The pH Scale: Videos & Practice Problems

The pH scale, ranging from 0 to 14, measures the acidity or basicity of aqueous solutions at room temperature (25 °C) and a molarity of one. A pH below 7 indicates acidity, with lower values signifying stronger acids, while a pH above 7 denotes basicity, with higher values indicating stronger bases. At pH 7, a solution is neutral, meaning the concentrations of H⁺ (hydrogen ions) and OH⁻ (hydroxide ions) are equal. The pH or pOH of a solution can be calculated if the molarity of H⁺ or OH⁻ is known, using the formulas:

$\mathrm{pH}=-\log \left[H_{+}\right]$

and

$\mathrm{pOH}=-\log \left[{\mathrm{OH}}_{-}\right]$

Additionally, H⁺ concentration can be found with 10 to the power of -pH, and OH⁻ concentration with 10 to the power of -pOH. The relationship between pH and pOH is such that their sum equals 14 under standard conditions. This framework is crucial for understanding acid-base chemistry and for performing calculations related to solution concentration and acidity.

The pH Scale

The pH scale is a crucial tool for classifying the acidity or basicity of aqueous solutions, typically ranging from 0 to 14 under standard conditions, which include a temperature of approximately 25 degrees Celsius and a molarity of 1. When the molarity deviates from 1, the pH can extend beyond this conventional range.

At a pH of 7, a solution is considered neutral, indicating that the concentrations of hydronium ions (H₃O⁺) and hydroxide ions (OH^-) are equal. Solutions with a pH below 7 are classified as acidic, with the acidity increasing as the pH decreases. Conversely, solutions with a pH above 7 are basic, with basicity increasing as the pH rises. This relationship highlights that stronger acids correspond to lower pH values, while stronger bases correspond to higher pH values.

For example, vinegar, which has a pH of around 3, is acidic due to a higher concentration of H₃O⁺ ions compared to OH^- ions. In contrast, purified water, with a pH of 7, is neutral, reflecting equal concentrations of H₃O⁺ and OH^- ions. Ammonia cleaner, with a pH of approximately 12, is basic, characterized by a greater concentration of OH^- ions than H₃O⁺ ions.

In summary, under normal conditions, the pH scale serves as a reliable indicator of a solution's acidity or basicity, with values below 7 indicating acidity, a value of 7 indicating neutrality, and values above 7 indicating basicity.

Least Acidic Solution Example

To determine the least acidic solution among the given options, we need to analyze the concentration of hydrogen ions (H⁺) in each solution. Acidity is directly related to the concentration of H⁺ ions; the higher the concentration, the more acidic the solution.

Here are the concentrations of H⁺ ions for each acid:

• Nitric acid: 1.2 M
• Hydrochloric acid (HCl): 0.025 M
• Sulfuric acid: 0.27 M
• Perchloric acid: 0.019 M

Among these, the solution with the lowest concentration of H⁺ ions is perchloric acid at 0.019 M. Therefore, it is the least acidic solution compared to the others.

In summary, the acidity of a solution can be assessed by its H⁺ concentration, and the solution with the lowest concentration of H⁺ ions is the least acidic. In this case, perchloric acid is the least acidic option.

pH and pOH Calculations

Understanding the relationship between pH, pOH, and the concentrations of hydrogen ions (H⁺) and hydroxide ions (OH^-) is essential in chemistry. The pH scale measures the acidity or basicity of a solution, while pOH measures the concentration of hydroxide ions. Both pH and pOH are logarithmic scales, where the term "p" stands for the negative logarithm.

The formula for calculating pH is given by:

pH = -\log[H^+]

Conversely, if you know the pH of a solution, you can determine the concentration of hydrogen ions using the inverse relationship:

[H⁺] = 10^{-pH}

Similarly, pOH can be calculated using the concentration of hydroxide ions:

pOH = -\log[OH^-]

To find the hydroxide ion concentration from pOH, the formula is:

[OH^-] = 10^{-pOH}

It is also important to note the relationship between pH and pOH. The sum of pH and pOH in any aqueous solution at 25°C is always 14:

pH + pOH = 14

This relationship allows for easy conversion between pH and pOH, as well as their respective ion concentrations. By mastering these formulas, you can effectively navigate between the acidity and basicity of solutions, enhancing your understanding of chemical properties and reactions.

pH Calculation Example

To determine the pH of a hydrocyanic acid solution, we start by understanding the relationship between hydrogen ion concentration and pH. The pH is calculated using the formula:

pH = -log[H⁺]

In this case, the concentration of hydrogen ions (H⁺) was found to be 0.34 moles in a 2-liter solution. To find the molarity (M), which is the concentration in moles per liter, we use the formula:

Molarity (M) = Moles / Liters

Substituting the values, we have:

M = 0.34 moles / 2 liters = 0.17 M

Now, we can calculate the pH by substituting the molarity into the pH formula:

pH = -log(0.17)

Calculating this gives us:

pH ≈ 0.77

This pH value indicates a relatively high concentration of hydrogen ions, as the pH scale ranges from 0 to 14, with lower values indicating higher acidity. A pH of 0.77 suggests that the solution is quite acidic, which is consistent with the presence of hydrocyanic acid, a strong acid that can generate a significant amount of H⁺ ions in solution.

