A solution of 6.42 g of a carbohydrate in 105.5 g of water has a density of 1.024 g/mL and an osmotic pressure of 4.61 atm at 20.0°C. What is the molar mass of the carbohydrate?

1 Answer
Jan 1, 2018

This is a fairly challenging solution problem. I think the only way to solve this is to make the approximation I did. Definitely made me scratch my head!

Let's first find the molarity,

#4.61atm = 1 * M * (0.08206L*atm)/(mol*K) * 293K#
#therefore M approx 0.192M#

Then, we'll calculate the percent mass of the carbohydrate,

#(6.42g)/(6.42g + 105.5g) approx 5.74%#

and assume we have one liter of solution, extrapolate the theoretical mass of the carbohydrate, and go from there,

#(1.024g)/(mL) * 10^3mL = 1024g * 0.0574 approx 58.7g#

of carbohydrate are theoretically in one liter.

Now, we know the molarity, so let's find the molar mass,

#0.192mol = 58.7g * 1/"MM"#
#therefore "MM" approx (306g)/(mol)#

This is a very reasonable and I'm curious to see if anyone has any other ideas. Good question!