Question

Which one of the following is not correct? (a) \(\mathrm{pH}=1 / \log \left[\mathrm{H}^{+}\right]\) (b) \(\mathrm{pH}=\log 1 /\left[\mathrm{H}^{+}\right]\) (c) \(\left[\mathrm{H}^{+}\right]=10-\mathrm{pH}\) (d) \(\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right]\)

Short answer

The incorrect option is (a).

Step-by-step solution

Recall the definition of pH

The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration. Mathematically, this is expressed as \( \mathrm{pH} = - \log \left[ \mathrm{H}^{+} \right] \).

Evaluate option (a)

Option (a) states: \( \mathrm{pH} = 1 / \log \left[ \mathrm{H}^{+} \right] \). This implies the reciprocal of the logarithm, rather than the negative of the logarithm, which does not match the definition of pH. Therefore, this expression is incorrect.

Evaluate option (b)

Option (b) states: \( \mathrm{pH} = \log 1 / \left[ \mathrm{H}^{+} \right] \). By the properties of logarithms, this expression can be rewritten as \( \mathrm{pH} = - \log \left[ \mathrm{H}^{+} \right] \), which matches the definition of pH. This option is correct.

Evaluate option (c)

Option (c) states: \( \left[ \mathrm{H}^{+} \right] = 10^{-\mathrm{pH}} \). This is a correct expression because it is derived directly from the definition \( \mathrm{pH} = - \log \left[ \mathrm{H}^{+} \right] \), leading to \( \left[ \mathrm{H}^{+} \right] = 10^{-\mathrm{pH}} \).

Evaluate option (d)

Option (d) states: \( \mathrm{pH} = - \log \left[ \mathrm{H}^{+} \right] \). This is the direct definition of pH. Therefore, this expression is correct.

Key concepts

Understanding Hydrogen Ion Concentration

Hydrogen ion concentration, represented as \([\text{H}^+]\), is central to understanding the acidity or basicity of a solution. In simple terms, it quantifies the number of hydrogen ions present in a given volume of solution.
The concentration of hydrogen ions is usually measured in moles per liter (mol/L), a common unit in chemistry known as "molarity." A higher concentration of hydrogen ions means a more acidic solution, while a lower concentration means a more basic, or alkaline, solution.
To relate hydrogen ion concentration to the pH, scientists use a mathematical expression. This relationship is key to converting between pH values and \([\text{H}^+]\). Remember that a change in hydrogen ion concentration means a change in the pH and thus alters the solution’s acidity or basicity.

Why Use a Logarithmic Scale?

In acid-base chemistry, the pH scale is a logarithmic scale, which helps us manage the wide range of hydrogen ion concentrations found in various substances.
A logarithmic scale based on base 10 means that each step up or down on the pH scale represents a tenfold change in hydrogen ion concentration. For example:

• pH 3 has ten times more \([\text{H}^+]\) ions than pH 4
• pH 2 has a hundred times more \([\text{H}^+]\) ions than pH 4

The logarithmic nature of the pH scale makes it easier to express very large or very small concentrations of hydrogen ions in a manageable way.
It's this property that allows us to transform the rather challenging math of multiplying hydrogen ion concentrations into simple addition and subtraction when dealing with pH values.

Core Principles of Acid-Base Chemistry

In acid-base chemistry, it’s vital to understand how acids and bases behave in water. Acids increase the hydrogen ion concentration in a solution, giving it a lower pH, while bases decrease the hydrogen ion concentration, resulting in a higher pH.
The pH scale ranges from 0 to 14:

• pH less than 7: acidic solution
• pH equal to 7: neutral solution, like pure water
• pH greater than 7: basic or alkaline solution

The strength of an acid or base depends on its ability to donate or accept hydrogen ions. Strong acids fully dissociate in water to release hydrogen ions, whereas weak acids only partially dissociate.
Understanding the behavior of acids and bases, along with the pH scale and hydrogen ion concentration, allows chemists to predict reactions and create solutions with desired properties.