Question

A solution of hydrochloric acid of unknown concentration was titrated with 0.10 M NaOH. If a 100.-mL sample of the HCl solution required exactly 1.0 mL of the NaOH solution to reach the equivalence point, what was the initial pH of the HCl solution

Answer 1

Answer: The initial pH of the HCl solution is 3

Explanation:

To calculate the concentration of acid, we use the equation given by neutralization reaction:

$n_1M_1V_1=n_2M_2V_2$

where,

$n_1,M_1\text{ and }V_1$ are the n-factor, molarity and volume of acid which is HCl

$n_2,M_2\text{ and }V_2$ are the n-factor, molarity and volume of base which is NaOH.

We are given:

$n_1=1\\M_1=?M\\V_1=100mL\\n_2=1\\M_2=0.10M\\V_2=1mL$

Putting values in above equation, we get:

$1\times M_1\times 100=1\times 0.10\times 1\\\\M_1=\frac{1\times 0.10\times 1}{1\times 100}=10M$

1 mole of HCl produces 1 mole of $H^+$ ions and 1 mole of $Cl^-$ ions

To calculate the pH of the solution, we use the equation:

$pH=-\log[H^+]$

We are given:

$[H^+]=0.001M$

Putting values in above equation, we get:

$pH=-\log (0.001)\\\\pH=3$

Hence, the initial pH of the HCl solution is 3