The pH Scale: Videos & Practice Problems

The pH scale, ranging from 0 to 14, measures the concentration of hydrogen ions (H⁺) and hydroxide ions (OH^-) in solutions. A neutral solution has a pH of 7, where H⁺ and OH^- are both 1.0 × 10^-7 M. Solutions with pH < 7 are acidic (H⁺ > 1.0 × 10^-7 M), while those with pH > 7 are basic (OH^- > 1.0 × 10^-7 M). The relationship between pH and pOH is given by the equation: $\mathrm{pH}+\mathrm{pOH}=14$.

pH and pOH

The pH scale is a crucial tool for understanding the acidity or basicity of solutions, particularly when dealing with very small concentrations of hydrogen ions (H⁺) and hydroxide ions (OH^-). Under standard conditions, where the concentrations of these ions are less than 1 molar, the pH scale ranges from 0 to 14. If the concentration of H⁺ exceeds 1 molar, the pH will be less than 0, while a concentration of OH^- greater than 1 molar results in a pH greater than 14.

The pH and pOH can be calculated using the negative logarithm of the respective ion concentrations:

pH = -log[H⁺] or pH = -log[H₃O⁺]

pOH = -log[OH^-]

This indicates that the "p" in pH and pOH signifies the negative logarithm of the ion concentration. Understanding the relationship between H⁺ and OH^- allows us to derive connections between pH and pOH. For instance, if we know the pH, we can find the H⁺ concentration using the formula:

[H⁺] = 10^-pH

Similarly, for OH^-, we can use:

[OH^-] = 10^-pOH

As pH increases, the concentration of H⁺ decreases while the concentration of OH^- increases, indicating a more basic solution. A solution with a pH of 7 is classified as neutral, where the concentrations of H⁺ and OH^- are equal, specifically at 1.0 x 10^-7 molar. This equality is derived from the ion product constant for water (K_w), which is 1.0 x 10^-14 at 25 degrees Celsius, expressed as:

K_w = [H⁺][OH^-]

For solutions with a pH greater than 7, they are classified as basic, meaning the concentration of OH^- exceeds that of H⁺. Conversely, solutions with a pH less than 7 are acidic, where the concentration of H⁺ is greater than that of OH^-. The relationship between pH and pOH is succinctly captured by the equation:

pH + pOH = 14

These foundational concepts regarding pH, pOH, and their relationship with ion concentrations set the stage for further exploration into the calculations of pH and pOH for various acids and bases.

pH and pOH

To determine the hydroxide ion (OH^-) and hydronium ion (H₃O⁺) concentrations in a solution with a pH of 5.88, we can use fundamental relationships between pH, pOH, and ion concentrations.

First, the concentration of hydronium ions can be calculated using the formula:

H₃O⁺ concentration = 10^-pH

Substituting the given pH value:

H₃O⁺ concentration = 10^-5.88 ≈ 1.32 × 10^-6 M

Next, to find the hydroxide ion concentration, we can use the relationship between pH and pOH:

pOH = 14 - pH

Calculating pOH:

pOH = 14 - 5.88 = 8.12

Now, we can find the hydroxide ion concentration using:

OH^- concentration = 10^-pOH

Substituting the calculated pOH:

OH^- concentration = 10^-8.12 ≈ 7.59 × 10^-9 M

Alternatively, we can use the ion product of water (K_w) at 25°C, which is:

K_w = [H₃O⁺][OH^-] = 1.0 × 10^-14

Using the previously calculated hydronium ion concentration, we can isolate the hydroxide ion concentration:

[OH^-] = K_w / [H₃O⁺]

Substituting the values:

[OH^-] = 1.0 × 10^-14 / (1.32 × 10^-6) ≈ 7.59 × 10^-9 M

Both methods yield the same hydroxide ion concentration, demonstrating the interconnectedness of pH, pOH, and ion concentrations. Understanding these relationships is crucial for performing acid-base calculations effectively.

pH and pOH Calculations 1

To determine the concentration of hydronium ions (\(H_3O^+\)) in a solution, it is essential to understand the relationship between pH and \(H^+\) ion concentration. The pH scale is logarithmic, meaning that each unit change in pH corresponds to a tenfold change in \(H^+\) concentration. Therefore, a lower pH indicates a higher concentration of \(H^+\) ions.

For instance, if we compare a solution with a pH of 4 to one with a pH of 5, the solution with pH 4 has ten times more \(H^+\) ions than the one with pH 5. Conversely, moving from a pH of 4 to a pH of 2 results in a significant increase in \(H^+\) concentration. Specifically, each unit decrease in pH leads to a tenfold increase in \(H^+\) concentration. Thus, moving down two units from pH 4 to pH 2 results in a \(10 \times 10 = 100\) fold increase in \(H^+\) concentration.

In summary, the lowest pH corresponds to the highest concentration of \(H^+\) ions and the lowest concentration of hydroxide ions (\(OH^-\)). This principle is crucial when analyzing solutions, especially strong acids like hydrobromic acid (HBr), where the complete dissociation into \(H^+\) and \(Br^-\) ions must be considered to determine the solution's properties accurately.

