Question

When the hydrogen ion concentration $\left[ H ^{+}\right]$changes by a factor of $1000$ , the value of $pH$ of the solution_____

• A. decreases by 3 units
• B. decreases by 2 units
• C. increases by 2 units
• D. increases by 1000 units

Answer 1

The Correct Option is A

To understand how the change in hydrogen ion concentration affects the pH of a solution, let's look at the relationship between pH and hydrogen ion concentration.

The pH is defined by the formula:

\(pH = -\log_{10} [H^+]\)

Where \([H^+]\) is the hydrogen ion concentration in moles per liter.

If the hydrogen ion concentration changes by a factor of 1000, it can be represented as:

\([H^+]' = 1000 \times [H^+]\)

To calculate the new pH after this change, we use the formula again:

\(pH' = -\log_{10}(1000 \times [H^+])\)

Using the property of logarithms, this can be simplified to:

\(pH' = -\log_{10}(1000) - \log_{10}([H^+])\)

\(pH' = -3 - \log_{10}([H^+])\)

Since \(pH = -\log_{10}([H^+])\), we can substitute and write:

\(pH' = pH - 3\)

This shows that the pH decreases by 3 units when the hydrogen ion concentration increases by a factor of 1000.

Thus, the correct answer is "decreases by 3 units".

• Option: decreases by 3 units (Correct)
• Option: decreases by 2 units (Incorrect, as shown by the calculations)
• Option: increases by 2 units (Incorrect, the pH decreases with increased \([H^+]\))
• Option: increases by 1000 units (Incorrect, such a change is not possible in normal pH calculations)