Chapter 6: Problem 2

Why does a change of only \(0.1 \mathrm{pH}\) unit represent a substantial \(\mathrm{pH}\) shift?

Short Answer

Expert verified

A change of only 0.1 pH units represents a substantial pH shift because the pH scale is logarithmic, meaning that even a small change in pH can result in a significant change in hydrogen ion concentration. A 0.1 pH unit change corresponds to a change in hydrogen ion concentration by a factor of approximately 1.26, or a 26% change. This can have a significant impact on biological systems or chemical reactions that are sensitive to changes in acidity or alkalinity.

Step by step solution

Recall the definition of pH

The pH is defined as the negative base-10 logarithm of the hydrogen ion (H+) concentration in a solution, as shown in the formula below: \[ pH = -\log_{10}([H^+]) \] A lower pH value indicates a higher concentration of hydrogen ions in the solution, making it more acidic. Conversely, a higher pH value indicates a lower concentration of hydrogen ions, making it more alkaline or basic.

Understand the logarithmic nature of the pH scale

Because the pH scale is logarithmic, each whole number change in pH results in a tenfold change in hydrogen ion concentration - a decrease of 1 pH unit corresponds to a 10-fold increase in [H+], and an increase of 1 pH unit corresponds to a 10-fold decrease in [H+]. This means that even a small change in pH can result in a significant change in hydrogen ion concentration.

Calculate the change in hydrogen ion concentration for a 0.1 pH change

Let's assume that we have a solution with an initial pH of \(pH_1\). We will calculate the change in H+ concentration when the pH changes by 0.1 units to \(pH_2 = pH_1 + 0.1\). First, we can express the initial and final H+ concentrations in terms of their pH values: \[ [H_1^+] = 10^{-pH_1} \] \[ [H_2^+] = 10^{-pH_2} \] Now, we can find the ratio of the H+ concentrations after and before the pH change: \[ \frac{[H_2^+]}{[H_1^+]} = \frac{10^{-pH_2}}{10^{-pH_1}} \] We know that the pH change is equal to 0.1 pH units, so \(pH_2 = pH_1 + 0.1\). Plugging this into the equation, we get: \[ \frac{10^{-(pH_1 + 0.1)}}{10^{-pH_1}} \]

Interpret the results

Simplifying the equation, we find that the ratio of the H+ concentrations is approximately 1.26: \[ \frac{10^{-(pH_1 + 0.1)}}{10^{-pH_1}} = 10^{-0.1} \approx 1.26 \] This means that a change of 0.1 pH units represents a 26% change in the hydrogen ion concentration, which can be considered a substantial change for biological systems or chemical reactions that are sensitive to small changes in acidity or alkalinity.

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Why does a change of only \(0.1 \mathrm{pH}\) unit represent a substantial \(\mathrm{pH}\) shift?

Short Answer

Step by step solution

Recall the definition of pH

Understand the logarithmic nature of the pH scale

Calculate the change in hydrogen ion concentration for a 0.1 pH change

Interpret the results

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