Thermodynamic Calculations for Gas Mixtures

[SAsurfa]

Hey guys I was just wondering if you could help me out as I really struggle with these thermo questions and can never figure them out, cheers for any help :)

Question 1)Air consists of 20% oxygen and 80% nitrogen (by volume). Calculate the Gibbs energy of mixing in Joules if 8 x 3.9 L of pure nitrogen is mixed with 2 x 3.9 L of pure oxygen at 1 atm pressure.

I was thinking of using the fromula G = n*R*T*ln(Xa*ln(Xa) + Xb*ln(Xb)) but I can't see how the volumes come into it? I have no chemistry background at all and I think this is why I struggle

Question 2)What is the minimum amount of energy in Joules which would be required to separate 2 x 1.6 L of pure oxygen from 10 x 1.6 L of air at 1 atm pressure?

I think this will be the same as the first one but in reverse..

Question 3)Calculate the number of grams of oxygen dissolved in 7 L of water at 25°C when it is in equilibrium with the air above it at 1 atm. (Assume Henry’s law applies and use K=4.34 x 104 atm. Note that the partial pressure of oxygen in air is 0.2 atm and 1L of water has a mass 1kg).

Question 4)Liquid Acetone and Chloroform mixtures satisfy Raoults law approximately. If the vapour pressure at 35°C of pure acetone is 347 Torr and of pure Chloroform is 293 Torr, calculate the vapour pressure in Torr of a mixture with 28 % mole fraction of Chloroform.


Cheers guys, I need all the help I can get

 

[siddharth]

1) What's the relation between the volume fraction and mole fraction? Hint: Use the ideal gas law

What have you tried for 3) and 4) ?

 

[SAsurfa]

No I haven't tried 3 and 4 but was thinking of using the formula pa = xa.pa*?

 

[siddharth]

No I haven't tried 3 and 4 but was thinking of using the formula pa = xa.pa*?

Have you read the definition of Henry's Law and do you understand what the terms mean? If you do that, you'll easily be able to figure out what to do.

 

[SAsurfa]

Hi, I still can't get the right answer so do you mind explaining the answers to me step by step as I need to know this and it would be good for revision. Cheers :)

 

[SAsurfa]

Ok for number 1 I have xa = .2 and xb = .8

Therfore if I plug into eqaution what do I use for n? is it 1 adn what do i use for T, do i just use the room temp which would be around 300K?

 

[SAsurfa]

I used n = 1 and R = 8.314 and T = 300 and got -1248.1, does that sound correct?

 

[SAsurfa]

And for question 2 I just did the same but put xa = .167 and xb = .8333 and got that G = -1123.79?

 

[SAsurfa]

Question 3 I had 7000/18 = 388.89*.2/(4.34*10^4) = .001792? Is this right, I have tried to input the answers to all these and I still get it wrong :( Please I need help urgently!

 

[siddharth]

Ok for number 1 I have xa = .2 and xb = .8

Yeah, cause the mol frac is the same as vol frac for an ideal gas. (Use the ideal gas law to show this).

Therfore if I plug into eqaution what do I use for n? is it 1 adn what do i use for T, do i just use the room temp which would be around 300K?

No, you don't use 1 mol for n.
AT STP, 22.4 L corresponds to 1 mol. So, 8 x 3.9 L corresponds to how much? Similarly, how many moles of Oxygen? So, what's the total no of moles?

And you're right in using T as room temp.

 

[SAsurfa]

So I use n = 31.2/22.4 +7.8/22.4 = 1.74mol, but where did you get 22.4 from?

 

[SAsurfa]

I got number 4 right, Ptotal = Pb* + (Pa* - Pb*)xa but am still getting the rest wrong :S

 

[siddharth]

So I use n = 31.2/22.4 +7.8/22.4 = 1.74mol, but where did you get 22.4 from?

Because, for 1 mol of gas, at 300 K, 1atm pressure, what do you get if you calculate V from the ideal gas law?

I got number 4 right, Ptotal = Pb* + (Pa* - Pb*)xa but am still getting the rest wrong :S

For question 3, can you post hery's law here and explain what each term in that means? That'll help you get the answer.