A solution of NaOH was prepared in a chemistry lab and the pOH was determined to be 9.3. What is the concentration of OH⁻ ions of this basic solution?

• A. 5 × 10⁻¹¹ M
• B. 5 × 10⁻¹⁰ M
• C. 2 × 10⁹ M
• D. 2 × 10⁸ M

Answer: (B)

Additional pH and pOH Calculations

The pH scale is a crucial concept in chemistry, typically ranging from 0 to 14 at a temperature of 25 degrees Celsius and a maximum concentration of 1 molar. Understanding the relationship between pH and pOH is essential for analyzing acidity and basicity in solutions. The fundamental equation connecting these two measures is:

pH + pOH = 14

This equation allows for the conversion between pH and pOH values. To delve deeper, we can express pH in terms of hydrogen ion concentration, represented as [H⁺]. The formula is:

pH = -\log[H⁺]

From this, we can derive the concentration of hydrogen ions:

[H⁺] = 10^{-pH}

Similarly, pOH can be defined in relation to hydroxide ion concentration, [OH^-], using the equation:

pOH = -\log[OH^-]

Thus, the concentration of hydroxide ions can be calculated as:

[OH^-] = 10^{-pOH}

These equations collectively form a comprehensive framework for understanding the interplay between pH and pOH, reinforcing the principle that their sum always equals 14. This knowledge is vital for various applications in chemistry, biology, and environmental science.

pH and pOH Example

To determine the pOH and the concentration of hydronium ions in a hydrochloric acid solution with a pH of 2.3 at 25 degrees Celsius, we can use the relationship between pH and pOH. The formula states that:

pH + pOH = 14

Given that the pH is 2.3, we can calculate the pOH by rearranging the equation:

pOH = 14 - pH = 14 - 2.3 = 11.7

Next, to find the concentration of hydronium ions (H₃O⁺), we use the formula:

[H₃O⁺] = 10^-pH

Substituting the pH value into the equation gives us:

[H₃O⁺] = 10^-2.3 ≈ 5.01187 × 10^-3 M

When rounding to significant figures, we express the concentration of hydronium ions as:

[H₃O⁺] ≈ 5.0 × 10^-3 M

In summary, for a hydrochloric acid solution with a pH of 2.3, the pOH is 11.7, and the concentration of hydronium ions is approximately 5.0 × 10^-3 M.

Calculate [OH⁻] of a lemon juice solution at 25°C with a [H⁺] = 5.7 × 10⁻⁴ M.

• A. 5.7 × 10¹⁰ M
• B. 4.7 × 10⁻¹¹ M
• C. 2.7 × 10⁻¹⁸ M
• D. 1.8 × 10⁻¹¹ M

Answer: (D)

A 345 mL bottle of antacid (Mg(OH)₂) contains 1.45 × 10⁻² moles of hydroxide ions. Determine pH and pOH of the antacid.

• A. pH = 12.384
  pOH = 1.616
• B. pH = 12.623
  pOH = 1.377
• C. pH = 12.161
  pOH = 1.839
• D. pH = 12.338
  pOH = 1.662

Answer: (B)

Which of the following statement(s) on aqueous solutions is/are correct?
a) aqueous solutions have a pH of 7
b) as concentration of hydronium ion increases, concentration of hydroxide ion decreases
c) solutions of weaker acids generally have a higher pOH then solutions of stronger acids
d) pH of pure water equals to 7 at 35º C.

• A. aqueous solutions have a pH of 7
• B. as concentration of hydronium ion increases, concentration of hydroxide ion decreases
• C. solutions of weaker acids generally have a higher pOH then solutions of stronger acids
• D. pH of pure water equals to 7 at 35º C.

Answer: (B)

Here’s what students ask on this topic:

What is the pH scale?

