Skip to main content
Ch.17 - Acids and Bases
Tro - Chemistry: A Molecular Approach 6th Edition
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Not the one you use?Change textbook
All textbooksTro 6th EditionCh.17 - Acids and BasesProblem 57
Chapter 17, Problem 57

Like all equilibrium constants, the value of Kw depends on temperature. At body temperature (37 °C), Kw = 2.4×10–14. What are the [H3O+] and pH of pure water at body temperature?

Verified step by step guidance
1
Identify the given values: Kw (the ion-product constant of water) at 37 °C is 2.4 * 10^-14.
Recall that for pure water, the concentrations of hydrogen ions [H3O+] and hydroxide ions [OH-] are equal. Therefore, [H3O+] = [OH-].
Set up the equation for Kw at equilibrium: Kw = [H3O+][OH-]. Since [H3O+] = [OH-], this can be rewritten as Kw = [H3O+]^2.
Solve for [H3O+] by taking the square root of Kw: [H3O+] = sqrt(Kw).
Calculate the pH of the solution using the formula pH = -log([H3O+]).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ion Product of Water (Kw)

Kw, the ion product of water, is the equilibrium constant for the self-ionization of water, represented as Kw = [H3O+][OH-]. Its value changes with temperature; at 25 °C, Kw is 1.0 x 10^-14, but at 37 °C, it increases to 2.4 x 10^-14. This indicates that the concentrations of hydronium ions [H3O+] and hydroxide ions [OH-] in pure water are equal at any temperature.
Recommended video:
Guided course
00:53
Production of Hydrogen Example

Hydronium Ion Concentration

In pure water, the concentration of hydronium ions [H3O+] is equal to the concentration of hydroxide ions [OH-]. At 37 °C, since Kw = 2.4 x 10^-14, we can find [H3O+] by taking the square root of Kw, leading to [H3O+] = [OH-] = √(2.4 x 10^-14). This concentration is crucial for determining the pH of the solution.
Recommended video:
Guided course
06:25
Hydronium Ion Concentration Example

pH Scale

The pH scale is a logarithmic scale used to measure the acidity or basicity of a solution, defined as pH = -log[H3O+]. A pH of 7 indicates neutrality, while values below 7 indicate acidity and above 7 indicate basicity. At body temperature, the calculated [H3O+] will yield a pH value that reflects the neutral nature of pure water at that temperature.
Recommended video:
Guided course
02:33
The pH Scale
Related Practice
Textbook Question

Calculate the pH of each acid solution. Explain how the resulting pH values demonstrate that the pH of an acid solution should carry as many digits to the right of the decimal place as the number of significant figures in the concentration of the solution. [H3O+] = 0.044 M [H3O+] = 0.045 M [H3O+] = 0.046 M

1224
views
Textbook Question

Calculate [H3O+] and [OH–] for each solution at 25 °C. a. pH = 8.55

2002
views
Textbook Question

Determine the concentration of H3O+ to the correct number of significant figures in a solution with each pH. Describe how these calculations show the relationship between the number of digits to the right of the decimal place in pH and the number of significant figures in concentration. pH = 2.50 pH = 2.51 pH = 2.52

2011
views
Textbook Question

The value of Kw increases with increasing temperature. Is the autoionization of water endothermic or exothermic?

2595
views
Textbook Question

Calculate [H3O+] and [OH–] for each solution at 25 °C. b. pH = 11.23 c. pH = 2.87

648
views
Textbook Question

Complete the table. (All solutions are at 25 °C.)

869
views