Question

How much water, in liters, must be added to $0.5$ liter of $6M$ $HCl$ to make it $2M$ ?
(A) $0.33$
(B) $0.5$
(C) $1$
(D) $1.5$
(E) $2$

Answer 1

The given question revolves around the concepts of concentration of a solution in terms of molarity. One must know the definition of molarity so as to solve the question. Molarity of a solution is defined as the number of moles of solute dissolved in one liter of solution. We are given the initial volume and molarity of solution and the final molarity of the solution after adding water. Since, no solute is added to the solution. Hence, the number of moles of solute remains constant. So, we equate the number of solutes before and after adding the water to solution in order to find the volume of water added.

Complete answer:
Molarity is the number of moles of solute per liter of a solution. So, formula for molarity of a solution is as follows:
$Molarity = \dfrac{{Number\,of\,moles\,of\,solute}}{{Volume\,(in\,litres)}}$
Now, we are given the molarity and volume of the $HCl$ solution before adding the water. So, we can calculate the number of moles of solute by substituting the values of known quantities in the formula.
So, rearranging and shifting the terms in the formula for molarity, we get,
$\Rightarrow Number\,of\,moles\,of\,solute = Molarity \times Volume\,(in\,litres)$
Now, substituting the values of molarity and volume of solution initially, we get,
$\Rightarrow Number\,of\,moles\,of\,solute = 6 \times 0.5$
$\Rightarrow Number\,of\,moles\,of\,solute = 3$
So, we get the number of moles of solute $HCl$ in the solution as $3$.
Now, we add water to the solution of $HCl$ to make the molarity of solution equal to $2M$.
Let the volume of water added be x. Then, the final volume of the solution after adding water to the solution is $\left( {x + 0.5} \right)$ liter. Now, we can calculate the number of moles of solute using the formula:
$Number\,of\,moles\,of\,solute = Molarity \times Volume\,(in\,litres)$
$\Rightarrow Number\,of\,moles\,of\,solute = 2 \times \left( {x + 0.5} \right)$
Opening the bracket and simplifying the expression, we get,
$\Rightarrow Number\,of\,moles\,of\,solute = 2x + 1$
Since we have not added any solute to the solution, the number of moles of the solute remains constant.
So, equating the number of moles of solute before and after adding water to solution, we get,
$\Rightarrow 2x + 1 = 3$
Now, we have to solve the above linear equation in x so as to get to our required answer.
Shifting all the constant terms to the right side of the equation, we get,
$\Rightarrow 2x = 2$
Dividing both sides of the equation by $2$, we get the value of x as,
$\Rightarrow x = 1$
So, the water to be added to $0.5$ liter of $6M$ $HCl$ to make it $2M$ solution is $1$ liter.
Hence, the option (C) is correct.

Note:
The component of the solution that is present in the largest amount is known as solvent. The formula for molarity is the ratio of the number of moles to the volume of solution in liters. One must take care of the calculations in order to solve the problem. We also must take care of the units while doing the calculations.