Question

Which of the following relationship is correct

• A. $C_{H^+} + C_{OH^-} = 14$
• B. $C_{H^+} \times C_{OH^-} = 14$
• C. $pH + pOH = 14$
• D. $pH \times pOH = 14$

Hint:

Remember: $pH + pOH$ is always 14 at standard room temperature.
If one goes up, the other must go down by the same amount.
This is why a high $pH$ (basic) implies a very low $pOH$, and vice versa.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question relates to the chemistry of aqueous solutions and the logarithmic scale used to express acidity and alkalinity.
Key Formula or Approach:
The ionic product of water ($K_w$) at $25^{\circ}C$ is a constant:
\[ [H^+][OH^-] = 1.0 \times 10^{-14} \]

Step 2: Detailed Explanation:

• Defining pH and pOH:
$pH$ is defined as the negative logarithm (base 10) of the hydrogen ion concentration:
\[ pH = -\log_{10}[H^+] \]
Similarly, $pOH$ is:
\[ pOH = -\log_{10}[OH^-] \]

• Deriving the Relationship:
Taking the negative logarithm of both sides of the ionic product equation:
\[ -\log([H^+][OH^-]) = -\log(10^{-14}) \]
Using logarithmic properties ($\log AB = \log A + \log B$):
\[ (-\log[H^+]) + (-\log[OH^-]) = 14 \]
Substituting the definitions of $pH$ and $pOH$:
\[ pH + pOH = 14 \]

• Significance in Soil Science:
This relationship allows soil scientists to easily calculate the hydroxyl ion activity if the $pH$ is known. For example, in a soil with $pH = 6.0$, the $pOH$ must be $8.0$.

• Analyzing Incorrect Options:
Options (A) and (B) involve direct concentrations rather than logs; their sum or product would be $10^{-14}$, not $14$. Option (D) incorrectly suggests a multiplicative relationship between the logs.

Step 3: Final Answer:
The fundamental logarithmic relationship in aqueous chemistry is $pH + pOH = 14$.