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Question: If the density of some lake water is \(1.25gm{L^{ - 1}}\) and contains \(92g\) of \(N{a^ + }\) ions ...

If the density of some lake water is 1.25gmL−11.25gm{L^{ - 1}} and contains 92g92g of Na+N{a^ + } ions per kg of water, calculate the molality of Na+N{a^ + } ions in the lake.

Explanation

Solution

We can calculate the molarity of sodium ions in the lake using the moles of solute to the mass of the solvent (in kilograms). The moles of solute are nothing but the moles of sodium ions. The moles of sodium ions are calculated using the mass of sodium ions divided by the molar mass of sodium ions.

Complete step by step answer:
Given data contains,
Density of some lake water is 1.25gmL−11.25gm{L^{ - 1}}.
Mass of the sodium ion is 92g92g.
Mass of the water is 1kg1kg.
Let us now calculate the moles of the sodium ions.
We know the molar mass of sodium is 23g/mol23g/mol. Mass of sodium ion divided by the molar mass of sodium ion would give the moles of sodium ion. The formula to calculate the moles of sodium ion is written as,
Moles=GramsMolar mass{\text{Moles}} = \dfrac{{{\text{Grams}}}}{{{\text{Molar mass}}}}
Let us substitute values the grams and molar mass in the above expression to get moles of sodium ion.
Moles=GramsMolar mass{\text{Moles}} = \dfrac{{{\text{Grams}}}}{{{\text{Molar mass}}}}
Moles=92g23g/molMoles = \dfrac{{92g}}{{23g/mol}}
Moles=4molMoles = 4mol
The moles of sodium ion is 4mol4mol.
We can calculate the molality of sodium ions using the moles of sodium ions and mass of water.
So, we calculate the molality of sodium ions as,
Molality of sodium ions=No. of moles of Na+ionsMass of water(in kg) = \dfrac{{{\text{No}}{\text{. of moles of N}}{{\text{a}}^ + }{\text{ions}}}}{{{\text{Mass of water}}\left( {{\text{in kg}}} \right)}}
Molality of sodium ions=4mol1kg\dfrac{{4mol}}{{1kg}}
Molality of sodium ions=4m4m
The molality of the sodium ions in the lake is 4m4m.

Note:
We have to know the major benefit of using molality as a unit of concentration is that molality is dependent on the amounts of solute and solvent that is not affected by changes in temperature and pressure. In many applications, the molality carries a major advantage because the mass or the amount of a substance is frequently more essential than its volume. Another major advantage of molality is that the molality of one solute present in a solution is independent of the absence (or) presence of other solutes.