Question

How much concentrated solution do you measure out and how much water do you need to add to make $500{\text{ml}}$ $0.1{\text{M}}HCl$ from $2{\text{M}}HCl$ ?

Answer 1

Molar concentration is a measure of the concentration of a chemical substance, in terms of amount of the substance per unit volume of the solution. The SI unit of molarity is ${\text{mold}}{{\text{m}}^{{\text{ - 3}}}}$ . However, when a solution has a concentration of $1{\text{mol/L}}$ it is said to be a 1 molar solution and is represented as $1M$ of the particular chemical substance that forms the solution.

Formulas used: We will be using the formula to find the number of moles of a substance provided we have the molarity of its solution, $n = MV$ where $n$ is the number of moles of the substance, $M$ is the molarity of the substance, and $V$ is the volume of the solution in litres.

Complete Step by Step answer
We know that the molarity is the measure of concentration of a chemical substance in its solution. A substance that has molarity $1M$ is nothing but that one mole of the chemical substance is dissolved in 1 litre of the solvent to form a solution with concentration $1M$ . Thus, from the definition of molarity we can infer that,
$1M = \frac{{1{\text{mole}}}}{{1L}}$
From the problem we can infer that $0.1M$ solution of $HCl$ is made with $500{\text{ml}}$ volume of water, we need to find the amount of $HCl$ that should be added to the $2M$ concentrated solution. This means that the number of moles of the chemical substance remains unchanged. Thus,
${M_1}{V_1} = n = {M_2}{V_2}$
${M_1}{V_1} = {M_2}{V_2}$
Substituting the known values of ${M_1} = 2{\text{M}},{V_1} = x,{M_2} = 0.1{\text{M}},{V_2} = 500{\text{mL}}$ we get,
$\left( {2.0{\text{M}}} \right) \times \left( x \right) = \left( {0.1} \right) \times 500{\text{mL}}$
Solving for ${V_1} = x$ ,
$x = \frac{{0.1 \times 500}}{{2.0}}$
$\Rightarrow x = \frac{{50}}{2} = 25{\text{mL}}$
Thus, to make a $2{\text{M}}$ concentrated solution we have to dilute $25{\text{mL}}$ in $475{\text{mL}}$ of water.

Note
In a laboratory the process can be done using a volumetric flask to ensure the total volume is $500{\text{mL}}$ . Also make sure that the water is not poured into the acid, this causes an exothermic explosive reaction. Concentration can also be expressed as molality, i.e. the number of moles of solute present in 1Kg of solvent.