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Chapter 2: Problem 15

Mathematical 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

Expert verified
(a) 3.98 x 10^-8 mol/L (b) 3.16 x 10^-4 mol/L (c) 6.31 x 10^-7 mol/L (d) 3.16 x 10^-12 mol/L (e) 1.58 x 10^-2 mol/L

Step by step solution

01

- Understand the Relationship Between pH and \([\text{H}^{+}]\)

The pH of a solution is defined by the negative logarithm (base 10) of the hydrogen ion concentration: \[\text{pH} = -\text{log}_{10}[\text{H}^{+}]\]To find \([\text{H}^{+}]\) from the pH, use the inverse relationship: \[[\text{H}^{+}] = 10^{-\text{pH}}\]
02

- Calculate \([\text{H}^{+}]\) for Blood Plasma (pH 7.4)

Using the formula \([\text{H}^{+}] = 10^{-\text{pH}}\):\[[\text{H}^{+}] = 10^{-7.4}\]Calculate:\[[\text{H}^{+}] \approx 3.98 \times 10^{-8} \text{ mol/L}\]
03

- Calculate \([\text{H}^{+}]\) for Orange Juice (pH 3.5)

Using the formula \([\text{H}^{+}] = 10^{-\text{pH}}\):\[[\text{H}^{+}] = 10^{-3.5}\]Calculate:\[[\text{H}^{+}] \approx 3.16 \times 10^{-4} \text{ mol/L}\]
04

- Calculate \([\text{H}^{+}]\) for Human Urine (pH 6.2)

Using the formula \([\text{H}^{+}] = 10^{-\text{pH}}\):\[[\text{H}^{+}] = 10^{-6.2}\]Calculate:\[[\text{H}^{+}] \approx 6.31 \times 10^{-7} \text{ mol/L}\]
05

- Calculate \([\text{H}^{+}]\) for Household Ammonia (pH 11.5)

Using the formula \([\text{H}^{+}] = 10^{-\text{pH}}\):\[[\text{H}^{+}] = 10^{-11.5}\]Calculate:\[[\text{H}^{+}] \approx 3.16 \times 10^{-12} \text{ mol/L}\]
06

- Calculate \([\text{H}^{+}]\) for Gastric Juice (pH 1.8)

Using the formula \([\text{H}^{+}] = 10^{-\text{pH}}\):\[[\text{H}^{+}] = 10^{-1.8}\]Calculate:\[[\text{H}^{+}] \approx 1.58 \times 10^{-2} \text{ mol/L}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

hydrogen ion concentration
Understanding hydrogen ion concentration is essential in acid-base chemistry. The concentration of hydrogen ions in a solution determines its acidity or alkalinity, which we often refer to in terms of pH.
To calculate the hydrogen ion concentration \(([\text{H}^+])\) from a given pH value, you use the inverse logarithmic relationship: \[ [\text{H}^+] = 10^{-\text{pH}} \] This means that if you know the pH of a solution, you can determine the concentration of hydrogen ions present.
  • For example, blood plasma has a pH of 7.4. Using the formula, we find \[ [3.98 \times 10^{-8} \text{ mol/L}] \]
  • Orange juice with a pH of 3.5 results in a hydrogen ion concentration of approximately \[ [3.16 \times 10^{-4} \text{ mol/L}] \]
This approach works for any substance listed. Just plug in the pH value and calculate the concentration of hydrogen ions accordingly. Remember, as the pH decreases, the hydrogen ion concentration increases, meaning the solution becomes more acidic.
logarithms in chemistry
Logarithms play a crucial role in chemistry, particularly when dealing with pH calculations. The pH scale itself is logarithmic, meaning each unit change in pH represents a tenfold change in hydrogen ion concentration.
The formula \[ \text{pH} = -\text{log}_{10}[\text{H}^+] \] shows the relationship between pH and hydrogen ion concentration. To reverse this, you use the inverse logarithm: \[ [\text{H}^{+}] = 10^{-\text{pH}} \] This is why understanding logarithms is helpful. They allow scientists to express wide-ranging concentrations in a more manageable form.
  • For instance, a pH of 11.5 for household ammonia results in an extremely low hydrogen ion concentration of approximately \[ [3.16 \times 10^{-12} \text{ mol/L}] \]
  • Similarly, a highly acidic gastric juice with pH 1.8 has a high hydrogen ion concentration of about \[ [1.58 \times 10^{-2} \text{ mol/L}] \]
Remember the key insight: Lower pH values indicate higher hydrogen ion concentrations, while higher pH values mean lower concentrations.
acid-base chemistry
Acid-base chemistry is a fundamental area of study that revolves around the properties of acids and bases, and how they interact. The pH scale is a critical tool in this field, ranging from 0 (very acidic) to 14 (very basic), with 7 being neutral.

The concentration of hydrogen ions \(([\text{H}^+])\) is central to determining the acidity or basicity of a solution. Acids release hydrogen ions when dissolved in water, lowering the pH, while bases absorb hydrogen ions, raising the pH.
  • For example, human urine typically has a pH of around 6.2, making it slightly acidic. The calculated hydrogen ion concentration is approximately \[ [6.31 \times 10^{-7} \text{ mol/L}] \]
  • Conversely, household ammonia, being a basic solution with a pH of 11.5, has a much lower hydrogen ion concentration
This relationship underpins many reactions in biochemistry and industrial processes. By mastering pH and hydrogen ion concentration, you can gauge the behavior and reactivity of a wide array of substances.

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Most popular questions from this chapter

Mathematical Define buffering capacity. How do the following buffers differ in buffering capacity? How do they differ in pH? Buffer a: \(0.01 \mathrm{M} \mathrm{Na}_{2} \mathrm{HPO}_{4}\) and \(0.01 \mathrm{M} \mathrm{NaH}_{2} \mathrm{PO}_{4}\) Buffer b: \(0.10 \mathrm{M} \mathrm{Na}_{2} \mathrm{HPO}_{4}\) and \(0.10 \mathrm{MNaH}_{2} \mathrm{PO}_{4}\) Buffer \(c: 1.0 M \mathrm{Na}_{2} \mathrm{HPO}_{4}\) and \(1.0 \mathrm{M} \mathrm{NaH}_{2} \mathrm{PO}_{4}\)

Reflect and Apply Many of the buffers used these days, such as HEPES and PIPES, were developed because they have desirable characteristics, such as resisting pH change with dilution. Why would resisting pH change with dilution be advantageous?

Biochemical Connections What is the relationship between \(\mathrm{p} K_{\mathrm{a}}\) and the useful range of a buffer?

Recall What are the requirements for molecules to form hydrogen bonds? (What atoms must be present and involved in such bonds?)

Reflect and Apply Aspirin is an acid with a \(\mathrm{p} K_{\mathrm{a}}\) of \(3.5 ;\) its structure includes a carboxyl group. To be absorbed into the bloodstream, it must pass through the membrane lining the stomach and the small intestine. Electrically neutral molecules can pass through a membrane more easily than can charged molecules. Would you expect more aspirin to be absorbed in the stomach, where the pH of gastric juice is about \(1,\) or in the small intestine, where the \(\mathrm{pH}\) is about \(6 ?\) Explain your answer.
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