Question

Two solutions of $1M$ $CaC{l_2}$ and $2M$ $AlC{l_3}$ were mixed in volume ratio of $1:2$ , calculate the concentration of $C{l^ - }$ in the resulting mixture:
A. $4.20M$
B. $4.50M$
C. $4.66M$
D. $4.95M$

Answer 1

Hint: Calcium chloride ($CaC{l_2}$) is a chemical compound consisting of one calcium divalent ion and two chloride monovalent ions in it. Similarly, aluminium chloride ($AlC{l_3}$) is a chemical compound consisting of one aluminium trivalent ion and three chloride monovalent ions.

Complete step by step answer:
The dissociation of calcium chloride in the solution into its corresponding ions takes place according to the following reaction:
$CaC{l_2} \to C{a^{2 + }} + 2C{l^ - }$
Similarly, the dissociation of aluminium chloride in the solution into its corresponding ions takes place according to the following reaction:
$AlC{l_3} \to A{l^{3 + }} + 3C{l^ - }$
According to the question, $1M$ $CaC{l_2}$ and $2M$ $AlC{l_3}$ were mixed in volume ratio of $1:2$.
Let the volume of calcium chloride be $x$ litres and the volume of aluminium chloride be $2x$ litres.
As we can see from the dissociation of calcium chloride, $1mole$ of $CaC{l_2}$ gives $2moles$ of $C{l^ - }$ ions.
So, in $x$ litres of $1M$ of $CaC{l_2}$solution = $2x$ moles of $C{l^ - }$ ions are present.
As we can see from the dissociation of aluminium chloride, $1mole$ of $AlC{l_3}$ gives $3moles$ of $C{l^ - }$ ions.
In $2M$ $AlC{l_3}$ solution = $2 \times 3 = 6moles$ of $C{l^ - }$ ions are present.
So, in $2x$ litres of $2M$ of $AlC{l_3}$solution = $2x \times 6 = 12x$ litres of $C{l^ - }$ ions are present.
Total moles of chloride ions in the resultant mixture of calcium chloride and aluminium chloride = $(12x + 2x)moles$ of $C{l^ - }$ ions.
Total volume of mixture = $(x + 2x)l = 3x$ litres
The concentration of chloride ions = $\dfrac{n}{V}$
Where, $n = $ number of moles of chloride ions in the mixture
$V = $ volume of mixture
$[C{l^ - }] = \dfrac{n}{V} = \dfrac{{2x + 12x}}{{3x}} = \dfrac{{14}}{3} = 4.66mol/l$
Thus, the correct option is C. $4.66M$ .

Note:
In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration.