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Chapter 13: Problem 14

Why is the \(\mathrm{pH}\) of water at \(25^{\circ} \mathrm{C}\) equal to \(7.00 ?\)

Short Answer

Expert verified
The pH of water at \(25^{\circ}\)C is equal to 7.00 because at this temperature, water undergoes auto-ionization, resulting in equal concentrations of H+ ions and OH- ions at approximately \(1 \times 10^{-7}\) M. When this concentration is plugged into the pH equation \( pH = -\log_{10}[H^+]\), it results in a pH value of 7, representing a neutral solution.

Step by step solution

01

Understanding pH scale and pH of water

The pH scale is a measure of the acidity or alkalinity of a solution. It is defined as the negative logarithm of the hydrogen ion (H+) concentration in a solution. Mathematically, pH is represented as: \( pH = -\log_{10}[H^+] \) Water undergoes a process called auto-ionization, in which a small number of water molecules naturally dissociate into hydrogen ions (H+) and hydroxide ions (OH-). At 25°C, the concentration of H+ ions and OH- ions in pure water is equal, and their concentrations are around \(1 \times 10^{-7}\) M. This can be represented as: \( H_2O \rightleftharpoons H^+ + OH^- \) with \( [H^+] = [OH^-] = 1 \times 10^{-7} M \) Now, we can calculate the pH of water at 25°C.
02

Calculate the pH of water

To find the pH of water, we need to plug the concentration of H+ ions into the pH formula: \( pH = -\log_{10}(1 \times 10^{-7}) \)
03

Simplify and solve for pH

Now, we can use the logarithm properties to simplify this expression: \( pH = -\log_{10}(1 \times 10^{-7}) \) \( pH = -(-7) \) \( pH = 7 \) So, the pH of water at 25°C is 7.00. In conclusion, the pH of water at \(25^{\circ}\)C is equal to 7.00 because at that temperature, the concentration of H+ ions and OH- ions is equal and their concentrations are around \(1 \times 10^{-7}\) M, which gives a pH value of 7 when plugged into the pH equation.

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Most popular questions from this chapter

Calculate the \(\mathrm{pH}\) of a \(1.0 \times 10^{-7}-M\) solution of \(\mathrm{NaOH}\) in water.

A solution of formic acid (HCOOH, \(K_{\mathrm{a}}=1.8 \times 10^{-4}\) ) has a pH of \(2.70 .\) Calculate the initial concentration of formic acid in this solution.

A typical aspirin tablet contains 325 mg acetylsalicylic acid \(\left(\mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4}\right) .\) Calculate the \(\mathrm{pH}\) of a solution that is prepared by dissolving two aspirin tablets in enough water to make one cup \((237 \mathrm{mL})\) of solution. Assume the aspirin tablets are pure acetylsalicylic acid, \(K_{\mathrm{a}}=3.3 \times 10^{-4}\)

Sodium azide (NaN, ) is sometimes added to water to kill bacteria. Calculate the concentration of all species in a \(0.010-M\) solution of \(\mathrm{NaN}_{3} .\) The \(K_{\mathrm{a}}\) value for hydrazoic acid \(\left(\mathrm{HN}_{3}\right)\) is \(1.9 \times 10^{-5}\)

Calculate the \(\mathrm{pH}\) of a \(0.050-M\) Al(NO_3)a solution. The \(K_{\mathrm{a}}\) value for \(\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\) is \(1.4 \times 10^{-5}\).
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