[cseil]

Hi,
here's my problem!

I have to calculate the osmotic pressure of a 1M solution of glucose in water at 25°C.
The molar volume of water is 18.05cm^3/mol.

The equation I want to use is:

[tex]\pi = \frac{-RTln(x_0)}{V_m}[/tex]

So:

[tex]\pi=\frac{RTx_1}{V_m}[/tex]

Now I have to calculate x2 in a 1M solution.
Knowing that [tex]\rho=1g/cm^3[/tex] I can write:

[tex]1000 \rho V = n_0M_0+n_1M_1[/tex]

[tex]\frac{c_1}{x_1}= \frac{n_1 1000 \rho (n_0+n_1)}{(n_0M_0+n_1M_1)n_1}[/tex]

and

[tex]x_1=\frac{n_0M_0 + n_1M_1}{1000 \rho (n_0+n_1)}[/tex]

I've put n1=1 and n0=55.55 (for a volume a 1L) and I've got x2=0.021.
I've put 0.021 into the other equation and got 28.5 atm and it's not the right answer.

I suppose the mistake is considering n1=1 and n0=55.55 but I can't understand why.

[mjc123]

Why do you assume n0 = 55.55? Do you think the glucose occupies no volume and displaces no water?
Don't assume ρ = 1 g/cc for a solution as concentrated as 1M. Look up the density: http://wiki.houptlab.org/wiki/Density_of_Sugar_Solutions
So 1L = 1066 g. What is the mass of 1 mol glucose? So what is the mass of water in 1L? How many moles?

[cseil]

Why do you assume n0 = 55.55? Do you think the glucose occupies no volume and displaces no water?
Don't assume ρ = 1 g/cc for a solution as concentrated as 1M. Look up the density: http://wiki.houptlab.org/wiki/Density_of_Sugar_Solutions
So 1L = 1066 g. What is the mass of 1 mol glucose? So what is the mass of water in 1L? How many moles?

The point is I can use only what the book says.
So I can't use a different value for density!

It is supposed to be solved just with that data.

[mjc123]

OK, so assume ρ = 1. Your assumption of n0 = 55.55 is still fallacious.
The mass of 1L of solution is n1M1 + n0M0 = 1000ρ. But substitute n1 = 1, n0 = 55.55 and ρ = 1 and you'll find the two sides are not equal. That's where you come unstuck.
I don't know where you get that complicated equation for c1/x1. If you know (or think you know) n0, then x1 is simply n1/(n1+n0) = 1/(n0+1)
So let's try again. 1L = 1000 g. What is the mass of 1 mol glucose? So what is the mass of water in 1L? How many moles?