# 74.0 ml of a 1.70 M solution is diluted to a total volume of 248 ml . A 124 ml portion n of that...

## Question:

{eq}\displaystyle 74.0 \text{ ml of a } 1.70 M {/eq} solution is diluted to a total volume of {eq}\displaystyle 248 \text{ ml . A } 124 ml \text{ portion } n {/eq} of that solution is diluted by adding {eq}\displaystyle 109ml {/eq} of water. What is the final concentration? Assume the volumes are additives.

## Principle of Dilution:

Dilution is a process in which more solvents are added to a solution, keeping the mass of the solute constant. As the volume increases during the addition of solvent, therefore, the concentration of solute in the solution decreases.

## Answer and Explanation: 1

According to the law of dilution, the following relation is obtained:

{eq}\rm C_1V_1=C_2V_2 {/eq}

- {eq}\rm C_1\;and\;C_2 {/eq} are the initial and final concentrations of a solution, respectively.

- {eq}\rm V_1\;and\;V_2 {/eq} are the initial and final volumes of a solution, respectively.

**1st dilution**

The following values are given:

{eq}\rm C_1=1.70\;M\\ \rm V_1=74.0\;mL\\ \rm V_2=248\;mL {/eq}

Substituting the above values, we get:

{eq}\rm (1.70\;M)\times (74.0\;mL)=C_2\times (248\;mL)\\ \rm \Rightarrow C_2=0.5073\;M {/eq}

Hence, the concentration of 248 mL diluted solution is 0.5073 M.

**2nd dilution**

As the volumes are additive, therefore, the final volume of solution is (124+109) mL or 233 mL. Hence, we can write:

{eq}\rm C_1=0.5073\;M\\ \rm V_1=124\;mL\\ \rm V_2=233\;mL {/eq}

Substituting the above values, we get:

{eq}\rm (0.5073\;M)\times (124\;mL)=C_2\times (233\;mL)\\ \rm \Rightarrow C_2=0.270\;M {/eq}

**Conclusion:**

The final concentration is **0.270 M**.

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Chapter 8 / Lesson 5Want to know how to calculate dilution factor? See dilution equations, the dilution formula, and learn how to dilute acid and how to dilute a solution.

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