Question

Phosphate buffers are important in regulating the \(\mathrm{pH}\) of intracellular fluids. If the concentration ratio of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-} / \mathrm{HPO}_{4}^{2-}\) in a sample of intracellular fluid is \(1.1: 1\), what is the \(\mathrm{pH}\) of this sample of intracullular fluid? \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(a q) \rightleftharpoons \mathrm{HPO}_{4}^{2-}(a q)+\mathrm{H}^{+}(a q) \quad K_{\mathrm{a}}=6.2 \times 10^{-\mathrm{s}}\)

Short answer

The pH of the intracellular fluid in the given sample is approximately 7.17.

Step-by-step solution

Write the expression for Ka

Ka is the equilibrium constant for the acid dissociation reaction. In this case, H2PO4- is the acidic species and its Ka is given. The Ka expression for the given reaction is: Ka = \(\dfrac{[\mathrm{H}^{+}][\mathrm{HPO}_{4}^{2-}]}{[\mathrm{H}_{2}\mathrm{PO}_{4}^{-}]}\) Where Ka = 6.2 x 10^-8 (provided in the question)

Write the parameters in terms of variables

Given the ratio H2PO4- / HPO42- = 1.1 : 1, let the concentrations of H2PO4- and HPO42- be 1.1x and x, respectively. Let's also assume the concentration of hydrogen ions [H+] to be y. Now we can rewrite our expression for Ka using these variables: Ka = \(\dfrac{y \cdot x}{1.1x}\) Since Ka = 6.2 x 10^-8, now we can substitute the value 6.2 x 10^-8 = \(\dfrac{y \cdot x}{1.1x}\)

Simplify the equation and solve for [H+]

We can cancel out the x in the numerator and the denominator, and then solve for y: 6.2 x 10^-8 = \(\dfrac{y}{1.1}\) Multiplying both sides by 1.1, we get: y = 6.2 x 10^-8 * 1.1 y = 6.82 x 10^-8

Calculate the pH of the solution

Now that we have the concentration of hydrogen ions [H+], we can calculate the pH using the following formula: pH = -log10([H+]) pH = -log10(6.82 x 10^-8) After evaluating the expression, we get: pH ≈ 7.17 So, the pH of this sample of intracellular fluid is approximately 7.17.

Key concepts

Equilibrium Constant (Ka)

The equilibrium constant, represented as Ka, is a crucial component when dealing with acid dissociation reactions. It measures the strength of an acid in a solution, specifically how well the acid releases protons (H+ ions).
For our phosphate buffer problem, the acid dissociation reaction involves H2PO4-. The equation is:

• Ka = \(\dfrac{[\mathrm{H}^{+}][\mathrm{HPO}_{4}^{2-}]}{[\mathrm{H}_{2}\mathrm{PO}_{4}^{-}]}\)

In this expression, the brackets denote the concentration of each species. Ka is given as \(6.2 \times 10^{-8}\) in the problem, and it indicates the position of the equilibrium. A smaller Ka value means the acid is weaker and dissociates less.
When working with Ka, it's helpful to know:

• Large Ka values indicate strong acids with more dissociation.
• Small Ka values are for weak acids with minimal dissociation.

As observed, understanding Ka allows us to calculate the concentration of hydrogen ions \([\mathrm{H}^{+}]\) leading to more accurate pH predictions.

Acid-Base Equilibria

Acid-base equilibria play a pivotal role in determining the pH of solutions, particularly for buffers like the phosphate buffer in question. These equilibria involve the reversible reaction between acid and base pairs, maintaining the balance of \([\mathrm{H}^{+}]\) and \([\mathrm{OH}^{-}]\) ions in a solution.
For our phosphate buffer, the equilibrium consists of:

• Acid: \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-} \), which can donate protons.
• Base: \( \mathrm{HPO}_{4}^{2-} \), which can accept protons.

Buffers resist changes in pH when small amounts of acid or base are added. This resistance is largely due to the equilibrium between the acid and base.
A few key points on acid-base equilibria:

• Dynamic equilibrium keeps the concentrations of an acid and its corresponding base constant within the buffer.
• Equilibria are affected by temperature and concentration changes.

Understanding acid-base equilibria helps predict how the buffer system will react to additional acids/bases, keeping physiological conditions stable.

pH Calculation

Calculating the pH is central to studying solutions and their properties, both in chemistry and biological systems. The pH scale measures the acidity or basicity of a solution based on the concentration of hydrogen ions (\([\mathrm{H}^{+}]\)).
Here’s the formula to find pH:

• pH = - \(\log_{10} ([\mathrm{H}^{+}]) \)

Notice how a lower pH indicates higher acidity, while a higher pH means the solution is more basic.
In the phosphate buffer problem, we found the \([\mathrm{H}^{+}]\) concentration first to compute the pH:

• \(\mathrm{y} = 6.82 \times 10^{-8} \)

Next, use the formula:

• pH = -\log_{10}(6.82 \times 10^{-8}) = 7.17

Some notes for pH calculations:

• pH values range typically from 0 to 14.
• Values near 7 are neutral, below 7 are acidic, and above 7 are basic.

Accurate pH calculations are essential in chemistry and biology to maintain balanced environments for reactions and cellular activities.