Question

Determine the \(\mathrm{H}_{3} \mathrm{O}^{4}\) concentration in the following solutions. Identify each solution as acidic, basic, or neutral. (a) household ammonia, \(\mathrm{pH}=11.00\) (b) blood, \(\mathrm{pH}=7.40\) (c) lime juice, \(\mathrm{pH}=1.90\)

Short answer

The \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration for the household ammonia is \(1 \times 10^{-11}\) M and it is basic. The \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration for the blood is \(4 \times 10^{-8}\) M and it is weakly basic. The \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration for the lime juice is \(1.26 \times 10^{-2}\) M and it is acidic.

Step-by-step solution

Calculate the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration for the household ammonia solution

The \(\mathrm{pH}\) of the solution of the household ammonia is given as 11.00. Using the formula: \[ \mathrm{H}_{3} \mathrm{O}^{+} \] concentration = \(10^{-\mathrm{pH}}\), we get \[ \mathrm{H}_{3} \mathrm{O}^{+} \] concentration = \(10^{-11.00}\) = \(1 \times 10^{-11}\) M.

Identify the household ammonia solution as acidic, basic, or neutral

Because the pH of the household ammonia solution is greater than 7, it is basic.

Calculate the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration for the blood solution

The \(\mathrm{pH}\) of the solution of blood is given as 7.40. Using the formula: \[ \mathrm{H}_{3} \mathrm{O}^{+} \] concentration = \(10^{-\mathrm{pH}}\), we get \[ \mathrm{H}_{3} \mathrm{O}^{+} \] concentration = \(10^{-7.40}\) = \(4 \times 10^{-8}\) M.

Identify the blood solution as acidic, basic, or neutral

Because the pH of the blood solution is close, but slightly more than 7, it is weakly basic.

Calculate the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration for the lime juice solution

The \(\mathrm{pH}\) of the solution of lime juice is given as 1.90. Using the formula: \[ \mathrm{H}_{3} \mathrm{O}^{+} \] concentration = \(10^{-\mathrm{pH}}\), we get \[ \mathrm{H}_{3} \mathrm{O}^{+} \] concentration = \(10^{-1.90}\) = \(1.26 \times 10^{-2}\) M.

Identify the lime juice solution as acidic, basic, or neutral

Because the pH of the lime juice solution is less than 7, it is acidic.

Key concepts

Acidic and Basic Solutions

When studying solutions in chemistry, it's essential to understand the characteristics of acidic and basic solutions. Acidic solutions contain a higher concentration of hydrogen ions \(\mathrm{H}^+\) or hydroxonium ions \(\mathrm{H}_3\mathrm{O}^+\) compared to pure water. On the other hand, basic solutions, also known as alkaline solutions, have a lower concentration of these ions and a higher concentration of hydroxide ions \(\mathrm{OH}^-\).

In a practical sense, how do we work out if a solution is acidic or basic? We refer to the \(\mathrm{pH}\) scale. For instance, if you were analyzing household ammonia with a \(\mathrm{pH}\) of 11.00, you could conclude that it's basic since its \(\mathrm{pH}\) is above 7, which is neutral on the \(\mathrm{pH}\) scale. Conversely, lime juice with a \(\mathrm{pH}\) of 1.90 is indeed acidic due to its lower \(\mathrm{pH}\) value.

It's not just the \(\mathrm{pH}\) value that indicates acidity or basicity; the chemical properties of the solutions are influenced as well. Acidic solutions can be corrosive and can react with metals, whereas bases can feel slippery and are commonly used in cleaning products due to their ability to neutralize acids.

pH Scale

The \(\mathrm{pH}\) scale is a numerical scale, typically ranging from 0 to 14, that represents the acidity or basicity of an aqueous solution. The scale is logarithmic, which means each whole \(\mathrm{pH}\) value below 7 (the neutral midpoint) is ten times more acidic than the next higher value. For example, a solution with a \(\mathrm{pH}\) of 2 is ten times more acidic than one with a \(\mathrm{pH}\) of 3.

The \(\mathrm{pH}\) of a solution is calculated by taking the negative logarithm (base 10) of the \(\mathrm{H}_3\mathrm{O}^+\) concentration. Let's say you have a blood sample with a \(\mathrm{pH}\) of 7.40; it indicates a \(\mathrm{H}_3\mathrm{O}^+\) concentration that is slightly lower than neutral water, making the blood weakly basic. Understanding the \(\mathrm{pH}\) level is crucial for various applications, such as maintaining the correct \(\mathrm{pH}\) in pools, ensuring soil health for agriculture, or validating the quality and safety in the food industry.

Hydroxonium Ion Concentration

The concentration of hydroxonium ions \(\mathrm{H}_3\mathrm{O}^+\) in a solution is a direct measure of the solution's acidity. In the \(\mathrm{pH}\) concentration calculation exercise we've walked through, the \(\mathrm{H}_3\mathrm{O}^+\) concentration was found using the formula \(10^{-\mathrm{pH}}\), where \(\mathrm{pH}\) is the power of the concentration of \(\mathrm{H}_3\mathrm{O}^+\) in moles per liter. For instance, lime juice with a calculated \(\mathrm{H}_3\mathrm{O}^+\) concentration of \(1.26 \times 10^{-2}\) M is more acidic than household ammonia, which has a much lower \(\mathrm{H}_3\mathrm{O}^+\) concentration of \(1 \times 10^{-11}\) M.

Knowing the \(\mathrm{H}_3\mathrm{O}^+\) concentration allows chemists to measure the exact strength of an acid or base quantitatively. This measurement is paramount in many chemical processes, such as titrations, which are used to determine the concentrations of acids and bases in a solution through neutralization reactions.