Question

What is the \(\mathrm{pH}\) of the following solutions? Identify each as acidic, basic, or neutral. (a) \(0.010 \mathrm{M} \mathrm{HNO}_{3}\) (b) \(0.020 \mathrm{M} \mathrm{HClO}_{4}\) (c) \(0.015 \mathrm{M} \mathrm{NaOH}\)

Short answer

The pH for solution (a) is 2, (b) is 1.7 and (c) is 12.3. Therefore, (a) and (b) are acidic and (c) is basic.

Step-by-step solution

Calculate the pH

Let's start with part (a) and (b) which are acidic solutions. For each acid, write out the acid dissociation expression and calculate [H+]. As these are strong acids they fully dissociate. Therefore, \( [H^{+}] = 0.010M \) for (a) and \( [H^{+}] = 0.020M \) for (b). Then, we can calculate the pH using the equation \( \mathrm{pH} = -\log[H^{+}] \).

Identify as Acidic, Basic, or Neutral

Use the calculated pH of each solution to identify it as acidic, basic, or neutral. Solutions with a pH less than 7 are considered acidic. Therefore, both (a) and (b) can be identified as acids.

Calculate the pOH for Basic Solution

(c) is a basic solution. Therefore, we need to find the pOH first. The [OH-] for the basic solution is simply the concentration of NaOH, which is 0.015M. We can find the pOH using \(pOH = -\log[OH^{-}]\).

Calculate the pH for Basic Solution

After calculating the pOH in step 3, we can find the pH of the solution using the equation \( \mathrm{pH} = 14 - \mathrm{pOH} \).

Identify as Acidic, Basic, or Neutral

Use the calculated pH of the solution to identify it as acidic, basic, or neutral. In this case, since the pH is more than 7, it is basic.

Key concepts

Acid and Base Dissociation

When acidic or basic substances dissolve in water, they undergo a process called dissociation. This is where the acid or base splits apart into ions. For acids, these ions are positive hydrogen ions (H+) and the corresponding negative ions. For bases, the process results in hydroxide ions (OH-) and positive ions.

Understanding the dissociation process is crucial for calculating the pH of a solution. Acids are substances that increase the concentration of H+ ions when they dissociate in water. For example, strong acids like HNO3 and HClO4 dissociate completely, releasing H+ ions equal to their original concentration. This is why in our initial calculation for solution (a) and (b), the concentration of H+ ions is equal to the molar concentration of the acids.

Complete vs Partial Dissociation

It's important to note that strong acids/bases fully dissociate in water, while weak acids/bases only partially dissociate. Because strong acids fully dissociate, this simplifies computation of the H+ ion concentration to directly equal the initial concentration of the acid, as demonstrated in the exercise. On the other hand, calculating the pH of weak acids or bases would require knowledge of the acid or base dissociation constant (Ka or Kb) to determine how much they dissociate.

Acidic and Basic Solution Identification

To identify whether a solution is acidic or basic, we look at the pH scale, which ranges from 0 to 14. A pH less than 7 indicates an acidic solution, a pH above 7 indicates a basic (alkaline) solution, and a pH of 7 is neutral.

In the textbook exercise, after calculating the pH of our solutions, we were able to classify them based on their pH values. The solutions with HNO3 and HClO4 were found to be acidic because their pH values were less than 7. This means they have a higher concentration of H+ ions in the solution.

Factors Affecting Solution Acidity

Several factors can influence the acidity or basicity of a solution, including the concentration of the acid or base, the presence of other substances that may affect the dissociation, and the temperature of the solution. In a simplistic scenario like our exercise, identifying the nature of the substance and calculating the pH is enough to determine the acidity or basicity of the solution.

pOH Calculation

Conversely to the pH which measures the concentration of hydrogen ions, the pOH measures the concentration of hydroxide ions (OH-) in a solution. The pOH is particularly useful for working with basic solutions, where it is more straightforward to calculate the concentration of OH- ions.

To calculate the pOH, as shown in the exercise for solution (c), we used the formula \( pOH = -\log[OH^-] \). The negative log of the hydroxide ion concentration (which for solution (c) was 0.015M) will yield the pOH. Once we have the pOH, we can use it to find the pH because pH and pOH are related by the equation \( pH = 14 - pOH \). This equation is based on the ionic product of water at 25°C, which is constant (\( K_w = [H^+][OH^-] = 1 \times 10^{-14} \)).

pH and pOH Relationship

In pure water at 25°C, the pH is 7 and so is the pOH, making it a neutral solution. Any increase or decrease in the pH will correspondingly decrease or increase the pOH so that their sum always equals 14, keeping \( K_w \) constant. This complementary relationship ensures we can always derive one from the other, simplifying our approach to analyzing solutions' acidity or alkalinity.