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

The molarity of this
`\rm NaOH` solution is approximately
`13.0\; \rm mol \cdot L^(-1)`.

Step-by-step 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 = (m)/(M) = (521\; \rm g)/(39.997\; \rm g \cdot mol^(-1)) \approx 13.0\; \rm mol`.

Apply the equation
`\displaystyle c = (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 &= (n)/(V) \\ &\approx (13.0\; \rm mol)/(1\; \rm L) = 13.0\; \rm mol\cdot L^(-1)\end{aligned}`.