Question

The \(\mathrm{pH}\) of a solution is 5 . To this solution acid was added so that its \(\mathrm{pH}\) value becomes \(2.0\). The increase in \(\mathrm{H}^{+}\) concentration is : (a) 100 times (b) 5 times (c) \(2.5\) times (d) 1000 times

Short answer

The increase in H+ concentration is 1000 times.

Step-by-step solution

Understanding pH and H+ concentration

The pH of a solution is a logarithmic measure of its hydrogen ion (H+) concentration. The pH scale is inversely proportional to the concentration of H+ ions, meaning that as pH decreases, the concentration of H+ ions increases. The relationship is given by the formula pH = -log10[H+], where [H+] is the concentration of hydrogen ions.

Determine the initial H+ concentration

For the initial solution with a pH of 5, find the concentration of hydrogen ions using the formula pH = -log10[H+]. Rewrite it to solve for [H+]: [H+] = 10^(-pH). Substituting the given pH value, we get [H+]initial = 10^(-5) M (molar).

Determine the final H+ concentration

Similarly, calculate the final concentration of hydrogen ions after the pH was reduced to 2. Using the formula [H+] = 10^(-pH), we find that [H+]final = 10^(-2) M.

Calculate the increase in H+ concentration

To find the increase in H+ concentration, divide the final concentration by the initial concentration: Increase = [H+]final / [H+]initial. Substituting the calculated values, we get Increase = 10^(-2) M / 10^(-5) M = 10^(5-2) = 10^3.

Key concepts

pH Scale in Chemistry

The pH scale is a key concept in chemistry that measures the acidity or basicity of an aqueous solution. It is a logarithmic scale, with values ranging from 0 to 14, where 7 is neutral, values less than 7 indicate an acidic solution, and values greater than 7 indicate a basic (alkaline) solution.

Understanding the pH scale is vital because it helps predict the behavior of substances in different environments, which is crucial for applications in biology, medicine, agriculture, and industry. For instance, the human body maintains a pH around 7.4 in the bloodstream, and slight deviations can have significant effects on health.

The pH scale is derived from the concentration of hydrogen ions (\( \text{H}^+ \) ions) in a solution. The greater the concentration of hydrogen ions, the lower the pH and hence more acidic the solution. On the other end, a higher pH indicates a lower concentration of hydrogen ions and a more basic solution.

Hydrogen Ion Concentration

Hydrogen ion concentration is the quantity of hydrogen ions per unit volume of solution, usually measured in molarity (\( M \), moles per liter). In chemistry, it is a fundamental measure used to determine the acidity of a solution.

The concentration of hydrogen ions directly influences the chemical reactions that take place in the solution, affecting rates, equilibria, and the solubility of compounds. A high concentration of hydrogen ions (low pH) typically increases the rate of acid-catalyzed reactions, while a low concentration (high pH) can facilitate base-catalyzed reactions.

To calculate the hydrogen ion concentration from pH, one uses the inverse logarithmic relationship: \[ \text{H}^+ = 10^{-\text{pH}} \]The exercise mentioned is a practical example, showing that adding an acid to a solution not only lowers its pH but drastically increases the concentration of hydrogen ions.

Logarithmic Relationships in pH

The pH of a solution is determined by the negative logarithm (base 10) of the hydrogen ion concentration. This means there is a logarithmic relationship between pH values and hydrogen ion concentrations. As a result, each one-unit change in pH represents a tenfold change in hydrogen ion concentration.

For instance, a solution with a pH of 6 has ten times more hydrogen ions than a solution with a pH of 7. To appreciate this logarithmic relationship, one must understand that each step on the pH scale indicates a concentration change by a factor of 10.

Hence, the impact of altering the pH of a solution can be more significant than one might initially presume. The pH is not a linear scale, and small changes in pH can reflect large changes in hydrogen ion concentration, which is a critical aspect in the context of chemical reactions and biological systems.

Calculating pH Changes

Calculating pH changes involves understanding how the addition or removal of an acid or base alters the hydrogen ion concentration in a solution. As seen in the exercise, adding an acid to increase the hydrogen ion concentration by 1000 times results in a decrease in pH from 5 to 2.

Using the formula \[ \text{increase} = \frac{\text{[H]}_\text{final}}{\text{[H]}_\text{initial}} \], we can determine the exact change in pH by comparing the initial and final hydrogen ion concentrations. It's crucial to note that because the pH scale is logarithmic, you cannot simply subtract the initial pH from the final pH to find the factor of increase in concentration. Instead, you use the powers of ten to reflect the exponential nature of the change.

The formula shows that a drop of 3 pH units (\( 5 - 2 = 3 \) units) corresponds to a \[ 10^3 = 1000 \] times increase in hydrogen ion concentration. Understanding this calculation is vital, for it gives a quantitative measure of how much more acidic or basic a solution has become due to a chemical process or addition of substances.