Question

Calculate the molarity of each of the ions in a solution when 3.0 litre of 4.0 M $NaCl$ and 4.0 litre of 2.0 M $CaC{l_2}$ are mixed and diluted to 10 litre.

Answer 1

Molarity of a given solution is defined as the total number of moles of solute per litre of solution.
$M = \dfrac{n}{V}$
Here,
$M$ is the molality of the solution that is to be calculated
$n$ is the number of moles of the solute
$V$ is the volume of solution given in terms of litres

Complete step by step answer:
To proceed with the question let us 1st find the number of moles of moles of $N{a^ + }$, $C{a^{2 + }}$ and $C{l^ - }$ present in the given solution,
Therefore,
Number of moles of $N{a^ + }$ ions = Molarity $\times$ Given Volume = $3 \times 4{\text{ }} = 12$
Number of moles of $C{a^{2 + }}$ ions = Molarity $\times$ Given Volume = $2 \times 4{\text{ }} = 8$
Number of moles of $C{l^ - }$ ions = Molarity $\times$ Given Volume = $3 \times 4 + 2 \times 4 \times 2{\text{ }} = 28$(because $C{l^ - }$ ions are present in both solution, therefore we need to add the number of moles of $C{l^ - }$ of both solution in order to find the number of moles).
As per the given question total volume of the mixture = 10L
Therefore, molarity of $N{a^ + }$, $C{a^{2 + }}$ and $C{l^ - }$ in 10L of solution is given by the formula =
$M = \dfrac{n}{V}$
Where,
$M$ is the molality of the solution that is to be calculated
$n$ is the number of moles of the solute
$V$ is the volume of solution given in terms of litres
Molarity of $N{a^ + }$ ions =$M = \dfrac{n}{V} = \dfrac{{12}}{{10}} = 1.2{\text{M}}$
Molarity of $C{a^{2 + }}$ ions =$M = \dfrac{n}{V} = \dfrac{8}{{10}} = 0.8{\text{M}}$
Molarity $C{l^ - }$ ions =$M = \dfrac{n}{V} = \dfrac{{28}}{{10}} = 2.8{\text{M}}$
Note:
Molarity is the number of moles of a solute per litre of solution and Molality is the number of moles of solute in 1 kg of solvent. Therefore, the relationship between Molarity and Molality is given by:
$m = \dfrac{{M \times 1000}}{{(d \times 1000) - M \times {M'}}}$
Where,
$m$= Molality
$M$= Molarity
$d$= Density
${M'}$= Molar mass of solute