Question

What volume of water would be needed to dilute 50ml of 3M \[{H_2}S{O_4}\] to 0.75M?
A.50ml
B.100ml
C.150ml
D.200ml
E.250ml

Answer 1

Hint: Molarity is used to calculate the volume of a solvent in a solution. Molarity is inversely proportional to volume i.e. volume increases if molarity of the solution decreases.
Formula used:
 \[{M_1}{V_1} = {M_2}{V_2}\]

Complete step by step answer:
In general, molarity is referred to the total number of moles of solute per litre volume of solution. It depends on the changes in pressure, volume and temperature. Its symbol M stands for molar unit concentration, which means molarity of a solution when one gram of solute is dissolved in one litre of solution.
It can be calculated by the following formula
\[M = \dfrac{{moles}}{{volume(in{\text{ }}litres)}}\]
From this formula, we derive another formula:
\[{M_1}{V_1} = {M_2}{V_2}\]
This equation is used when a stock solution of higher molarity is provided and we are supposed to dilute it to a lower molarity by adding more solvent. This dilution formula is used to calculate any of the four quantities when values of rest of the three are provided. We are given in the question-
\[{M_1}\]= 3M , \[{V_1}\]= 50ml and \[{M_2}\]= 0.75M
Putting these values in the formula, we can get the value of \[{V_2}\]
\[{M_1}{V_1} = {M_2}{V_2}\]
\[\therefore 3M \times 50ml = 0.75M \times {V_2}\]
So, \[{V_2}\]= 200ml
But we already have 50ml of water out of 200ml, so we need only 150ml to dilute 3M \[{H_2}S{O_4}\] to 0.75M.

Hence, the correct option is (C).

Note:
This relationship is just moles = moles i.e. the number of moles of solute remains constant, only volume and molarity changes. This means that adding more solvent will not change the number of moles. This can be used for two different solutions and also for dilution purposes.