# Question #140c8

Feb 12, 2015

In Chemistry, ${V}_{f} \mathmr{and} {V}_{i}$ mean final volume and initial volume, and have to do with the dilution of solutions, where ${M}_{i} {V}_{i} = {M}_{f} {V}_{f}$. ${M}_{i}$ = initial concentration in moles/L, and ${M}_{f}$ = the final concentration in moles/L. If you know three of the four variables, you can calculate the unknown.

Example: What is the concentration of a solution prepared by diluting 25.0 mL of 6.00 M HCl to a total volume of 50.0 mL?

Given:
${V}_{i} = \text{25.0 mL}$
${M}_{i} = \text{6.00 M = 6 mol/L}$
${V}_{f} = \text{50.0 mL}$

Unknown:
${M}_{f}$

: Equation:
${M}_{i} {V}_{i} = {M}_{f} {V}_{f}$

First we need to convert given volume to liters (because molarity is mol/L).
${V}_{i} = \text{25.0 mL x 1L/1000 mL= 0.0250 L}$
${V}_{f} = \text{50.0 mL x 1L/1000mL=0.0500 L}$

Solution:
${M}_{i} {V}_{i} = {M}_{f} {V}_{f}$

Rearrange the variables and isolate ${M}_{f}$. Solve for ${M}_{f}$.

${M}_{f} = \frac{{M}_{i} {V}_{i}}{{V}_{f}} = \text{6.00 mol/L x 0.0250 L"/"0.0500L"="3.00 mol/L} = 3.00 M$