The pH of a solution, whose hydrogen ion concentration is 1 × 10 -5 mole per litre, will be ________.
5
Understanding pH and Hydrogen Ion Concentration
The question asks us to determine the pH of a solution given its hydrogen ion concentration. pH is a measure of the acidity or alkalinity of a solution. It is defined based on the concentration of hydrogen ions (H⁺) present in the solution.
Calculating pH from Hydrogen Ion Concentration
The pH of a solution is calculated using the negative logarithm (base 10) of the molar concentration of hydrogen ions. The formula is:
\(\text{pH} = -\log_{10}[\text{H}^+]\)
Where \([\text{H}^+]\) represents the molar concentration of hydrogen ions in moles per litre.
Applying the pH Formula to the Given Concentration
We are given that the hydrogen ion concentration, \([\text{H}^+]\), is \(1 \times 10^{-5}\) mole per litre.
Now, let's substitute this value into the pH formula:
\(\text{pH} = -\log_{10}(1 \times 10^{-5})\)
Using the properties of logarithms, we know that \(\log_{10}(a \times b) = \log_{10}(a) + \log_{10}(b)\). So, we can write:
\(\text{pH} = -(\log_{10}(1) + \log_{10}(10^{-5}))\)
We also know that \(\log_{10}(1) = 0\) and \(\log_{10}(10^x) = x\). Applying these rules:
\(\text{pH} = -(0 + (-5))\)
\(\text{pH} = -(-5)\)
\(\text{pH} = 5\)
Therefore, the pH of the solution with a hydrogen ion concentration of \(1 \times 10^{-5}\) mole per litre is 5.
Analyzing the Options
The calculated pH is 5. Let's compare this with the given options:
- Option 1: 6
- Option 2: 5
- Option 3: 4
- Option 4: 7
Our calculated pH matches Option 2.
Final Conclusion on pH Calculation
Based on the calculation using the definition of pH, the solution with a hydrogen ion concentration of \(1 \times 10^{-5}\) mole per litre has a pH of 5.
| Hydrogen Ion Concentration (\([\text{H}^+]\)) | Calculation | pH |
|---|---|---|
| \(1 \times 10^{-5}\) mol/L | \(-\log_{10}(1 \times 10^{-5})\) | 5 |
Revision Table: Key Concepts of pH
| Concept | Description | Formula |
|---|---|---|
| pH | Measure of acidity/alkalinity; related to hydrogen ion concentration. | \(\text{pH} = -\log_{10}[\text{H}^+]\) |
| \([\text{H}^+]\) | Molar concentration of hydrogen ions (H⁺) in mol/L. | |
| Acidity/Alkalinity | pH < 7 is acidic; pH = 7 is neutral; pH > 7 is alkaline (basic). |
Additional Information: The pH Scale and Water
The pH scale typically ranges from 0 to 14, though values outside this range are possible for very strong acids or bases. A neutral solution, like pure water at 25°C, has a pH of 7. This is because the concentration of hydrogen ions \([\text{H}^+]\) and hydroxide ions \([\text{OH}^-]\) are equal, both being \(1 \times 10^{-7}\) mol/L. Solutions with pH less than 7 are acidic, meaning they have a higher concentration of \([\text{H}^+]\) than \(1 \times 10^{-7}\) mol/L. Solutions with pH greater than 7 are alkaline (or basic), meaning they have a lower concentration of \([\text{H}^+]\) than \(1 \times 10^{-7}\) mol/L (and a higher concentration of \([\text{OH}^-]\)).
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