A saturated solution contains 12.0\text{ g} of sodium hydroxide (\text{NaOH}) dissolved in… — JAMB UTME

A saturated solution contains $12.0\text{ g}$ of sodium hydroxide ( $\text{NaOH}$ ) dissolved in $500\text{ cm}^3$ of solution at $25^\circ\text{C}$ . What is the solubility of sodium hydroxide in $\text{mol dm}^{-3}$ at this temperature?
[Molar mass of $\text{NaOH} = 40.0\text{ g mol}^{-1}$ ]

A
$0.30\text{ mol dm}^{-3}$
$0.60\text{ mol dm}^{-3}$ Answer
C
$1.20\text{ mol dm}^{-3}$
D
$24.0\text{ mol dm}^{-3}$

Answer

0.60\text{ mol dm}^{-3}

To find the solubility in

\text{mol dm}^{-3}

, first determine the number of moles of

\text{NaOH}

by dividing the mass (

12.0\text{ g}

) by the molar mass (

40.0\text{ g mol}^{-1}

), yielding

0.30\text{ mol}

. Next, convert the volume to cubic decimeters (

500\text{ cm}^3 = 0.50\text{ dm}^3

). Finally, divide the amount in moles by the volume in

\text{dm}^3

to get

0.60\text{ mol dm}^{-3}

Step-by-Step Solution

Calculate the amount of

\text{NaOH}

in moles

\text{Moles} = \frac{12.0\text{ g}}{40.0\text{ g mol}^{-1}} = 0.30\text{ mol}

Solubility in

\text{mol dm}^{-3}

requires expressing the amount of solute in moles.

Convert the solution volume from

\text{cm}^3

\text{dm}^3

\text{Volume} = \frac{500\text{ cm}^3}{1000\text{ cm}^3\text{ dm}^{-3}} = 0.50\text{ dm}^3

Standard concentration units require volume expressed in cubic decimeters.

Divide the number of moles by the volume in

\text{dm}^3

\text{Solubility} = \frac{0.30\text{ mol}}{0.50\text{ dm}^3} = 0.60\text{ mol dm}^{-3}

Solubility is the maximum amount of solute in moles that dissolves per

\text{dm}^3

of solution at a given temperature.

Key Concept

Solubility calculation in mol/dm³

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