Problem Set: 9.2 Ph And Poh Answers

Acidity and alkalinity are fundamental concepts in chemistry, influencing a wide range of natural and industrial processes. Understanding pH and pOH, along with their calculations, is crucial for fields ranging from environmental science to medicine. Problem sets focusing on pH and pOH provide a practical approach to mastering these concepts. Let's delve into a comprehensive exploration of pH and pOH, accompanied by detailed solutions to typical problem set questions.

Understanding pH and pOH

pH (potential of hydrogen) is a measure of the concentration of hydrogen ions (H+) in a solution. It quantifies the acidity or basicity of an aqueous solution. The pH scale ranges from 0 to 14:

• pH < 7: Acidic solution (higher concentration of H+ ions)
• pH = 7: Neutral solution (equal concentration of H+ and OH- ions)
• pH > 7: Basic or alkaline solution (lower concentration of H+ ions)

The mathematical definition of pH is:

pH = -log10[H+]

Where [H+] represents the molar concentration of hydrogen ions in moles per liter (mol/L or M).

pOH (potential of hydroxide) is a measure of the concentration of hydroxide ions (OH-) in a solution. It complements pH in describing the basicity of a solution. The mathematical definition of pOH is:

pOH = -log10[OH-]

Where [OH-] represents the molar concentration of hydroxide ions in moles per liter (mol/L or M).

Relationship between pH and pOH: In aqueous solutions, the concentration of H+ and OH- ions are related by the ion product of water (Kw):

Kw = [H+][OH-] = 1.0 x 10-14 at 25°C

Taking the negative logarithm of both sides, we get:

pH + pOH = 14

This relationship is crucial for converting between pH and pOH, enabling us to determine the acidity or basicity of a solution regardless of whether we know the [H+] or [OH-] concentration.

Problem Set: 9.2 pH and pOH – Example Questions and Answers

Let's explore a series of problems related to pH and pOH, providing detailed solutions to enhance understanding.

Question 1: Calculate the pH of a solution with a hydrogen ion concentration of 3.2 x 10-5 M.

Solution:

Using the formula pH = -log10[H+], we have:

pH = -log10(3.2 x 10-5) pH = -(-4.49) pH = 4.49

Therefore, the pH of the solution is 4.49. This indicates an acidic solution.

Question 2: Determine the pOH of a solution with a hydroxide ion concentration of 7.5 x 10-3 M.

Solution:

Using the formula pOH = -log10[OH-], we have:

pOH = -log10(7.5 x 10-3) pOH = -(-2.12) pOH = 2.12

Therefore, the pOH of the solution is 2.12.

Question 3: What is the pH of a solution if its pOH is 9.6?

Solution:

Using the relationship pH + pOH = 14, we can find the pH:

pH = 14 - pOH pH = 14 - 9.6 pH = 4.4

Therefore, the pH of the solution is 4.4. This indicates an acidic solution.

Question 4: Calculate the hydrogen ion concentration [H+] in a solution with a pH of 8.2.

Solution:

To find [H+] from pH, we use the formula:

[H+] = 10-pH [H+] = 10-8.2 [H+] = 6.31 x 10-9 M

Therefore, the hydrogen ion concentration is 6.31 x 10-9 M.

Question 5: Determine the hydroxide ion concentration [OH-] in a solution with a pOH of 3.9.

Solution:

To find [OH-] from pOH, we use the formula:

[OH-] = 10-pOH [OH-] = 10-3.9 [OH-] = 1.26 x 10-4 M

Therefore, the hydroxide ion concentration is 1.26 x 10-4 M.

Question 6: A solution has a pH of 6.8. Is the solution acidic, basic, or neutral?

Solution:

Since the pH is less than 7, the solution is acidic.

Question 7: A solution has a pOH of 7.3. Is the solution acidic, basic, or neutral?

Solution:

First, find the pH using the relationship pH + pOH = 14:

pH = 14 - pOH pH = 14 - 7.3 pH = 6.7

Since the pH is less than 7, the solution is acidic.

Question 8: Calculate the pH and pOH of a 0.001 M HCl solution. (HCl is a strong acid and completely dissociates in water).

Solution:

Since HCl is a strong acid, it completely dissociates in water:

HCl → H+ + Cl-

Therefore, [H+] = 0.001 M

Calculate the pH:

pH = -log10[H+] pH = -log10(0.001) pH = -log10(1 x 10-3) pH = -(-3) pH = 3

Now, calculate the pOH:

pH + pOH = 14 pOH = 14 - pH pOH = 14 - 3 pOH = 11

Therefore, the pH of the 0.001 M HCl solution is 3, and the pOH is 11.

Question 9: Calculate the pH and pOH of a 0.0005 M NaOH solution. (NaOH is a strong base and completely dissociates in water).

Solution:

Since NaOH is a strong base, it completely dissociates in water:

NaOH → Na+ + OH-

Therefore, [OH-] = 0.0005 M

Calculate the pOH:

pOH = -log10[OH-] pOH = -log10(0.0005) pOH = -log10(5 x 10-4) pOH = -(-3.30) pOH = 3.30

Now, calculate the pH:

pH + pOH = 14 pH = 14 - pOH pH = 14 - 3.30 pH = 10.70

Therefore, the pH of the 0.0005 M NaOH solution is 10.70, and the pOH is 3.30.

Question 10: What is the hydrogen ion concentration [H+] of a neutral solution at 25°C?

Solution:

In a neutral solution, [H+] = [OH-]. Since Kw = [H+][OH-] = 1.0 x 10-14 at 25°C:

[H+]2 = 1.0 x 10-14 [H+] = √(1.0 x 10-14) [H+] = 1.0 x 10-7 M

Therefore, the hydrogen ion concentration of a neutral solution at 25°C is 1.0 x 10-7 M.

