Question

What is the mass of \[HCl\] in a \[500mL\] sample of \[6.0M\;\] \[HCl\] ?

Answer 1

Hint: Here you should recall the basic concept of molarity. A solution's molarity tells you about the number of moles of solute that is present in 1 L of solution. You can say:
$Molarity(M) = \dfrac{{moles{\text{ }}of{\text{ solute}}}}{{1{\text{ }}litre{\text{ of }}solution{\text{ }}}}$

Complete step by step answer:
We know that in order to calculate a solution's molarity, you should know the number of moles of solute that is present in 1 L i.e. 1000 mL of solution.
We can use the molar mass of a compound to determine the number of moles present in the sample so number of moles of a compound can be calculated by applying the following formula:
$Number{\text{ }}of{\text{ }}moles = \dfrac{{Mass(g)}}{{Molar{\text{ }}mass(gmo{l^{ - 1}})}}$
In the given question, we already know the molarity as well as volume of the solution which are as follows:
\[\begin{array}{*{20}{l}}
  {Molarity = 6.0} \\
  {Volume = 500mL = 0.5L}
\end{array}\]
Substituting these given values in the formula of molarity, we will calculate the number of moles as depicted below:
$
  6.0 = \dfrac{{moles{\text{ }}of{\text{ }}solute}}{{0.5{\text{ }}}} \\
  number{\text{ }}of{\text{ }}moles{\text{ }}of{\text{ }}solute = 3.0{\text{ }}moles{\text{ }}of{\text{ }}HCl \\
$
We know that the molar mass of any compound can be found out by adding the relative atomic masses of each element present in that particular compound. From the chemical formula of \[HCl\] , it is clear that \[HCl\] comprises of one atom of hydrogen and one atom of chlorine and thus molar mass of this compound can be easily calculated by adding the mass of one hydrogen atom and one chlorine atom. We already know the atomic mass of hydrogen and chlorine which are:
$\begin{gathered}
  H = 1.0078u \\
  Cl = 35.45u \\
\end{gathered} $
Thus, molar mass of \[HCl\] will be:
$Molar{\text{ }}mass{\text{ }}of{\text{ HCl = }}(1 \times H) + (1 \times Cl) = (1 \times 1.0078) + (1 \times 35.45) = 36.4578gmo{l^{ - 1}}$
Now, substituting the values in in the formula for number of moles, we can calculate the mass of \[HCl\] as shown below:
 \[\begin{gathered}
  3.0 = \dfrac{{Mass(g)}}{{36.4578}} \\
  Mass = 109.3g \\
\end{gathered} \]
Hence, the mass of \[HCl\] in a \[500mL\] sample of \[6.0M\;\] \[HCl\] is \[109.3g\] .

Note: The mole concept is very significant and useful in chemistry. It is actually the base of stoichiometry and it provides the best option to express the amounts of reactants as well as products that are consumed and formed during a chemical reaction.