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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

Expert verified
[H^+] concentrations are: (a) 3.16 脳 10^{-7} mol/L (b) 1.26 脳 10^{-7} mol/L (c) 5.01 脳 10^{-5} mol/L (d) 6.31 脳 10^{-4} mol/L

Step by step solution

01

Understand the pH scale

The pH scale is a measure of hydrogen ion concentration, \(\text{\textbackslash left[\text\backslash mathrm\text{\textbackslash H}^+\text{\textbackslash right]}}\). pH is defined as \(\text{\textbackslash pH = -\text{\textbackslash log}_\text{\textbackslash 10} \text{\textbackslash left[\text{\textbackslash H}^+\text{\textbackslash right]}}}\).
02

Formula to calculate \(\text{\textbackslash left[\text{\textbackslash mathrm\text{\textbackslash H}^+\text{\textbackslash right]}}}\)

To find \(\text{\textbackslash left[\text{\textbackslash mathrm\text{\textbackslash H}^+\text{\textbackslash right]}}}\) from pH, use the formula: \[ \text{\textbackslash left[\text{\textbackslash mathrm\text{\textbackslash H}^+\text{\textbackslash right]}} = \text{\textbackslash 10}^{-\text{\textbackslash pH}} \text \text{\textbackslash; unit: mol/L} \]
03

Calculation for saliva (pH 6.5)

For saliva with pH 6.5: \[ \text{\textbackslash left[\text{\textbackslash mathrm\text{\textbackslash H}^+\text{\textbackslash right]}} = 10^{-\text{\textbackslash 6.5}} \text = 3.16 \times 10^{-7} \text{ mol/L} \]
04

Calculation for intracellular fluid of liver (pH 6.9)

For intracellular fluid with pH 6.9: \[ \text{\textbackslash left[\text{\textbackslash mathrm\text{\textbackslash H}^+\text{\textbackslash right]}} = 10^{-\text{\textbackslash 6.9}} \text = \text{\textbackslash 1.26} \times \text{\textbackslash 10}^{-\text{\textbackslash 7}} \text{ mol/L} \]
05

Calculation for tomato juice (pH 4.3)

For tomato juice with pH 4.3: \[ \text{\textbackslash left[\text{\textbackslash mathrm\text{\textbackslash H}^+\text{\textbackslash right]}} = 10^{-\text{\textbackslash 4.3}} \text = \text{\textbackslash 5.01} \times \text{\textbackslash 10}^{-\text{\textbackslash 5}} \text{ mol/L} \]
06

Calculation for grapefruit juice (pH 3.2)

For grapefruit juice with pH 3.2: \[ \text{\textbackslash left[\text{\textbackslash mathrm\text{\textbackslash H}^+\text{\textbackslash right]}} = 10^{-\text{\textbackslash 3.2}} \text = \text{\textbackslash 6.31} \times \text{\textbackslash 10}^{-\text{\textbackslash 4}} \text{ mol/L} \]

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Key Concepts

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

pH Scale
The pH scale is a measure used to specify the acidity or basicity of an aqueous solution. It ranges from 0 to 14, where 7 is considered neutral. A pH value less than 7 indicates an acidic solution, while a value greater than 7 indicates a basic (alkaline) solution.
pH is defined mathematically as the negative logarithm (base 10) of the hydrogen ion concentration: \( \text{pH} = -\text{log} \left[ \text{H}^{+} \right] \). Because the pH scale is logarithmic, each whole pH value below 7 is ten times more acidic than the next higher value.
This scale helps us easily compare the acidity between different substances. For example, a substance with a pH of 4 is significantly more acidic than a substance with a pH of 6.
Acid-Base Chemistry
Acid-base chemistry revolves around the concepts of acids and bases, which involve the transfer of hydrogen ions (H鈦). Acids are substances that increase the concentration of hydrogen ions in a solution, whereas bases decrease this concentration. Acids donate H鈦 ions, while bases accept them.
In water, acids dissociate to release H鈦 ions. For instance, hydrochloric acid (HCl) dissociates to produce H鈦 and Cl鈦 ions. Conversely, bases, such as sodium hydroxide (NaOH), dissociate to produce OH鈦 ions, which can combine with H鈦 ions to form water.
The balance between these H鈦 ions and hydroxide ions (OH鈦) in solution determines the overall pH. A strong acid fully dissociates and releases many H鈦 ions, leading to a low pH, whereas a weak acid only partially dissociates.
Logarithmic Calculations
Understanding how to use logarithms is crucial in pH calculations. The pH formula involves a logarithmic function: \( \text{pH} = -\text{log} \left[ \text{H}^{+} \right] \). This means that if you know the pH of a solution, you can calculate the hydrogen ion concentration (\( [\text{H}^{+}] \)) using: \[ \left[ \text{H}^{+} \right] = 10^{-\text{pH}} \]
This is especially useful in contexts like biology and chemistry, where the pH influences various biochemical processes. To work with these calculations, you'll need to be comfortable using scientific notation and the properties of logarithms. For instance, in a scientific calculator, you'd input the pH value and then use the inverse log function to find the hydrogen ion concentration.
Biological Fluids pH
The pH of biological fluids is tightly regulated because many biochemical processes are pH-sensitive. For example:
  • Saliva, which typically has a pH around 6.5, helps in food digestion and maintaining oral health.
  • Intracellular fluid in the liver, with a pH of about 6.9, is key in metabolism and detoxification.
  • Tomato juice, with a pH of 4.3, is acidic and impacts digestion positively.
  • Grapefruit juice has a pH of 3.2, making it one of the more acidic fruit juices, affecting its taste and potential impact on dental health.
Maintaining the correct pH in biological fluids ensures that enzymatic reactions and other cellular processes function optimally. Deviations in pH can lead to conditions such as acidosis or alkalosis, which require medical intervention.

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Most popular questions from this chapter

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

Reflect and Apply Another characteristic of modern buffers such as HEPES is that their pH changes little with changes in temperature. Why is this desirable?

Biochemical Connections A frequently recommended treatment for hiccups is to hold one's breath. The resulting condition, hypoventilation, causes buildup of carbon dioxide in the lungs. Predict the effect on the pH of blood.

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 \(1.0 \mathrm{M} \mathrm{NaH}_{2} \mathrm{PO}_{4}\)

Mathematical A catalog in the lab has a recipe for preparing 1 L of a TRIS buffer at \(0.0500 \mathrm{M}\) and with \(\mathrm{pH} 8.0\) : dissolve \(2.02 \mathrm{g}\) of TRIS (free base, \(\mathrm{MW}=121.1 \mathrm{g} / \mathrm{mol}\) ) and \(5.25 \mathrm{g}\) of TRIS hydrochloride (the acidic form, \(\mathrm{MW}=157.6 \mathrm{g} / \mathrm{mol}\) ) in a total volume of \(1 \mathrm{L}\). Verify that this recipe is correct.

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