Question 11: If a solution has a pH of 5.6, what is the hydroxide ion concentration [OH-]?

Solution:

First, calculate the pOH:

pH + pOH = 14 pOH = 14 - pH pOH = 14 - 5.6 pOH = 8.4

Now, calculate the hydroxide ion concentration:

[OH-] = 10-pOH [OH-] = 10-8.4 [OH-] = 3.98 x 10-9 M

Therefore, the hydroxide ion concentration is 3.98 x 10-9 M.

Question 12: A solution is prepared by dissolving 0.365 g of HCl in 1.0 L of water. Calculate the pH of the solution. (Molar mass of HCl = 36.5 g/mol)

Solution:

First, calculate the number of moles of HCl:

moles of HCl = mass / molar mass moles of HCl = 0.365 g / 36.5 g/mol moles of HCl = 0.01 mol

Since the volume of the solution is 1.0 L, the molar concentration of HCl is:

[HCl] = moles / volume [HCl] = 0.01 mol / 1.0 L [HCl] = 0.01 M

Since HCl is a strong acid and completely dissociates, [H+] = [HCl] = 0.01 M

Now, calculate the pH:

pH = -log10[H+] pH = -log10(0.01) pH = -log10(1 x 10-2) pH = -(-2) pH = 2

Therefore, the pH of the solution is 2.

Question 13: A solution is prepared by dissolving 0.40 g of NaOH in 1.0 L of water. Calculate the pH of the solution. (Molar mass of NaOH = 40 g/mol)

Solution:

First, calculate the number of moles of NaOH:

moles of NaOH = mass / molar mass moles of NaOH = 0.40 g / 40 g/mol moles of NaOH = 0.01 mol

Since the volume of the solution is 1.0 L, the molar concentration of NaOH is:

[NaOH] = moles / volume [NaOH] = 0.01 mol / 1.0 L [NaOH] = 0.01 M

Since NaOH is a strong base and completely dissociates, [OH-] = [NaOH] = 0.01 M

Calculate the pOH:

pOH = -log10[OH-] pOH = -log10(0.01) pOH = -log10(1 x 10-2) pOH = -(-2) pOH = 2

Now, calculate the pH:

pH + pOH = 14 pH = 14 - pOH pH = 14 - 2 pH = 12

Therefore, the pH of the solution is 12.

Question 14: The pH of a rainwater sample is found to be 5.3. Calculate the hydrogen ion concentration in the rainwater.

Solution:

To find [H+] from pH, we use the formula:

[H+] = 10-pH [H+] = 10-5.3 [H+] = 5.01 x 10-6 M

Therefore, the hydrogen ion concentration in the rainwater is 5.01 x 10-6 M.

Question 15: A scientist measures the pOH of a soil sample to be 8.9. Determine the pH of the soil sample and state whether the soil is acidic or alkaline.

Solution:

First, calculate the pH using the relationship pH + pOH = 14:

pH = 14 - pOH pH = 14 - 8.9 pH = 5.1

Since the pH is less than 7, the soil is acidic.

Advanced Concepts and Considerations

While the basic calculations of pH and pOH are straightforward, several factors can complicate these calculations in real-world scenarios:

• Temperature Dependence: The value of Kw, and consequently the relationship between pH and pOH, is temperature-dependent. The value of 1.0 x 10-14 is only accurate at 25°C. At different temperatures, Kw will change, affecting the pH of a neutral solution.
• Strong vs. Weak Acids and Bases: Strong acids and bases completely dissociate in water, making the calculation of [H+] and [OH-] relatively simple. However, weak acids and bases only partially dissociate, requiring the use of equilibrium constants (Ka and Kb) to determine the concentrations of H+ and OH-.
• Buffers: Buffer solutions resist changes in pH upon the addition of small amounts of acid or base. They typically consist of a weak acid and its conjugate base or a weak base and its conjugate acid. The pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation.
• Activity vs. Concentration: At high ionic strengths, the effective concentration of ions (activity) differs from the actual concentration. This difference can affect pH measurements, especially in concentrated solutions.

The Importance of pH and pOH

Understanding and accurately measuring pH and pOH is vital in numerous fields:

• Environmental Science: Monitoring the pH of water bodies and soil is essential for assessing environmental health and the impact of pollution.
• Agriculture: Soil pH affects nutrient availability and plant growth. Farmers often adjust soil pH to optimize crop yields.
• Medicine: Maintaining proper blood pH is crucial for human health. Deviations from the normal pH range can indicate underlying medical conditions. pH also plays a vital role in drug efficacy and formulation.
• Chemistry and Biology: pH affects the rates of chemical reactions, enzyme activity, and protein structure. Many biochemical processes are highly sensitive to pH changes.
• Food Science: pH affects the taste, texture, and safety of food products. Controlling pH is essential for food preservation and quality control.
• Industrial Processes: Many industrial processes, such as wastewater treatment, chemical manufacturing, and pharmaceutical production, require precise pH control.

Conclusion

Mastering the concepts of pH and pOH is essential for anyone working in chemistry, biology, environmental science, or related fields. By understanding the definitions, relationships, and calculations involved, one can accurately assess the acidity or basicity of solutions and predict their behavior in various applications. The problem set provided above offers a practical approach to solidifying this knowledge and developing problem-solving skills. Remember to consider the limitations and complexities of pH and pOH measurements in real-world scenarios, such as temperature dependence, the behavior of weak acids and bases, and the effects of ionic strength. Continuous learning and practice are key to achieving a comprehensive understanding of these fundamental concepts.