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## Chapter 5: Solution Chemistry

### Chapter 5: Solution Chemistry

A protein solution with concentration 80 g/L has an osmotic pressure of 0.0205 atm at 27oC. What is the approximate molecular weight of the protein? (The gas constant is 0.082 L-atm/K-mol.)

A) 96,000
B) 192,000
C) 48,000
D) 1,500

Explanation: n/V = Π/RT
= 0.0205 / (0.082 x 300)
= 0.00083 M
Now, 1 L contains 80 g of protein.
Therefore, mw = 80 g / 0.00083 mol
= 96,000 g/mol

Hi there, as we can see from the explanation above, the value of 0.0205 has been given as the value of V, how is this possible, when 0.0205 is in atm, therefore one would assume it is used for pressure....can anyone explain

Thanks
Legend786

Posts: 6
Joined: Tue Apr 01, 2014 12:14 am

### Re: Chapter 5: Solution Chemistry

"the value of 0.0205 has been given as the value of V, how is this possible, when 0.0205 is in atm, therefore one would assume it is used for pressure."
- You are correct to assume that 0.0205 atm is pressure, in fact, the question stem says "osmotic pressure of 0.0205 atm" and the symbol for osmotic pressure is Π (as opposed to V being the symbol for volume).

Thus: Π/RT = 0.0205 / (0.082 x 300) = 0.00083 M (notice that R is given and all the units are correct; also notice the value of T in degrees kelvin being 27 + 273 = 300)

Now here comes part 2. Now we will evaluate the left hand side of the equation which is = n/V

We are given a solution with a concentration of 80 g/L meaning that 1 L contains 80 g of protein. So we take V = volume = 1 L.

Now our equation simplifies to n = 0.00083 M

We know it Chemistry that n = (mass)/(molecular weight) or you can determine this by dimensional analysis since:

moles = (grams) / (grams/mole)

Since we have a mass of 80 g, we get:

n = 80/mw = 0.00083 mol

Therefore, mw = 80 g / 0.00083 mol
= 96,000 g/mol

Side notes:
- There is very little to memorize here, it is mostly dimensional analysis making it a common type of GAMSAT question in chem/phys.
- Please post future questions in one of the sticky chapter threads (for example, you'll find there is a thread already for Chapter 5: Solution Chemistry). Thanks.
goldstanda3269

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Joined: Wed Aug 25, 2010 10:59 pm

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