Understanding these concepts allows for effective predictions of how changes in pH affect ion concentrations, which is fundamental in various chemical and biological processes.

pH and pOH Calculations 1

To determine the mass of HBr needed to create a solution with a pH of 3.850 in 250 mL of water, we start by calculating the concentration of hydrogen ions (H⁺) using the pH formula. The relationship between pH and H⁺ concentration is given by:

[H⁺] = 10^{-pH}

Substituting the pH value:

[H⁺] = 10^{-3.850} \approx 1.4124 \times 10^{-4} \text{ M}

Next, we convert the volume from milliliters to liters:

250 \text{ mL} = 0.250 \text{ L}

Using the molarity formula, which states that molarity (M) equals moles (n) over liters (V), we can rearrange it to find moles:

n = M \times V

Substituting the values we have:

n = (1.4124 \times 10^{-4} \text{ mol/L}) \times (0.250 \text{ L}) \approx 3.531 \times 10^{-5} \text{ mol}

Since HBr is a strong acid, it dissociates completely in solution, meaning that the number of moles of HBr is equal to the number of moles of H⁺. Therefore, we have:

n(HBr) = 3.531 \times 10^{-5} \text{ mol}

To find the mass of HBr, we need its molar mass. The molar mass of HBr is calculated by adding the atomic masses of hydrogen (H) and bromine (Br):

M(HBr) = M(H) + M(Br) = 1.00794 \text{ g/mol} + 79.904 \text{ g/mol} \approx 80.912 \text{ g/mol}

Now, we can calculate the mass of HBr using the formula:

\text{mass} = n \times M

Substituting the values:

\text{mass} = (3.531 \times 10^{-5} \text{ mol}) \times (80.912 \text{ g/mol}) \approx 0.002857 \text{ g}

Thus, the mass of HBr required to achieve a pH of 3.850 in 250 mL of water is approximately 0.002857 grams. This calculation illustrates the importance of understanding the relationship between pH, concentration, and the properties of strong acids in solution.

What is the hydronium ion concentration in a solution having a pOH of 3.62?

• A. 3.8 × 10⁻⁵ M
• B. 4.2 × 10⁻¹¹ M
• C. 3.8 × 10⁻⁴ M
• D. 2.6 × 10⁻¹¹ M
• E. 5.1 × 10⁻¹⁰ M

Answer: (B)

Here’s what students ask on this topic:

What is the pH scale and how is it used to measure acidity and basicity?

The pH scale ranges from 0 to 14 and measures the concentration of hydrogen ions (H⁺) in a solution. A pH of 7 is neutral, meaning the concentrations of H⁺ and hydroxide ions (OH^-) are equal at 1.0 × 10^-7 M. Solutions with pH < 7 are acidic (H⁺ > 1.0 × 10^-7 M), while those with pH > 7 are basic (OH^- > 1.0 × 10^-7 M). The pH is calculated using the formula: $\mathrm{pH}=-{\log }_{H_{+}}$. This scale helps determine the acidity or basicity of a solution, which is crucial in various chemical and biological processes.

How do you calculate pH from the concentration of hydrogen ions?

To calculate pH from the concentration of hydrogen ions (H⁺), use the formula: $\mathrm{pH}=-{\log }_{H_{+}}$. For example, if the concentration of H⁺ is 1.0 × 10^-3 M, the pH is calculated as follows: $\mathrm{pH}=-{\log }_{{\mathrm{1.0}}_{\times }}$, which simplifies to pH = 3. This method allows you to determine the acidity of a solution accurately.

What is the relationship between pH and pOH?

The relationship between pH and pOH is given by the equation: $\mathrm{pH}+\mathrm{pOH}=14$. This means that if you know either the pH or pOH of a solution, you can easily calculate the other. For example, if the pH of a solution is 5, the pOH can be calculated as follows: $\mathrm{pOH}=14-\mathrm{pH}$, which simplifies to pOH = 14 - 5 = 9. This relationship is crucial for understanding the balance between hydrogen and hydroxide ions in a solution.

How do you determine if a solution is acidic, basic, or neutral based on its pH?

A solution's pH determines whether it is acidic, basic, or neutral. A pH of 7 is neutral, indicating equal concentrations of H⁺ and OH^- ions at 1.0 × 10^-7 M. If the pH is less than 7, the solution is acidic, meaning the concentration of H⁺ ions is greater than 1.0 × 10^-7 M. Conversely, if the pH is greater than 7, the solution is basic, indicating a higher concentration of OH^- ions than H⁺ ions. This classification helps in understanding the chemical nature and potential reactivity of the solution.

What is the significance of the ion product constant for water (Kw) in the pH scale?

The ion product constant for water (K_w) is significant in the pH scale as it defines the relationship between H⁺ and OH^- concentrations in water. At 25°C, K_w is 1.0 × 10^-14. This means that the product of the concentrations of H⁺ and OH^- ions in water is always 1.0 × 10^-14. Mathematically, $K_w=H_{+}\times {\mathrm{OH}}_{-}$. This constant helps in calculating pH and pOH and understanding the equilibrium state of water and aqueous solutions.