# How to find osmolarity of a solution contatining salt and glucose?

What is the osmolarity of a solution that contains $$4.00\%$$ (m/v) $$\ce{NaCl}$$ $$(M = \pu{58.44 g mol-1})$$ and $$3.00\%$$ (m/v) glucose $$(M = \pu{180.18 g mol-1})?$$

I know you have to convert percentages to mass soultion/Liter solution and multiply by number of moles in $$\ce{NaCl},$$ which is 2 moles:

$$\pu{2 osmol}$$ $$\ce{NaCl}$$ / $$\pu{1 mol}$$ $$\ce{NaCl}$$

but I'm being thrown off by being given molar mass.

• Hint: Osmolarity is osmotic molarity. Molarity is ... The adjective osmotic means... – Poutnik Oct 20 '19 at 7:22

Let's begin by finding the molarity of each solute in that solution. We'll get to osmolarity later.

## NaCl

The concentration of NaCl given in the problem is $$0.04 \frac{\text{g}}{\text{mL}}=40 \frac{\text{g}}{\text{L}}$$. We can divide by the molar mass, getting $$\frac{40\text{g}}{\text{L}}\cdot\frac{\text{mol}}{58.44\text{g}}\approx0.6845\text{ M.}$$ (M represents molar, or mol/L.)

## Glucose

The concentration of glucose given in the problem is $$0.03 \frac{\text{g}}{\text{mL}}=30 \frac{\text{g}}{\text{L}}$$. We can divide by the molar mass, getting $$\frac{30\text{g}}{\text{L}}\cdot\frac{\text{mol}}{180.18\text{g}}\approx0.1665\text{ M.}$$

It is at this point that we consider the distinction between osmolarity and molarity.

According to Wikipedia,

$$\text{osmolarity}=\displaystyle\sum_{i}\phi_in_iC_i$$

where

• $$\phi$$ is the osmotic coefficient, which accounts for the degree of non-ideality of >the >solution. In the simplest case it is the degree of dissociation of the solute. >Then, $$\phi$$ is between 0 and 1 where 1 indicates 100% dissociation. However, $$\phi$$ can >also be larger than 1 (e.g. for sucrose). For salts, electrostatic effects cause $$\phi$$ >to be smaller than 1 even if 100% dissociation occurs (see Debye–Hückel equation);
• n is the number of particles (e.g. ions) into which a molecule dissociates.
• C is the molar concentration of the solute;
• the index i represents the identity of a particular solute.

For the moment, we are going to ignore $$\phi$$ and assume that that everything dissociates perfectly. We can make this assumption because glucose and NaCl generally dissolve near-completely in water.

From that, we get $$\text{osmolarity}=\displaystyle\sum_{i}n_iC_i=n_\text{NaCl}C_\text{NaCl}+n_\text{glucose}C_\text{glucose}$$

We know that NaCl dissociates into two ions: Na$$^+$$ and Cl$$^-$$, so $$n_\text{NaCl}=2.$$ Glucose, however, does not dissociate, but rather stays as a single molecule. Therefore, $$n_\text{glucose}=1.$$

We now have $$\text{osmolarity}=2\cdot0.6845+1\cdot0.1665=\boxed{1.5355 \text{ osmolar}}$$