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.

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.