Question

500mL of a 0.2M solution has 200mL of water added to it. What is the resulting molarity of the solution?
A) $0.5\,M$
B) $0.28\,M$
C) $0.70\,M$
D) $0.14\,M$
E) $0.48\,M$

Answer 1

Whenever we say mass or volume of the solution, you need to add the respective masses and volumes of all the components of the solution. Do NOT commit the error of taking the mass or volume of only the solute or solvent in the denominators of the above expressions.
The concentration of a solution is most of the time expressed as the number of moles of solute present in $1\,L$ of the solution
Molarity: Number of moles of solute present per liter of solution.

Complete step by step solution:
Equation for dilution
${M_1}{V_1} = {M_2}{V_2}$
${M_1}$ =initial molarity =$0.2M$
${V_1}$ = initial volume = $500\,mL$
${M_2}$= final molarity=?
${V_2}$=final volume = $500\,mL$ + $200\,mL$ = $700\,mL$
$0.2 \times 500 = {M_2} \times 700$
${M_2} = \dfrac{{{M_1}{V_1}}}{{{V_2}}} = \dfrac{{500 \times 0.2}}{{700}} = 0.14M$

**The correct option is D. $0.14M$

Note: **
Dilution is the process whereby the concentration of a solution is lessened by the addition of solvent. For example, we might say that a glass of iced tea becomes increasingly diluted as the ice melts. The water from the melting ice increases the volume of the solvent (water) and the overall volume of the solution (iced tea), thereby reducing the relative concentrations of the solutes that give the beverage its taste
Dilution is also a common means of preparing solutions of the desired concentration. By adding solvent to a measured portion of a more concentrated stock solution, we can achieve a particular concentration.
Equation for dilution is ${C_1}{V_1} = {C_2}{V_2}$