Question

100 mL of 1 M HCl is mixed with 50 mL of 2 M HCl. Hence, \[[{{H}_{3}}{{O}^{+}}]\]is________.
(A) 1.00 M
(B) 1.50 M
(C) 1.33 M
(D) 3.00 M

Answer 1

Hint: There is a formula to calculate the concentration of the solution.
\[M=\dfrac{n}{V}\]
M = molarity of the solution
n = number of moles
V = volume of the solution

Complete step by step solution:
-In the question it is given that 100 mL of the 1 M HCl with 50 mL of 2 M HCl.
-We have to find the concentration of the \[[{{H}_{3}}{{O}^{+}}]\] in the resulting solution.
-Number of moles in 100 mL of 1 M HCl is
\[{{M}_{1}}=\dfrac{{{n}_{1}}}{{{V}_{1}}}\]
\[{{M}_{1}}\] = Molarity of HCl = 1 M
\[{{n}_{1}}\]= number of moles of HCl = ?
\[{{V}_{1}}\]= Volume of the HCl = 100 mL = 0.1 L
Therefore
\[\begin{align}
& {{M}_{1}}=\dfrac{{{n}_{1}}}{{{V}_{1}}} \\
& {{n}_{1}}={{M}_{1}}\times {{V}_{1}} \\
& {{n}_{1}}=1\times 0.1 \\
& {{n}_{1}}=0.1 \\
\end{align}\]
-Therefore \[{{n}_{1}}\]= number of moles of HCl = 0.1
-Number of moles in 50 mL of 2 M HCl is
\[{{M}_{2}}=\dfrac{{{n}_{2}}}{{{V}_{2}}}\]
\[{{M}_{2}}\] = Molarity of HCl = 2 M
\[{{n}_{2}}\]= number of moles of HCl = ?
\[{{V}_{2}}\]= Volume of the HCl = 50 mL = 0.05 L
\[\begin{align}
& {{M}_{2}}=\dfrac{{{n}_{2}}}{{{V}_{2}}} \\
& {{n}_{2}}={{M}_{2}}\times {{V}_{2}} \\
& {{n}_{2}}=2\times 0.05 \\
& {{n}_{2}}=0.1 \\
\end{align}\]
-Therefore \[{{n}_{2}}\]= number of moles of HCl = 0.1
-Total number of moles of the mixture of 100 mL of 1 M HCl and 50 mL of 2 M HCl is
\[\begin{align}
& n={{n}_{1}}+{{n}_{2}} \\
& n=0.1+0.1 \\
& n=0.2 \\
\end{align}\]
-Total volume of the solution by adding 100 mL of 1 M HCl and 50 mL of 2 M HCl is
V = 100+50 = 150 mL = 0.15 L
-Therefore Total concentration of the solution is
\[\begin{align}
& M=\dfrac{n}{V} \\
& M=\dfrac{0.2}{0.15}=1.33M \\
\end{align}\]
M = molarity of the solution
n = number of moles
V = volume of the solution
-\[[{{H}_{3}}{{O}^{+}}]\] = M = 1.33 M.
-The molarity or the concentration of \[[{{H}_{3}}{{O}^{+}}]\] = 1.33 M.

Therefore the correct option is C.

Note: We are calculating the total concentration of the resulting solution so we have to consider the number moles of the 100 mL of 1 M HCl and 50 mL of 2 M HCl. Then only we will get the concentration (M) of the solution.