cz. According to the textbook, Cx=Cy=Cz=1/2R. So, if you were to plug in these values, you would get that Cv=3/2R. Hope that helps too!

Edward Suarez 1I
Posts: 75
Joined: Fri Sep 28, 2018 12:27 am

### Re: Ch 8 #31 (8.31)

janavi_patel_2K wrote:The formula to calculate the heat released is q = m*C*change in temperature. To calculate the heat capacity, C, for a constant pressure, the formula is 5/2R, which gives a value of 20.8 (J/mol)/(degree C). m is for the mass of the substance so you have to get the mass in grams. To do so, you do 5.025 g of Kr divided by the molar mass of Kr, which is 83.80 g/mol, which gives a value of 0.06 g. Now, you just plug in all the values to the equation: q = (0.06 g)(20.8 J/mol * degree C ^-1)(25.0 degrees C - 97.6 degrees C) = -90.6 J.
You would do the same for part B, except the formula to calculate to heat capacity at a constant volume is 3/2 *R.

hi i had a question about this explanation. can you . explain the "m is for the mass of the substance so you have to get the mass in gram" isn't it already given in grams, so it would give you it in mols? also why do we use g instead of kg

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