Question

MATHEMATICAL Calculate the hydrogen ion concentration, \(\left[\mathrm{H}^{+}\right]\) for each of the following materials: (a) Saliva, pH 6.5 (b) Intracellular fluid of liver, pH 6.9 (c) Tomato juice, pH 4.3 (d) Grapefruit juice, pH 3.2

Short answer

Saliva: \( \backslashapprox 3.16 \times 10^{-7} \text{M}\); Intracellular fluid of liver: \( \backslashapprox 1.26 \times 10^{-7} \text{M}\); Tomato juice: \( \backslashapprox 5.01 \times 10^{-5} \text{M}\); Grapefruit juice: \( \backslashapprox 6.31 \times 10^{-4} \text{M}\)

Step-by-step solution

Understanding pH and \(\backslashleft[\backslashmathrm{H}^{+}\backslashright]\)

The pH of a solution is a measure of its acidity or basicity. It is defined as the negative logarithm (base 10) of the hydrogen ion concentration: \(\text{pH} = -\text{log}_{10} \backslashleft[\backslashmathrm{H}^{+}\backslashright]\). To find the hydrogen ion concentration, \(\backslashleft[\backslashmathrm{H}^{+}\backslashright]\), we use the formula \( \backslashleft[\backslashmathrm{H}^{+}\backslashright] = 10^{-\text{pH}}\).

Calculate \( \backslashleft[\backslashmathrm{H}^{+}\backslashright] \) for Saliva (pH 6.5)

Use the formula: \( \backslashleft[\backslashmathrm{H}^{+}\backslashright] = 10^{-6.5} \) to find the hydrogen ion concentration. \[\backslashleft[\backslashmathrm{H}^{+}\backslashright] = 10^{-6.5} \approx 3.16 \times 10^{-7} \text{ M}\]

Calculate \( \backslashleft[\backslashmathrm{H}^{+}\backslashright] \) for Intracellular fluid of liver (pH 6.9)

Use the formula: \( \backslashleft[\backslashmathrm{H}^{+}\backslashright] = 10^{-6.9} \) to find the hydrogen ion concentration. \[\backslashleft[\backslashmathrm{H}^{+}\backslashright] = 10^{-6.9} \approx 1.26 \times 10^{-7} \text{ M} \]

Calculate \( \backslashleft[\backslashmathrm{H}^{+}\backslashright] \) for Tomato juice (pH 4.3)

Use the formula: \( \backslashleft[\backslashmathrm{H}^{+}\backslashright] = 10^{-4.3} \) to find the hydrogen ion concentration. \[\backslashleft[\backslashmathrm{H}^{+}\backslashright] = 10^{-4.3} \approx 5.01 \times 10^{-5} \text{ M} \]

Calculate \( \backslashleft[\backslashmathrm{H}^{+}\backslashright] \) for Grapefruit juice (pH 3.2)

Use the formula: \( \backslashleft[\backslashmathrm{H}^{+}\backslashright] = 10^{-3.2} \) to find the hydrogen ion concentration. \[\backslashleft[\backslashmathrm{H}^{+}\backslashright] = 10^{-3.2} \approx 6.31 \times 10^{-4} \text{ M} \]

Key concepts

pH calculation

pH is a measure of the acidity or basicity of a solution. The lower the pH, the more acidic the solution, while a higher pH indicates a more basic solution. The pH scale typically ranges from 0 to 14. To calculate the hydrogen ion concentration \(\backslashleft[\mathrm{H}^{+}\backslashright]\), we use the formula related to pH: \(\text{pH} = -\log_{10} \backslashleft[\mathrm{H}^{+}\backslashright]\). This means that if you know the pH of a solution, you can find the hydrogen ion concentration by rearranging the formula to: \(\backslashleft[\mathrm{H}^{+}\backslashright] = 10^{-\text{pH}}\). The logarithmic relationship indicates that a small change in pH corresponds to a large change in \(\backslashleft[\mathrm{H}^{+}\backslashright]\). For example, a pH decrease from 5 to 4 indicates that the hydrogen ion concentration has increased by a factor of 10.

acid-base chemistry

Acids and bases are substances that can donate or accept protons (H+ ions) respectively. Acids donate H+ ions in solution, increasing the hydrogen ion concentration and decreasing the pH. Bases accept H+ ions or donate OH- ions, thus reducing the H+ ion concentration and increasing the pH. The strength of an acid or base is determined by its ability to ionize in water. Strong acids (like hydrochloric acid) fully ionize, significantly lowering the pH, while weak acids (like acetic acid) partially ionize. Similarly, strong bases, like sodium hydroxide, completely dissociate to increase the pH, whereas weak bases, like ammonia, partially dissociate.

logarithmic functions

Logarithmic functions, like those used in pH calculations, are a way of expressing very large or very small numbers in a compact form. A logarithm answers the question of how many times one number must be multiplied by itself to get another number. For example, \(\log_{10}(100) = 2\) because 10\(\^2\)= 100. In the context of pH, we use the base-10 logarithm. The pH is given by the negative logarithm of the hydrogen ion concentration. So if \(\backslashleft[\mathrm{H}^{+}\backslashright] = 10^{-7}\ M\), then \(\text{pH} = 7\). This means that for each change in pH unit, the hydrogen ion concentration changes tenfold.

solution acidity

The acidity of a solution depends on how much it can dissociate to release hydrogen ions (H+). This is where the pH value comes into play. Less than 7 indicates an acidic solution (more H+ ions), exactly 7 is neutral (pure water), and above 7 is basic (fewer H+ ions). For example, grapefruit juice has a pH of 3.2, making it quite acidic. Lower pH means higher acidity. Intracellular fluid of the liver has a pH of 6.9, which is close to neutral but still slightly acidic. Everyday substances have a wide range of pH values. Saliva, with a pH around 6.5, is slightly acidic, whereas tomato juice, with a pH of 4.3, is moderately acidic. Knowing the pH helps in understanding the chemical nature of a solution and predicting how it will interact with other substances.