The pH scale is a measure of how acidic or basic (alkaline) a solution is. It ranges from 0 to 14, with 7 being neutral. Solutions with a pH less than 7 are considered acidic, while those with a pH greater than 7 are considered basic or alkaline. The scale is logarithmic, meaning each whole pH value below 7 is ten times more acidic than the next higher value, and each whole pH value above 7 is ten times more alkaline than the next lower value. For example, a solution with a pH of 6 is ten times more acidic than a solution with a pH of 7, and a solution with a pH of 8 is ten times more alkaline than a solution with a pH of 7. This scale is crucial in chemistry, biology, and environmental science, as it affects chemical reactions, biological processes, and the health of ecosystems.

How do you calculate pH?

To calculate the pH of a solution, you need to know the concentration of hydrogen ions (H⁺) or hydronium ions (H₃O⁺) in moles per liter (Molarity). The pH is calculated using the following formula:

$\mathrm{pH}=-\log \left[H^{+}\right]$

Here's a step-by-step process:

1. Determine the concentration of hydrogen ions in the solution in molarity (M). This is often given, but if not, you may need to derive it from the concentration of an acid or base.
2. Take the negative logarithm (base 10) of the hydrogen ion concentration. This means you use a scientific calculator to find the log of the H⁺ concentration and then multiply that number by -1.

For example, if the hydrogen ion concentration is 1 x 10^-7 M, the pH is:

$\mathrm{pH}=-\log (1x{10}^{-7})=7$

Remember that a pH less than 7 is acidic, a pH of 7 is neutral, and a pH greater than 7 is basic or alkaline. The pH scale typically ranges from 0 to 14.

What is the relationship between the pH scale and concentration?

The pH scale is a measure of the acidity or alkalinity of a solution, which is determined by the concentration of hydrogen ions (H+) present. The scale ranges from 0 to 14, with 7 being neutral. A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates an alkaline (basic) solution.

The relationship between pH and hydrogen ion concentration is logarithmic, not linear. This means that each unit change in pH represents a tenfold change in H+ concentration. A decrease in pH by 1 unit reflects a tenfold increase in acidity (more H+ ions), while an increase in pH by 1 unit reflects a tenfold decrease in acidity (fewer H+ ions).

For example, a solution with a pH of 6 has ten times more hydrogen ions than a solution with a pH of 7. Conversely, a solution with a pH of 8 has ten times fewer hydrogen ions than a solution with a pH of 7. This logarithmic relationship allows the pH scale to cover a wide range of hydrogen ion concentrations in a compact scale.

How do you calculate H⁺ from pH?

To calculate the concentration of hydrogen ions (H⁺) from pH, you can use the following formula:

$\left[H^{+}\right]={10}^{-\mathrm{pH}}$

Here, [H⁺] represents the concentration of hydrogen ions in moles per liter (M), and pH is the measure of acidity or alkalinity of a solution.

The pH scale typically ranges from 0 to 14, with 7 being neutral. A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates a basic (alkaline) solution. The pH scale is logarithmic, which means each whole pH value below 7 is ten times more acidic than the next higher value. For example, a solution with a pH of 3 is ten times more acidic than a solution with a pH of 4.

To perform the calculation, simply take the negative of the pH value and use it as the exponent for 10. For instance, if the pH of a solution is 3.5, the concentration of H⁺ ions is:

$\left[H^{+}\right]={10}^{-3.5}=3.16\times {10}^{-4}\text{M}$

This means there are 3.16 × 10^-4 moles of hydrogen ions per liter of solution.

How to calculate OH^- from pH?

To calculate the concentration of hydroxide ions (OH^-) from the pH, you can use the following steps:

1. Remember that pH is a measure of the hydrogen ion concentration [H⁺], and it is related to [H⁺] by the formula: $\mathrm{pH}=-\log \left[H\right]$.
2. Understand that the product of the concentrations of hydrogen ions [H⁺] and hydroxide ions [OH^-] in water at 25°C is always $1.0x{10}^{-14}$. This is known as the ion-product constant for water (K_w).
3. Use the pH to find the [H⁺] by reversing the pH formula: $\left[H\right]={10}^{-pH}$.
4. Once you have [H⁺], use the ion-product constant to find [OH^-]: $\left[\mathrm{OH}\right]=K$_w/[H].
5. Plug in the values: $\left[\mathrm{OH}\right]=1.0x{10}^{-14}/\left[H\right]$.
6. Calculate the [OH^-] using the [H⁺] you found from the pH.

For example, if the pH is 7, $\left[H\right]={10}^{-7}$ M. To find [OH^-], you would calculate $\left[\mathrm{OH}\right]=1.0x{10}^{-14}/{10}^{-7}={10}^{-7}$ M. Therefore,