What is the osmotic pressure of a solution of 12.5g of sucrose in 225g water at 50 degrees C? Assume the density of the solution is 1g/ml.

Question

I got 4.30 atm but its wrong where did i mess up

12.5g x 1 mol/342 g / 0.225 L = 0.162

R = 0.08206 Latm/Kmol

T = temperature in K = 50ºC + 273 = 323K

π = (1)(0.162 mol/L)(0.0821 Latm/Kmol)(323K) = 4.30 atm

Answer 1

I don't see anything wrong with your approach. The only possibility might be that the problem states that the density of the SOLUTION is 1g/ml. Using this, I still arrive at the same answer that you have, i.e. 0.162 M sucrose. Using π = iMRT and substituting 1 for i (van't Hoff factor), 0.162 for M, 0.0821 Latm/Kmol for R and 323K for T, a value of 4.296 atm if obtained. Rounding this to 3 significant figures is 4.30 atm. Is it possible that they want the answer reported to 1 significant figure based on 1 g/ml density? If so, it would round to 4 atm. Other than those possibilities, I don't see how to correct the answer.

I certainly hope whoever wrote the question didn't expect you to calculate molality instead of molarity. Usually when a problem gives mass of water, it is so you can find kg and calculate molality. But osmotic pressure is not based on molality, but rather on molarity.

Answer 2

Hi Cassie R.,

It looks fine to me, unless your teacher is out to grind the concept of significant figures into you. In that case, the "1 g/mL" might be rounded, as opposed to exact, and you wouldn't be justified in keeping more than 1 significant digit of answer (4 atm), would you. You COULD probably look up densities of sucrose solutions vs. concentration and temperature, to address that definitively?

By the way, significant digits are only an approximation of how scientists calculate the propagation of indeterminate error (when it is known for each datum supplied) through a calculation. A slightly more involved way might be to check the result at the limits for each of the +/- ranges (appropriately picked to generate extremes of the answer); but for the most accurate work, every figure used in the calculation arrives with its own stated range of indeterminate error (as a standard deviation), and these combine in known mathematical ways ("propagate" through a calculation). Probably not where you need to be, right now, though!

Not a bad idea to check, you have an app online: http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/ospcal.html .

Cheers, -- Mr. d.