-1
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ Hint: Osmolarity is osmotic molarity. Molarity is ... The adjective osmotic means... $\endgroup$ – Poutnik Oct 20 at 7:22
1
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.