Question

Sodium hydroxide is extremely soluble in water. At a certain temperature, a saturated solution contains 521 g of NaOH(s) per liter of solution. Calculate the molarity of this saturated NaOH(aq) solution.

Answer 1

Answer:

The molarity of this $\rm NaOH$ solution is approximately $13.0\; \rm mol \cdot L^{-1}$.

Explanation:

The molarity of a substance gives its quantity (in number of moles) in each liter of the solution.

According to the question, there are $521\; \rm g$ of $\rm NaOH$ in each liter of this solution. The goal is to find the number of moles of formula units in that

$\rm NaOH$ contains three elements: Na, O, and H. Look up a modern periodic table for the relative atomic mass of each element:

• Na: 22.990.
• O: 15.999.
• H: 1.008.

Calculate the formula mass of $\rm NaOH$.

$M(\rm NaOH) = 22.990 + 15.999 +1.008 = 39.997\; \rm g \cdot mol^{-1}$.

That's the mass of each mole of $\rm NaOH$ formula units. Calculate the number of moles of formula units in that $521\; \rm g$ of

$\displaystyle n = \frac{m}{M} = \frac{521\; \rm g}{39.997\; \rm g \cdot mol^{-1}} \approx 13.0\; \rm mol$.

Apply the equation $\displaystyle c = \frac{n}{V}$ to find the molar concentration $c$ of this solution. In this equation, $n$ is the number of moles of the solute, and $V$ is the volume of the solution.

$\begin{aligned}c &= \frac{n}{V} \\ &\approx \frac{13.0\; \rm mol}{1\; \rm L} = 13.0\; \rm mol\cdot L^{-1}\end{aligned}$.