Question

200 mL of 1M $HCl$ is mixed with 300 mL of 6M $HCl$ and the final solution is diluted to 1000 mL. The molar concentration of $\left[ {{H}^{+}} \right]$ ions is?

Answer 1

To solve this, firstly you have to calculate the number of moles of hydrochloric acid in both the solutions separately. Remember that the number of moles of $HCl$ will remain the same even after the solution is diluted to 1000 m L. Also, the molar concentration of the required ions will be the number of moles divided by the total volume.

Complete step by step solution: To solve this, we must remember that molar concentration is nothing but molarity. Molarity is basically a term that we use to describe the concentration of a solution. Molarity is given by the number of moles of solute per litre of the solution.
So, to find the molar concentration of $\left[ {{H}^{+}} \right]$ ions, firstly let calculate the number of moles of $HCl$ in both the solutions.
The first solution is 200 mL i.e. 0.2 L of 1M $HCl$. We have already discussed that molarity is the number of moles per litre of solution.
So, number of moles of $HCl$ = $0.2\times 1$ = $0.2 moles$
In the second solution, we have 300 mL i.e. 0.3 L of 6M $HCl$.
Therefore, number of moles of $HCl$ = $0.3\times 6$ = $0.18 moles$
So, the total number of moles of $HCl$ in the mixture of the two solutions = $0.18 + 0.2$ = $2 moles$.
The mixture is diluted to 1000 mL i.e. 1L. So, the molar concentration of $\left[ {{H}^{+}} \right]$ ions = $\dfrac{2}{1}$ = 2M.

Therefore, the correct answer is 2M.

Note: We should not be confused between normality, molarity and molality of a solution even though we use them for the same purpose i.e. concentration of solution. Molality is the number of moles of solute per kilogram of solvent. Normality of a solution is the gram equivalent of solute per litre of the solvent and we’ve already discussed molarity above.