Question

Calculate the hydrogen ion concentration, \(\left[\mathrm{H}^{+}\right]\) for each of the following materials: (a) Blood plasma, pH 7.4 (b) Orange juice, pH 3.5 (c) Human urine, pH 6.2 (d) Household ammonia, pH 11.5 (e) Gastric juice, pH 1.8

Short answer

a) \[ 3.98 \times 10^{-8} \text{ M} \] b) \[ 3.16 \times 10^{-4} \text{ M} \] c) \[ 6.31 \times 10^{-7} \text{ M} \] d) \[ 3.16 \times 10^{-12} \text{ M} \] e) \[ 1.58 \times 10^{-2} \text{ M} \].

Step-by-step solution

- Understand the Relationship Between pH and Hydrogen Ion Concentration

Recall that pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration: \ \text{pH} = -\text{log}([\text{H}^{+}]). To find the \( [\text{H}^{+}] \), rearrange this equation to \[ [\text{H}^{+}] = 10^{-\text{pH}} \].

- Calculate Hydrogen Ion Concentration for Blood Plasma

Substitute pH = 7.4 into the formula \[ [\text{H}^{+}] = 10^{-\text{pH}} \] \[ [\text{H}^{+}] = 10^{-7.4} \]. Calculate the value: \[ [\text{H}^{+}] \approx 3.98 \times 10^{-8} \text{ M} \].

- Calculate Hydrogen Ion Concentration for Orange Juice

Substitute pH = 3.5 into the formula \[ [\text{H}^{+}] = 10^{-\text{pH}} \] \[ [\text{H}^{+}] = 10^{-3.5} \]. Calculate the value: \[ [\text{H}^{+}] \approx 3.16 \times 10^{-4} \text{ M} \].

- Calculate Hydrogen Ion Concentration for Human Urine

Substitute pH = 6.2 into the formula \[ [\text{H}^{+}] = 10^{-\text{pH}} \] \[ [\text{H}^{+}] = 10^{-6.2} \]. Calculate the value: \[ [\text{H}^{+}] \approx 6.31 \times 10^{-7} \text{ M} \].

- Calculate Hydrogen Ion Concentration for Household Ammonia

Substitute pH = 11.5 into the formula \[ [\text{H}^{+}] = 10^{-\text{pH}} \] \[ [\text{H}^{+}] = 10^{-11.5} \]. Calculate the value: \[ [\text{H}^{+}] \approx 3.16 \times 10^{-12} \text{ M} \].

- Calculate Hydrogen Ion Concentration for Gastric Juice

Substitute pH = 1.8 into the formula \[ [\text{H}^{+}] = 10^{-\text{pH}} \] \[ [\text{H}^{+}] = 10^{-1.8} \]. Calculate the value: \[ [\text{H}^{+}] \approx 1.58 \times 10^{-2} \text{ M} \].

Key concepts

hydrogen ion concentration

The hydrogen ion concentration \(\left[\mathrm{H}^{+}\right]\) is an important measure in chemistry and biology. It represents the concentration of hydrogen ions in a solution. This concentration is crucial for understanding the acidity or basicity of a solution.

Acids have higher hydrogen ion concentrations, while bases have lower hydrogen ion concentrations.

To calculate hydrogen ion concentration from pH, use the formula \([\mathrm{H}^{+}] = 10^{−\mathrm{pH}}\). For example, to find the concentration for a pH of 3.5, plug in the pH value into the formula:

\[ [\mathrm{H}^{+}] = 10^{−3.5} = 3.16 \times 10^{-4} \; \mathrm{M} \]

This calculation helps determine the exact concentration of hydrogen ions in the solution.

acid-base chemistry

Acid-base chemistry is the study of acids, bases, and their interactions.

Acids are substances that increase the hydrogen ion concentration in a solution, while bases decrease it.

The pH scale is used to measure how acidic or basic a solution is. Here's a quick rundown of pH values:

• Low pH (0-6): Acidic
• Neutral pH (7): Neutral
• High pH (8-14): Basic

The formula \([\mathrm{H}^{+}] = 10^{−\mathrm{pH}}\) helps connect the pH scale to the actual concentration of hydrogen ions. For instance, a pH of 1.8 corresponds to a highly acidic solution like gastric juice, with a high hydrogen ion concentration \([\mathrm{H}^{+}] = 1.58 \times 10^{-2} \; \mathrm{M}\).

Understanding this is crucial in many fields such as medicine, environmental science, and biochemistry.

logarithms in biochemistry

Logarithms are mathematical tools that are extremely useful in biochemistry, especially for dealing with pH calculations.

The pH scale itself is logarithmic. A small change in pH means a large change in hydrogen ion concentration.

The formula \([\mathrm{H}^{+}] = 10^{−\mathrm{pH}}\) highlights this relationship, showing that the pH is the negative logarithm (base 10) of the hydrogen ion concentration. This makes it easier to handle very large or very small numbers, which are common in biochemistry.

For instance, consider household ammonia with a pH of 11.5. The hydrogen ion concentration is:

\[ [\mathrm{H}^{+}] = 10^{−11.5} = 3.16 \times 10^{-12} \; \mathrm{M} \]

The logarithmic scale makes it easier to communicate and understand these concentrations without dealing with cumbersome numbers.

Mastering logarithms is essential for anyone studying biochemistry or related fields.