Question

Calculate the final Molarity when $2.0L$ of $3.0M$ Sugar solution and $3.0L$ of $2.5M$ sugar solution are mixed and then diluted up to $10liters$ with water.

Answer 1

Molarity is an intrinsic property and changes from solution to solution and hence cannot be added directly when two solutions are mixed but, molarity depends on the number of moles which can be added directly. Hence, The number of moles in the new solution should be equal to the number of moles in solutions being mixed.
Formula used:
${M_3}{V_3} = {M_1}{V_1} + {M_2}{V_2}$
$M = Molarity,V = Volume$

Complete step by step answer:
Let us first understand what Molarity means and how it is affected when mixing takes place.
Molarity is a unit which is used to represent concentration.
$Molarity = \dfrac{{number\,of\,moles\,of\,solute}}{{Volume\,of\,solution}}$
This formula can be rearranged to determine the value of Molarity for the number of moles in the solute.$number\,of\,moles = Molarity(M) \times Volume(V)$
The number of moles in a solute do not change with dilution and they can be added by scalar addition.
Hence, when two solutions of different molarity are mixed, their moles undergo scalar addition and the total number of moles in the new solution would be the addition of the moles of the two solutions which are mixed.
The volume of the new solution which is being formed has been given to us in the question.
In the solution we will refer the solution as
$1 = Solution\,1$, $2 = Solution2$ and $3 = new\,solution\,formed\,after\,mixing$
Hence let us write the values which are given to us in the question
${M_1} = 3M,{M_2} = 2.5M,{M_3} = Unknown$
${V_1} = 2L,{V_2} = 3L,{V_3} = 10L$
Now let us apply the information from above into a formula.
We said that the total moles after mixing of two solutions will be equal to the sum of moles in the solutions which are being mixed.
we also know that, $number\,of\,moles = Molarity(M) \times Volume(V)$
hence we can say,
${M_3}{V_3} = {M_1}{V_1} + {M_2}{V_2}$
Substituting the values we get:
$10 \times M = 2 \times 3 + 3 \times 2.5$
solving , we get;
$M = 1.35M$

Note: Molarity is affected by temperature and hence, if the solutions are being mixed at different temperatures, then simple scalar addition wouldn’t be done since the volume of the liquids will change with temperature as volume is a temperature dependent property. Molarity also depends on the volume of the solution, hence change in volume due to temperature will lead to change in molarity with temperature.