# Ideal gas

1. Aug 28, 2009

### songoku

1. The problem statement, all variables and given/known data
A can filled with nitrogen has pressure 10 Pa, volume 10 cm3, and temperature 300 K.
(i) Find the volume at STP
(ii) Find the mass of the nitrogen
(iii) Find the change of pressure over temperature at 300 K
(iv) Find the energy of each molecule of nitrogen

2. Relevant equations
PV = nRT

3. The attempt at a solution
(i)
$$\frac{P_1 V_1}{P_2 V_2}=\frac{n_1 R T_1}{n_2 R T_2}$$

Assuming n1=n2 : ------> Is this right ?

$$\frac{10*10}{10^5*V_2}=\frac{300}{273}$$

$$V_2=2.73 x 10^{-3}\; m^3$$

(ii)
P1V 1= nRT1
10*10-5=n *8.31* 300
n = 4.011 x 10-8 mole

m = n*Mr = 4.011 x 10-8*28 = 1.12308 x 10-6

(iii) Is the question asking the change at 300 K compared to STP ?

$$\frac{\Delta P}{\Delta T}=\frac{P_2-P_1}{V_2-V_1}=\frac{10-10^5}{10^{-5}-2.73 x 10^{-3}}\approx 3.68 x 10^7 \frac{Pa}{m^3}$$ ??

(iv)
$$E=\frac{3}{2}nRT$$

Not sure about using T = 300 K or T = 273 K (STP)

Thanks

2. Aug 28, 2009

### kuruman

(i) Incorrect input value for volume - should be in m3. Also, the value "2.73" is suspicious. The ratio 300/273 is close to one and the other side is all powers of 10.

(ii) Mass calculation looks OK, but no units are given.

(iii) Method OK but calculation needs to be redone because it depends on answer in (i).

(iv) 300 K is not much different from 273 K. Expression is incorrect. You are asked to find the energy per molecule, not the total energy.

3. Aug 28, 2009

### songoku

Hi kuruman

I've revised my answer for the (i), (ii), and (iii) according to your correction :)

For the last one :

$$\text{Energy per molecule}=\frac{3}{2}\frac{nRT}{N_A} ??$$

Thanks

4. Aug 29, 2009

### kuruman

For the total energy of an ideal gas, I prefer the form

$$E = \frac{3}{2}N k T$$

where N is the number of molecules and k the Boltzmann constant. Then the energy per molecule is simply
$$\epsilon = \frac{3}{2}k T$$

5. Sep 6, 2009

### songoku

Hi kuruman

Ok I get it now.

Thanks a lot for your help