Answer to Question #113933 in General Chemistry for Jonathan

Question

9.) A 50 ml solution of unknown base has 2.92 g/L of base in solution. Calculate the molar mass of the solution, and use that to calculate the concentration and pH of the solution.

Answer 1

Calculate the molar concentration of the solution:

$$c=\frac{n}{V}=\frac{m}{\Mu V}=\frac{\rho}{\Mu}.$$

The molar mass is

$$\Mu=\frac{m}{n}.$$

We could find the amount of substance by dividing the solution volume by the molar volume

$$n=\frac{V}{V_m}.$$

but it works for gases only. Therefore, without knowing the amount of substance of the base, it is impossible to solve this problem.

If we could find the concentration, since we deal with base, we could calculate the pOH:

$$\text{pOH}=-\text{log}[OH^-]-\text{log}[c].$$

We know that

$$\text{pOH}+\text{pH}=14,\\ \text{pH}=14-\text{pOH}=14+\text{log}[c]=14+\text{log}\bigg[\frac{\rho}{\Mu}\bigg].$$