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Chapter 14: Problem 1

Consider two beakers of pure water at different temperatures. How do their \(\mathrm{pH}\) values compare? Which is more acidic? more basic? Explain.

Short Answer

Expert verified
The pH values of the two beakers of pure water at different temperatures differ because the ion product of water, \(K_w\), changes with temperature. In beaker A (higher temperature), the pH value is higher due to increased self-ionization, while in beaker B (lower temperature), the pH value is lower. However, neither beaker is more acidic or more basic than the other, as the water in both beakers remains neutral, with equal concentrations of \(H^+\) and \(OH^-\) ions. The only difference is their temperatures, which affect the ion product of water and the pH values.

Step by step solution

01

Understanding the pH of pure water

First, let us recap the concept of pH. The pH of a solution is defined as the negative logarithm of the concentration of hydrogen ions \([H^+]\) in the solution: \[pH = -\log_{10} [H^+]\] For pure water, it undergoes a self-ionization process, forming equal amounts of hydrogen ions (\(H^+\)) and hydroxide ions (\(OH^-\)): \[2H_2O \rightleftharpoons H_3O^+ + OH^-\] Since pure water is neutral and not acidic or basic, the concentration of hydrogen ions \([H^+]\) equals the concentration of hydroxide ions \([OH^-]\).
02

Ion product of water

The ion product of water (\(K_w\)) is the product of the concentrations of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) in water at equilibrium: \[K_w = [H^+][OH^-]\] At 25°C, the value of \(K_w\) is \(1.0\times10^{-14}\), which means the concentration of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) are equal, and each has a concentration of \(1.0\times10^{-7}\) M. Thus, the pH of pure water at 25°C is: \[pH = -\log_{10} [H^+] = -\log_{10}(1.0\times10^{-7}) = 7\]
03

The effect of temperature on pH of pure water

The ion product of water, \(K_w\), increases with the increase in temperature due to an increase in the self-ionization process. It means that, at temperatures higher than 25°C, the concentrations of \(H^+\) and \(OH^-\) will be higher than \(1.0\times10^{-7}\) M but still equal to each other. When the temperature goes down, on the other hand, the ion product of water decreases. This means that the concentrations of \(H^+\) and \(OH^-\) will be lower than \(1.0\times10^{-7}\) M, but still equal to each other.
04

Comparing the pH values

Now we have two beakers of pure water at different temperatures. Let's denote them as beaker A (higher temperature) and beaker B (lower temperature). Since the ion product of water is higher in beaker A, the concentrations of \(H^+\) and \(OH^-\) are higher too, and so is the pH value. In beaker B, all those values are lower due to lower ion self-ionization, which results in a lower pH value.
05

Determining which is more acidic or more basic

As we mentioned before, in both beakers, the concentration of hydrogen ions (\(H^+\)) is equal to the concentration of hydroxide ions (\(OH^-\)); hence, both beakers contain neutral water. Even though beaker A has a higher pH value than beaker B, neither beaker is more acidic or more basic than the other. In both cases, the water is neutral, with the only difference being their temperatures, which affect the ion product of water and the pH values.

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Most popular questions from this chapter

An acid HX is \(25 \%\) dissociated in water. If the equilibrium concentration of \(\mathrm{HX}\) is \(0.30 \mathrm{M}\), calculate the \(K_{\mathrm{a}}\) value for \(\mathrm{HX}\).

Write out the stepwise \(K_{\mathrm{a}}\) reactions for the diprotic acid \(\mathrm{H}_{2} \mathrm{SO}_{3}\)

What are the major species present in the following mixtures of bases? a. \(0.050 \mathrm{M} \mathrm{NaOH}\) and \(0.050 \mathrm{M} \mathrm{LiOH}\) b. \(0.0010 \mathrm{M} \mathrm{Ca}(\mathrm{OH})_{2}\) and \(0.020 \mathrm{M} \mathrm{RbOH}\) What is \(\left[\mathrm{OH}^{-}\right]\) and the \(\mathrm{pH}\) of each of these solutions?

A \(10.0\) -mL sample of an \(\mathrm{HCl}\) solution has a \(\mathrm{pH}\) of \(2.000\). What volume of water must be added to change the \(\mathrm{pH}\) to \(4.000\) ?

Aluminum hydroxide is an amphoteric substance. It can act as either a Brønsted-Lowry base or a Lewis acid. Write a reaction showing \(\mathrm{Al}(\mathrm{OH})_{3}\) acting as a base toward \(\mathrm{H}^{+}\) and as an acid toward \(\mathrm{OH}^{-}\).
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