Problem 2 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

For a sample of pure water, (a) pH increases and pOH decreases with increase in temperature. (b) pH decreases and pOH increases with increase in temperature. (c) both \(\mathrm{pH}\) and \(\mathrm{pOH}\) increases with increase in temperature. (d) both \(\mathrm{pH}\) and \(\mathrm{pOH}\) decrease with increase in temperature.

Step-by-Step Solution

Answer

With an increase in temperature, both pH and pOH of pure water decrease. Therefore, the correct answer is (d).

Step 1: Understanding pH and pOH

The pH is a measure of the hydrogen ion concentration \( [H^+] \) in a solution, and pOH is a measure of the hydroxide ion concentration \( [OH^-] \) in a solution. They are related by the equation \( pH + pOH = 14 \) at 25°C (298 K). For pure water, \( [H^+] = [OH^-] \) since water dissociates into equal amounts of hydrogen ions and hydroxide ions.

Step 2: Understanding the Effect of Temperature on Water Ionization

As the temperature of water increases, the ionization of water also increases. This results in an increase in the concentrations of both \( [H^+] \) and \( [OH^-] \) ions.

Step 3: Analyzing pH Change with Temperature

An increase in the hydrogen ion concentration \( [H^+] \) due to increased temperature would typically result in a decrease in pH, because pH is the negative logarithm of \( [H^+] \) concentration.

Step 4: Analyzing pOH Change with Temperature

An increase in the hydroxide ion concentration \( [OH^-] \) as temperature rises would cause pOH to decrease, since pOH is defined as the negative logarithm of the \( [OH^-] \) concentration.

Step 5: Concluding the Correct Option Based on Temperature Effect

Considering the above information, the correct statement is that with an increase in temperature, pH decreases due to increased \( [H^+] \) and pOH also decreases due to increased \( [OH^-] \) concentration. Therefore, answer (d) 'both \(\mathrm{pH}\) and \(\mathrm{pOH}\) decrease with increase in temperature' is correct.

Key Concepts

Temperature Effects on Water Ionization

The process of water molecules breaking down into hydrogen ions (\( H^+ \)) and hydroxide ions (\( OH^- \) is known as water ionization. One key aspect to grasp is how temperature plays a crucial role in this process. As the temperature of water increases, the energy within the water molecules increases as well, leading to an enhanced rate of water ionization.

This heightened state of ionization boosts both the hydrogen and hydroxide ion concentrations. The relationship is not difficult to understand; higher temperature equals more energetic water molecules, which then leads to more of them splitting into ions. To provide you with a real-world scenario, think of a pot of water boiling on a stove - as the heat increases, so does the activity within the pot, leading to a greater number of water molecules undergoing ionization.

To sum up, higher temperatures drive the ionization equilibrium towards a greater number of ions, directly impacting the pH and pOH levels of the water, which brings us to our next concept involving hydrogen ion concentration.

Hydrogen Ion Concentration

Hydrogen ion concentration, symbolized as \( [H^+] \) is a pivotal factor in the study of chemical reactions and solutions. It is the cornerstone of the concept of pH, which is a measure of how acidic or basic a solution is, on a scale ranging typically from 0 to 14.

Now, what you need to remember is that the pH is inversely proportional to the hydrogen ion concentration. This means that the lower the pH, the higher the concentration of hydrogen ions. Anytime you hear that the pH is low, you can be sure that the environment is quite acidic, teeming with hydrogen ions.

Our previous discussion about temperature showed that as it rises, the concentration of hydrogen ions increases, which then decreases the pH - a hotter solution is thus more acidic. Remember the equation \( pH = -\text{log}_{10} [H^+] \) and imagine trying to solve a math problem; if the hydrogen ions go up (\( [H^+] \) increases), the pH number gets smaller - it's like the scales tipping in opposite directions.

Hydroxide Ion Concentration

Switching gears to the hydroxide ion concentration, symbolized as \( [OH^-] \) – this concept runs parallel to that of hydrogen ions. pOH provides a gauge for the hydroxide ion concentration and reflects the basicity of a solution. In essence, lower pOH indicates a higher \( [OH^-] \) concentration and therefore, a more basic solution.

Remember the balance between pH and pOH, that \( pH + pOH = 14 \) at 25°C? This is where it gets interesting; as temperature rises, the hydroxide ion concentration also goes up. But unlike with pH, an increase in \( [OH^-] \) causes the pOH value to drop, according to the equation \( pOH = -\text{log}_{10} [OH^-] \) - it's counterintuitive but true.

So, what does this mean in layman's terms? If our water gets warmer, it becomes more basic because there are more hydroxide ions bouncing around. It's like the number on the thermostat and the number of ice creams eaten on a hot day; one goes up, the other inevitably follows.

Autoionization of Water

Diving into autoionization of water, it's like watching a dance of molecules where two water molecules partner up briefly only to split apart into a hydrogen ion (\( H^+ \) and a hydroxide ion (\( OH^- \) - a delicate balance of creation and destruction that occurs naturally even in pure water.

The fascinating bit about this is that it's a reversible reaction. Water molecules (\( H_2O \) constantly switch between being part of a liquid and existing as ions. The autoionization constant (\( K_w \) is the mathematical expression of this equilibrium and it's important to note that it changes with temperature. For every increase in temperature, \( K_w \) grows larger, meaning more hydrogen and hydroxide ions are present, disrupting the harmony.

In simpler terms, increasing temperature shakes up the water's equilibrium, pushing it to produce more ions, which is crucial for students to understand as it directly impacts the pH and pOH of the water. It's a lot like as the volume of music goes up in a room, the number of people dancing increases - a direct response to an energetic stimulus.