Question
$$25.3\,g$$ of sodium carbonate, $$N{a_2}C{O_3}$$ is dissolved in enough water to make $$250\, mL$$ of solution. If sodium carbonate dissociates completely, molar concentration of sodium ion, $$N{a^ + }$$ and carbonate ion, $$CO_3^{2 - }$$ are respectively ( Molar mass of $$N{a_2}C{O_3} = 106\,g\,mo{l^{ - 1}}$$ )
A.
$$0.955\,M\,{\text{and}}\,1.910\,M$$
B.
$$1.910\,M\,{\text{and}}\,0.955\,M$$
C.
$$1.90\,M\,{\text{and}}\,1.910\,M$$
D.
$$0.477\,M\,{\text{and}}\,0.477\,M$$
Answer :
$$1.910\,M\,{\text{and}}\,0.955\,M$$
Solution :
$$\eqalign{
& {\text{Molarity}} \cr
& = \frac{{{\text{Number of moles of solute}}}}{{{\text{Volume of solution (in }}mL{\text{)}}}} \times 1000 \cr
& = \frac{{25.3 \times 1000}}{{106 \times 250}} \cr
& = 0.9547 \approx 0.955\,M \cr} $$
$$N{a_2}C{O_3}$$ in aqueous solution remains dissociated as
$$\mathop {N{a_2}C{O_3}}\limits_x \rightleftharpoons \mathop {2\,N{a^ + }}\limits_{2x} + \mathop {CO_3^{2 - }}\limits_x $$
Since, the molarity of $$N{a_2}C{O_3}$$ is $$0.955\,M,$$ the molarity of $$CO_3^{2 - }$$ is also $$0.955\,M$$ and that of $$N{a^ + }$$ is $$2 \times 0.955 = 1.910\,M$$