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

Blood plasma: 3.98x10^-8 M, Orange juice: 3.16x10^-4 M, Human urine: 6.31x10^-7 M, Household ammonia: 3.16x10^-12 M, Gastric juice: 1.58x10^-2 M

Step-by-step solution

Understand the Relationship Between pH and Hydrogen Ion Concentration

The pH of a solution is related to the hydrogen ion concentration \(\text{{[\text{H}^{+}]}}\) by the equation: \( \text{{pH}} = -\text{{log}}_{10} (\text{{[\text{H}^{+}]]}} }\) This equation can be rearranged to solve for hydrogen ion concentration: \[ \text{{[\text{H}^{+}]}} = 10^{-\text{{pH}}} \]

Calculate \(\text{{[\text{H}^{+}]}}\) for Blood Plasma

Given: pH = 7.4. Use the formula \[ \text{{[\text{H}^{+}]}} = 10^{-7.4} \] Compute the value: \[ \text{{[\text{H}^{+}]}} = 3.98 \times 10^{-8} \text{{ M}} \]

Calculate \(\text{{[\text{H}^{+}]}}\) for Orange Juice

Given: pH = 3.5. Use the formula \[ \text{{[\text{H}^{+}]}} = 10^{-3.5} \] Compute the value: \[ \text{{[\text{H}^{+}]}} = 3.16 \times 10^{-4} \text{{ M}} \]

Calculate \(\text{{[\text{H}^{+}]}}\) for Human Urine

Given: pH = 6.2. Use the formula \[ \text{{[\text{H}^{+}]}} = 10^{-6.2} \] Compute the value: \[ \text{{[\text{H}^{+}]}} = 6.31 \times 10^{-7} \text{{ M}} \]

Calculate \(\text{{[\text{H}^{+}]}}\) for Household Ammonia

Given: pH = 11.5. Use the formula \[ \text{{[\text{H}^{+}]}} = 10^{-11.5} \] Compute the value: \[ \text{{[\text{H}^{+}]}} = 3.16 \times 10^{-12} \text{{ M}} \]

Calculate \(\text{{[\text{H}^{+}]}}\) for Gastric Juice

Given: pH = 1.8. Use the formula \[ \text{{[\text{H}^{+}]}} = 10^{-1.8} \] Compute the value: \[ \text{{[\text{H}^{+}]}} = 1.58 \times 10^{-2} \text{{ M}} \]

Key concepts

Hydrogen Ion Concentration

Understanding hydrogen ion concentration is crucial in acid-base chemistry. This concentration, often denoted as \(\text{[\text{H}^{+}]}\text{\), measures the number of hydrogen ions in a solution. The hydrogen ion concentration determines the acidity or basicity of that solution. For highly acidic substances, the concentration of hydrogen ions is high. Conversely, basic (or alkaline) solutions have lower hydrogen ion concentrations.
The relationship between hydrogen ion concentration and pH is inverse. As one goes up, the other goes down. For example, consider blood plasma with a pH of 7.4. Using the formula \[ \text{{[\text{H}^{+}]}} = 10^{-7.4} \] you find that it has a hydrogen ion concentration of \(3.98 \times 10^{-8} \text{{ M}}\). This means blood plasma is slightly basic, since its pH is higher than 7.
In contrast, orange juice has a much lower pH of 3.5. Its hydrogen ion concentration can be found using the same formula: \[ \text{{[\text{H}^{+}]}} = 10^{-3.5} \] Resulting in \(3.16 \times 10^{-4} \text{{ M}}\), indicating a highly acidic nature.

pH Equation

The pH equation is the backbone of calculating hydrogen ion concentration. pH is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. The equation is: \(\text{{pH}} = -\text{{log}}_{10} (\text{{[\text{H}^{+}]})}\)
This means that pH is the negative base-10 logarithm of the hydrogen ion concentration. To find the hydrogen ion concentration from pH, you can rearrange this equation to: \[ \text{{[\text{H}^{+}]}} = 10^{-\text{{pH}}} \]
It makes it easy to understand that each unit change in pH represents a tenfold change in hydrogen ion concentration. For example, a decrease in pH from 6 to 5 means the hydrogen ion concentration is ten times higher in the solution with a pH of 5.
To further clarify, let's use human urine with a pH of 6.2. Applying the equation: \[ \text{{[\text{H}^{+}]}} = 10^{-6.2} \] You get a hydrogen ion concentration of \(6.31 \times 10^{-7} \text{{ M}}\), showing that it is less acidic compared to orange juice.

Acid-Base Chemistry

Acid-base chemistry involves the study of acids, bases, and their reactions. It is essential to many fields, including biochemistry, medicine, and environmental science. The pH scale, ranging from 0 to 14, indicates how acidic or basic a substance is. A pH of 7 is neutral, below 7 is acidic, and above 7 is basic (alkaline).
Some key points to remember:

• Low pH (0-6) indicates high hydrogen ion concentration (acidic).
• High pH (8-14) indicates low hydrogen ion concentration (basic).
• Neutral pH (7) means equal amounts of hydrogen and hydroxide ions.

For instance, household ammonia, a common cleaning agent, has a high pH of 11.5. Using our pH formula: \[ \text{{[\text{H}^{+}]}} = 10^{-11.5} \] We find the hydrogen ion concentration to be \(3.16 \times 10^{-12} \text{{ M}}\), making it highly basic.
On the other hand, gastric juice has a pH of 1.8, indicating it's very acidic. Its hydrogen ion concentration is given by: \[ \text{{[\text{H}^{+}]}} = 10^{-1.8} \] Resulting in \(1.58 \times 10^{-2} \text{{ M}}\).