Question

The pII of a solution is \(5.0 .\) To this solution sufficicnt acid is added to decrease the \(\mathrm{pH}\) to \(2.0 .\) The increase in hydrogen ion concentration is (1) 1000 times (2) \(5 / 2\) times (3) 100 times (4) 5 times

Short answer

1000 times

Step-by-step solution

Understand the pH Scale

The pH scale is a measure of the hydrogen ion concentration \(\text{[H}^{+}]\). A lower pH means a higher concentration of hydrogen ions.

Use the pH Formula

The pH is related to the hydrogen ion concentration by the formula \( \text{pH} = -\text{log}(\text{[H}^{+}] ) \).

Calculate Initial Hydrogen Ion Concentration

For \( \text{pH} = 5.0 \), we have \( 5.0 = -\text{log}(\text{[H}^{+}] ) \). So, \(\text{[H}^{+}] = 10^{-5} \text{ M}\).

Calculate Final Hydrogen Ion Concentration

For \( \text{pH} = 2.0 \), we have \( 2.0 = -\text{log}(\text{[H}^{+}] ) \). So, \[ \text{[H}^{+}] = 10^{-2} \text{ M}\].

Determine the Increase in Hydrogen Ion Concentration

Calculate the ratio of the final to the initial hydrogen ion concentration: \( \frac{10^{-2} \text{ M}}{10^{-5} \text{ M}} = 1000 \).

Key concepts

Hydrogen Ion Concentration

Hydrogen ion concentration, often represented as \(\text{[H}^{+}]\), is crucial in understanding the acidity or alkalinity of a solution. It refers to the amount of hydrogen ions present in a given volume of solution. The more hydrogen ions present, the more acidic the solution is. An acidic solution will have a high \(\text{[H}^{+}]\), while a basic (alkaline) solution will have a low \(\text{[H}^{+}]\).
For example, if the hydrogen ion concentration is high, the pH value will be low, indicating an acidic solution. Conversely, a low hydrogen ion concentration corresponds to a high pH value, indicating a basic solution. This relationship is key to understanding how pH changes affect the nature of a solution.

pH Formula

The pH formula is a fundamental concept in chemistry for determining the acidity or basicity of a solution. It is defined as:
\[ \text{pH} = -\text{log}(\text{[H}^{+}] ) \]
This logarithmic equation indicates that pH is inversely related to the hydrogen ion concentration. A higher \(\text{[H}^{+}]\) results in a lower pH, while a lower \(\text{[H}^{+}]\) leads to a higher pH.
For example, in a solution with a hydrogen ion concentration of \(10^{-5} \text{ M}\), the pH is calculated as follows:
\[ \text{pH} = -\text{log}(10^{-5}) = 5.0 \]
Similarly, for a concentration of \(10^{-2} \text{ M}\), the pH would be:
\[ \text{pH} = -\text{log}(10^{-2}) = 2.0 \]
Understanding and using the pH formula allows chemists and students to quantify and make sense of the acidity of different solutions.

Logarithmic Calculations

Logarithmic calculations are essential for working with the pH formula. They help convert the wide range of hydrogen ion concentrations into a manageable pH scale.

• Logarithms simplify the handling of very large or very small numbers by transforming them into a more straightforward range of values.
• For the pH scale, the logarithm base used is 10, hence it’s denoted as \(\text{log}10 \) or just \( \text{log}\).

For example, if you have a hydrogen ion concentration of \(10^{-5} \text{ M}\), finding the pH involves the negative logarithm of this value:
\[ \text{pH} = -\text{log}(10^{-5}) = 5.0 \]
If the concentration changes to \(10^{-2} \text{ M}\), the pH changes too:
\[ \text{pH} = -\text{log}(10^{-2}) = 2.0 \]
To understand the increase in hydrogen ion concentration, we compare these values:
\[ \frac{10^{-2} \text{ M}}{10^{-5} \text{ M}} = 1000 \]
Thus, the concentration increases by 1000 times. Grasping logarithmic calculations helps in accurately interpreting how pH levels shift with the concentration changes of hydrogen ions.