The Question is from NEET guide , and it was created by the author THIRUPATHI REDDY

Question

What is the pH of a $10^{-8}$ M HCl solution?

THIRUPATHI REDDY · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
 **Primary Concept**: pH calculation for weak acids and the influence of autoionization of water.
 **Related Topics**: Acid-base equilibrium, autoprotolysis of water, strong acids, weak acids.
 **Prerequisites**: Understanding of pH scale, $pH = -log_{10}[H^+]$ ,  $K_w = [H^+][OH^-] = 10^{-14}$ at 25°C.
## SOLUTION PATHWAY
**Given Information**:
  $[HCl] = 10^{-8}$ M
  HCl is a strong acid, so it completely dissociates in water.
**Method & Steps**:
 1. Calculate the initial $[H^+]$ from HCl dissociation.
  Reasoning:  Since HCl is a strong acid, $[H^+]_{HCl} = 10^{-8}$ M.
  Formula/Rule: $HCl ightarrow H^+ + Cl^-$ 
 2. Consider the autoionization of water.
  Working: Water also contributes $H^+$ ions through autoionization: $2H_2O ightleftharpoons H_3O^+ + OH^-$.  The concentration of $H^+$ from water is $x$.  Then $[H^+]_{total} = 10^{-8} + x$ and $[OH^-] = x$.
  Key Point: We must consider the autoionization of water because the concentration of HCl is very low.
 3. Use the ion product of water to solve for x.
  $K_w = [H^+][OH^-] = (10^{-8} + x)(x) = 10^{-14}$
  Solving the quadratic equation (or making an approximation, as x will be close to $10^{-7}$):
  $x^2 + 10^{-8}x - 10^{-14} = 0$
  Solving this quadratic equation gives $x \approx 9.5 	imes 10^{-8}$ M (Approximation:  neglecting $10^{-8}x$ gives $x \approx 10^{-7}$ which is acceptable for this question).
  Therefore, $[H^+]_{total} \approx 10^{-8} + 9.5 	imes 10^{-8} \approx 1.05 	imes 10^{-7}$ M
  $pH = -log_{10}(1.05 	imes 10^{-7}) \approx 6.98$
  Result: pH is slightly less than 7.
  Verification: The pH should be slightly acidic because of the HCl, but very close to 7 due to the low concentration of HCl.
 ## OPTION ANALYSIS
[A] 8 :x: Incorrect. This would be the pH if only the HCl concentration was considered, ignoring the contribution from water.
[B] 7 :x: Incorrect. The solution is slightly acidic due to the presence of HCl.
[C] Slightly less than 7 ✓: Correct. The calculated pH is approximately 6.98.
[D] Slightly greater than 7 :x: Incorrect. The presence of HCl makes the solution acidic.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Ignoring the autoionization of water: This is crucial when dealing with very dilute strong acid solutions.
   How to avoid: Always check if the concentration of the acid is comparable to or smaller than $10^{-7}$ M. If it is, consider the contribution from water.
  2.Incorrectly solving the quadratic equation:  Approximations can be made if justified.
   How to avoid: Use a calculator or suitable software for accurate calculation, especially if the approximation is not valid.
 **Quick Tips**:
  1.If the concentration of a strong acid is less than $10^{-6}$ M, expect the pH to be slightly less than 7.
  2.Remember that water always contributes $H^+$ and $OH^-$ ions.

THIRUPATHI REDDY · Answer

8

THIRUPATHI REDDY · Answer

7

THIRUPATHI REDDY · Answer

The correct Option is "Slightly less than 7"

THIRUPATHI REDDY · Answer

Slightly greater than 7

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