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# If the density of some lake water is $1.25gm{L^{ - 1}}$ and contains $92g$ of $N{a^ + }$ ions per kilogram of water, calculate molality of $N{a^ + }$ ions in the lake.

Last updated date: 16th Jun 2024
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Hint: Density of a substance is the measure of the mass of that substance present per unit volume. Density is inversely proportional to the volume of a substance. Molality is the measure of the number of moles of a substance present per kilogram of solvent.
Formula used: number of moles$= \dfrac{m}{M}$
molality$= \dfrac{n}{{{M_s}}}$
Where $m$ is given mass of substance, $M$ is molecular mass of substance, $n$ is number of moles,${M_s}$ is mass of solvent in kilogram

As we know the density of a substance is mass per unit volume of that substance and molality is the number of moles present per kilogram of solvent.
In this question we have given:
Density of lake water$= 1.25gm{L^{ - 1}}$
Mass of sodium ions $\left( m \right) = 92g$
Mass of solvent $\left( {{M_s}} \right) = 1Kg$
We know molecular mass of sodium $\left( M \right)$ is $23g$
Therefore number of moles of sodium ions $\left( n \right)$ is $\dfrac{m}{M}$
$\ n = \dfrac{{92}}{{23}} \\ n = 4 \\ \$
Now, we know $n = 4$ and ${M_s} = 1$ and we know formula to calculate molality (written above)
Molality of sodium ions$= \dfrac{n}{{{M_s}}}$
molality$= \dfrac{4}{1} = 4m$
So, the molality of sodium ions is $4m$.
Additional information: Sodium is a chemical element with symbol $Na$. Its atomic number is $11$. It is highly reactive due to which it is stored in kerosene oil. It reacts violently with air and water. This reaction is highly exothermic due to which hydrogen evolved catches fire. Accidents may also happen because of these reasons. To avoid such accidents this metal is stored in kerosene oil. Free State of this metal does not occur in nature and must be prepared from compounds. Many salts of sodium are water-soluble.

Note:
The terms molality and molarity are different. Molality is the measure of a number of moles present per kilogram of solvent and molarity is the measure of a number of moles present per liter of solution. In molality mass of the solvent is used and in molarity volume of solution is used.