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The concentration (molarity) of the solution changes as the temperature changes, and this concentration change at a given temperature is estimated using a mathematical procedure called the correction for thermal expansion.

$\frac{C\text{'}}{d}=\frac{c}{d}$,

where,

$C\text{'}$is the concentration of the solution at the applied temperature,

role="math" localid="1663310790523" $d\text{'}$is the density of the solution at the applied temperature,

c is the concentration of the solution at the applied temperature, and

d is the density of the solution at the applied temperature.

Given:

The concentration of ${\mathrm{KMnO}}_4$at $24掳C$is 0.05138M .

The density of water at $24掳C$is 0.997299g/mL .

The density of water at $16掳C$is 0.997299g/mL .

The correction for thermal expansion is

$\frac{c\text{'}}{d}=\frac{c}{d}$.

The concentration and density of water at $16掳C$and $24掳C$are plugged into the above equation, and some rearrangement is performed to produce the concentration of potassium permanganate ( $KMn{O}_4$) at $16掳C$.

$\frac{\mathrm{c}\text{'}\mathrm{at}16掳\mathrm{c}}{0.9989460\mathrm{g}/\mathrm{mL}}=\frac{0.05138\mathrm{M}}{0.9972995\mathrm{g}/\mathrm{mL}}$

$C\text{'}$at$16掳\mathrm{C}=\frac{0.05138\mathrm{M}}{0.9972995\mathrm{g}/\mathrm{mL}}脳0.9989460\mathrm{g}/\mathrm{mL}$

$=0.05146\mathrm{M}$.

Thus, the concentration of potassium permanganate ( ${\mathrm{KMnO}}_4$) at $16掳C$is $0.05146\mathrm{M}$.