Question

The problem involves mixing two $\mathrm{HCl}$ solutions of different molarities in a given volume ratio. Here's the step-by-step solution:

Given:

  • $1 \mathrm{M}$ $\mathrm{HCl}$
  • $2 \mathrm{M}$ $\mathrm{HCl}$
  • Volume ratio of $4:1$

Let the volume of $1 \mathrm{M}$ $\mathrm{HCl}$ be $4V$ and the volume of $2 \mathrm{M}$ $\mathrm{HCl}$ be $1V$.

The total volume $V_{\text{total}}$ of the mixture is: $$ V_{\text{total}} = 4V + 1V = 5V $$

The number of moles of $\mathrm{HCl}$ from each solution:

  • From $1 \mathrm{M}$ $\mathrm{HCl}$: $$ \text{Moles} = \text{Molarity} \times \text{Volume} = 1 \times 4V = 4V $$
  • From $2 \mathrm{M}$ $\mathrm{HCl}$: $$ \text{Moles} = \text{Molarity} \times \text{Volume} = 2 \times 1V = 2V $$

The total number of moles of $\mathrm{HCl}$ in the mixture: $$ \text{Total moles} = 4V + 2V = 6V $$

The molarity of the final solution is: $$ \text{Molarity} = \frac{\text{Total moles}}{\text{Total volume}} = \frac{6V}{5V} = 1.2 \mathrm{M} $$

Thus, the final molarity of the $\mathrm{HCl}$ solution is:

C. $1.2$

✨ Free AI Tools for You

Powered by Chatterbot AI

Answer

To determine the molarity of the resulting $\mathrm{HCl}$ solution when mixing $1 \mathrm{M}$ $\mathrm{HCl}$ and $2 \mathrm{M}$ $\mathrm{HCl}$ in a $4:1$ volume ratio:

  1. Calculate the moles of $\mathrm{HCl}$ in each solution being mixed:

    • For $1 \mathrm{M}$ $\mathrm{HCl}$:

      Let the volume be $4V$, thus total moles = $1 \mathrm{M} \times 4V = 4V$.

    • For $2 \mathrm{M}$ $\mathrm{HCl}$:

      Let the volume be $V$, thus total moles = $2 \mathrm{M} \times V = 2V$.

  2. Add the moles together to find the total moles of $\mathrm{HCl}$ in the mixture: $$ \text{Total moles} = 4V + 2V = 6V $$

  3. Determine the total volume of the mixed solution: $$ \text{Total volume} = 4V + V = 5V $$

  4. Calculate the final molarity of the solution: $$ [\mathrm{HCl}] = \frac{\text{Total moles}}{\text{Total volume}} = \frac{6V}{5V} = 1.2 \mathrm{M} $$

Therefore, the final molarity of the $\mathrm{HCl}$ solution is $1.2 \mathrm{M}$.

Final Answer: C


Was this helpful?

India's 1st AI Doubt Solver for CBSE, JEE, and NEET

Ask a Question for Free

and then it's just ₹212 a month