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Question: You have one Litre each of \( 0.5M{\text{ }}NaOH\& 0.25M{\text{ }}NaOH \) solution. What maximum vol...

You have one Litre each of 0.5M NaOH&0.25M NaOH0.5M{\text{ }}NaOH\& 0.25M{\text{ }}NaOH solution. What maximum volume of 0.3M NaOH0.3M{\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

Explanation

Solution

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=no.of moles of soluteVol of Solution(L)Molarity = \dfrac{{no.of{\text{ moles of solute}}}}{{Vol{\text{ of Solution}}(L)}}
If the molarity of one solution is M1{M_1} and volume of that solution is V1{V_1} . The molarity and volume of another solution be M2&V2{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×V= M \times V
Hence, we can say that M1V1=M2V2{M_1}{V_1} = {M_2}{V_2}
If two solutions of different concentrations are given the relation can be also written as: c1V1=c2V2{c_1}{V_1} = {c_2}{V_2} where c1&c2{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: M1V1+M2V2=Mf(V1+V2){M_1}{V_1} + {M_2}{V_2} = {M_f}({V_1} + {V_2})
Where Mf{M_f} is the final molarity of the solution obtained and V1+V2{V_1} + {V_2} is the resultant volume.
In this question we are given two solutions of 0.5M NaOH&0.25M NaOH0.5M{\text{ }}NaOH\& 0.25M{\text{ }}NaOH
The given information is: M1=0.5M,M2=0.25M,Mf=0.3M,V1=1L,V2=1L{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,
0.5×1+0.25×1=Mf(1+1)0.5 \times 1 + 0.25 \times 1 = {M_f}(1 + 1)
Mf=0.5+0.252=0.375M{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=2L1 + 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.