Question

You have one Litre each of $ 0.5M{\text{ }}NaOH\& 0.25M{\text{ }}NaOH $ solution. What maximum volume of $ 0.3M{\text{ }}NaOH $ can be obtained from these solutions without using water?
A) 2 litre
B) 1.25 Litre
C) 1.5 Litre
D) 1 Litre

Answer 1

Hint: To solve this problem we’ll have to understand what Molarity is. Molarity is the no. of moles of substance per Litre of the solution. It is denoted by ‘M’ and is also known as concentration of the solution.

Complete Step By Step Answer:
The formula for molarity will be: $ Molarity = \dfrac{{no.of{\text{ moles of solute}}}}{{Vol{\text{ of Solution}}(L)}} $
If the molarity of one solution is $ {M_1} $ and volume of that solution is $ {V_1} $ . The molarity and volume of another solution be $ {M_2}\& {V_2} $ . The no. of moles of solute in each of the solutions will remain the same/constant. From the above formula, the no. of moles $ = M \times V $
Hence, we can say that $ {M_1}{V_1} = {M_2}{V_2} $
If two solutions of different concentrations are given the relation can be also written as: $ {c_1}{V_1} = {c_2}{V_2} $ where $ {c_1}\& {c_2} $ are concentrations of the solutions.
Similarly, if two or more solutions are mixed together, the no. of moles of solute in the final solution will be constant and can be given as: $ {M_1}{V_1} + {M_2}{V_2} = {M_f}({V_1} + {V_2}) $
Where $ {M_f} $ is the final molarity of the solution obtained and $ {V_1} + {V_2} $ is the resultant volume.
In this question we are given two solutions of $ 0.5M{\text{ }}NaOH\& 0.25M{\text{ }}NaOH $
The given information is: $ {M_1} = 0.5M,{M_2} = 0.25M,{M_f} = 0.3M,{V_1} = 1L,{V_2} = 1L $
Substituting the values in the above equation we get,
  $ 0.5 \times 1 + 0.25 \times 1 = {M_f}(1 + 1) $
 $ {M_f} = \dfrac{{0.5 + 0.25}}{2} = 0.375M $
The final molarity found is the same as the Molarity given to us, hence the maximum volume of Solution that can be obtained is $ 1 + 1 = 2L $ .
The correct answer is Option (A).

Note:
Remember that if the solution is diluted the no. of moles of solute per unit volume will decrease, hence the Molarity will decrease with dilution. Molarity is the measure of how much of a compound is being dissolved in the solution.