Question

If the \(\mathrm{pH}\) of a solution is 2, the hydrogen ion concentration in moles per litre is (a) \(1 \times 10^{-14}\) (b) \(1 \times 10^{-2}\) (c) \(1 \times 10^{-7}\) (d) \(1 \times 10^{-12}\)

Short answer

The hydrogen ion concentration is (b) 1 x 10^-2 moles per litre.

Step-by-step solution

Understand the pH Scale

The pH of a solution is the negative logarithm to base 10 of the hydrogen ion concentration. It is given by the formula pH = -log10[H+], where [H+] is the hydrogen ion concentration in moles per litre.

Calculate the Hydrogen Ion Concentration

To find the hydrogen ion concentration from a pH of 2, use the inverse of the logarithmic relationship: [H+] = 10^-pH. Here, [H+] = 10^-2.

Convert to Scientific Notation

Express the hydrogen ion concentration in scientific notation: [H+] = 1 x 10^-2 moles per litre.

Key concepts

Understanding the pH Scale

The pH scale plays a crucial role in chemistry, particularly in the study of acids and bases. It's a measure of how acidic or basic a water-based solution is. The scale ranges from 0 to 14, with 7 being neutral, values below 7 indicating acidity, and values above 7 indicating alkalinity. Pure water, with a pH of 7, is considered neutral because it has equal concentrations of hydrogen (H+) and hydroxide (OH-) ions.

When a solution has a higher concentration of H+ ions, it becomes more acidic and therefore has a lower pH value. Conversely, a higher concentration of OH- ions makes a solution more basic, resulting in a higher pH value. The pH scale is logarithmic, which means that each whole pH value below 7 is ten times more acidic than the next higher value. For example, a solution with a pH of 2 is ten times more acidic than a solution with a pH of 3 and a hundred times more acidic than a solution with a pH of 4.

Calculation of Hydrogen Ion Concentration

To calculate hydrogen ion concentration from pH, we use the correlation that the pH of a solution is the negative logarithm (base 10) of its hydrogen ion concentration. The formula is:
\[ \mathrm{pH} = -\log_{10} [\mathrm{H}^+] \]
where \( [\mathrm{H}^+] \) represents the concentration of hydrogen ions in moles per litre (M). If we know the pH of a solution, we can find the hydrogen ion concentration using the inverse mathematical operation. For a solution with a pH of 2, the calculation would be:
\[ [\mathrm{H}^+] = 10^{-\mathrm{pH}} \]
Plugging in the pH value, we get:
\[ [\mathrm{H}^+] = 10^{-2} = 0.01 \]
So the hydrogen ion concentration in moles per litre is \( 0.01 \) or, in scientific notation, \( 1 \times 10^{-2} \). It's important to follow these steps accurately to ensure the calculated hydrogen ion concentration is correct.

Scientific Notation in Chemistry

Scientific notation is a method of expressing very large or very small numbers in a more compact form. It's particularly useful in chemistry for dealing with the vast range of quantities we encounter, from the size of atoms to the amount of substances in moles. The format for scientific notation is:
\[ a \times 10^{b} \]
where \( a \) is a number between 1 and 10 (it can include decimals), and \( b \) is an integer that represents the number of places the decimal point has been moved.

In the context of hydrogen ion concentration, scientific notation allows chemists to express very small quantities in a clear and concise manner. For example, a hydrogen ion concentration of 0.01 moles per litre is written as \( 1 \times 10^{-2} \) M, showing the scale of its concentration without the need for many zeros.