Question

The pH of HCl is 1. The amount of NaOH to be added to 100ml of such HCl solution to get a pH of 7 is-
[A] 4g
[B] 0.4g
[C] 4mg
[D] 0.4mg

Answer 1

Hint: pH 1 means the solution is acidic and pH=7 means the solution is completely neutralised. A neutral solution is formed when the number of hydroxyl ions and hydronium ions are equal. To find the weight of NaOH, we can use the simply use the formula $(W{{t}_{NaOH}}\times 1000)\div ({{M}_{NaOH}}\times 100)$.

Complete answer:
pH is the measure of acidity of the solution. It is equal to the negative log the molar concentration of hydronium ions released in the solution.
As we can see in the question, for HCl, pH = 1 i.e the pH of the 100ml HCl solution is also 1.
We know, $pH=-\log [{{H}^{+}}]$
Or, from the above two equations, we can write,
$-\log [{{H}^{+}}]=1$
\[\therefore [{{H}^{+}}]={{10}^{-1}}=0.1molar\]
As we need to make the pH =7, it means the solution has to be neutral i.e. complete neutralization takes place.
It means, all the moles of hydronium ions are neutralized by the hydroxyl ions.
$\therefore [{{H}^{+}}]=[O{{H}^{-}}]=0.1molar$
$NaOH\to N{{a}^{+}}+O{{H}^{-}}$
So, we can calculate the concentration of hydroxyl ions using the formula-
$[O{{H}^{-}}]=(W{{t}_{NaOH}}\times 1000)\div ({{M}_{NaOH}}\times 100)=0.1$
As we know, Atomic weight of sodium=23
Atomic weight of oxygen=16
Atomic weight of hydrogen=1
So, molar mass of NaOH= 23+16+1=40
Therefore, from the above formula,
$\begin{align}
  & \therefore (W{{t}_{NaOH}}\times 10)\div 40=0.1 \\
 & \Rightarrow W{{t}_{NaOH}}\times 10=4 \\
 & \Rightarrow W{{t}_{NaOH}}=0.4g \\
\end{align}$
Therefore, 0.4g of NaOH is needed to neutralize 100ml solution of HCl which has a pH of 1.
Therefore, the correct answer is option [B] 0.4g.

ADDITIONAL INFORMATION:
If a solution has pH 1-6 it is referred to as an acidic solution. If the pH is 7 the solution is neutral and if the pH is higher than7, then the solution is alkaline in nature.

Note: It is important to remember here that the number of hydroxyl ions will be equal to the number of hydronium ions. The solution is neutral which means the hydronium ions produced by HCl is completely neutralised by the hydroxyl ions produced by NaOH, which will result in pH=7.
It is also important to remember here the atomic weights of the molecules in order to find out the molar mass.