Question

he\[pH\]of a solution is 5.0. To this solution sufficient acid is added to decrease the\[pH\]to 2.0. The increase in hydrogen ion concentration is:
A.100 times
B.10 times
C.1000 times
D.2.5 times

Answer 1

Hint: Calculate the concentration of the hydrogen by using the below formula
     \[pH=-[\log {{H}^{+}}]\]
\[pH\]is the negative logarithm of the hydrogen ion concentration present in the given solution.

Complete step by step answer:
The pH of the given solution is 5.0.
Given that a sufficient amount of acid is added to decrease the pH to 2.0.
Now, we have to calculate the increase in concentration of hydrogen.
                                            \[\begin{align}
  & \text{Initially pH of the solution = 5} \\
 & \text{ }\Rightarrow \text{ -log }\!\![\!\!\text{ }{{\text{H}}^{\text{+}}}\text{ }\!\!]\!\!\text{ = 5} \\
 & \text{ }\Rightarrow \text{ }\!\![\!\!\text{ }{{\text{H}}^{\text{+}}}\text{ }\!\!]\!\!\text{ = 1}{{\text{0}}^{\text{-5}}}\text{ (Initial)} \\
\end{align}\]
After addition of acid solution the pH reduced to 2.0.
\[\begin{align}
  & \text{means the pH of the solution = 2}\text{.0} \\
 & \text{ }\Rightarrow \text{-log }\!\![\!\!\text{ }{{\text{H}}^{\text{+}}}\text{ }\!\!]\!\!\text{ = 2} \\
 & \text{ }\Rightarrow \text{ }[{{\text{H}}^{\text{+}}}\text{ }\!\!]\!\!\text{ = 1}{{\text{0}}^{\text{-2}}}\text{ (Final)} \\
 & \\
\end{align}\]
Now we have to calculate how many times the hydrogen ion concentration.
Hydrogen ion concentration increased is the ratio of final concentration to the initial concentration.
\[\begin{align}
  & \text{= }\dfrac{\text{final concentration of the solution}}{\text{initial concentration of the solution}} \\
 & =\text{ }\dfrac{{{10}^{-2}}}{{{10}^{-5}}} \\
 & =\text{ 1}{{\text{0}}^{\text{3}}} \\
 & =\text{ 1000 times } \\
\end{align}\]
So, the concentration of the hydrogen is going to increase by 1000 times.

So, the correct option is C.

Note: Don’t be confused with the words initial concentration and final concentration.
Initial concentration: The concentration of the solution without adding any other chemicals is called initial concentration.
Final concentration: The initial concentration of the solution is going to change after adding some chemical to the solution is called final concentration.
The final concentration of the solution may decrease or increase. It is going to depend on which chemical we are going to add.