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Chapter 16: Problem 61

Obtain the \(\mathrm{pH}\) corresponding to the following hydronium-ion concentrations. a. \(1.0 \times 10^{-8} M\) b. \(5.0 \times 10^{-12} M\) c. \(7.5 \times 10^{-3} M\) d. \(6.35 \times 10^{-9} M\)

Short Answer

Expert verified
a. pH = 8 b. pH 鈮� 11.3 c. pH 鈮� 2.1 d. pH 鈮� 8.2

Step by step solution

01

Understanding the concept of pH

The pH of a solution is a measure of the hydrogen ion concentration. It is calculated using the formula: \( \mathrm{pH} = -\log_{10}(\mathrm{[H_3O^+]}) \), where \( \mathrm{[H_3O^+]} \) is the concentration of hydronium ions in moles per liter.
02

Calculate the pH for concentration a

For \( \mathrm{[H_3O^+]} = 1.0 \times 10^{-8} \ M \), the pH is calculated as follows: \[ \mathrm{pH} = -\log_{10}(1.0 \times 10^{-8}) = 8 \].
03

Calculate the pH for concentration b

For \( \mathrm{[H_3O^+]} = 5.0 \times 10^{-12} \ M \), the pH calculation is performed as: \[ \mathrm{pH} = -\log_{10}(5.0 \times 10^{-12}) \approx 11.3 \].
04

Calculate the pH for concentration c

For \( \mathrm{[H_3O^+]} = 7.5 \times 10^{-3} \ M \), the pH is computed with:\[ \mathrm{pH} = -\log_{10}(7.5 \times 10^{-3}) \approx 2.1 \].
05

Calculate the pH for concentration d

For \( \mathrm{[H_3O^+]} = 6.35 \times 10^{-9} \ M \), calculate the pH as follows: \[ \mathrm{pH} = -\log_{10}(6.35 \times 10^{-9}) \approx 8.2 \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Hydronium Ion Concentration
Hydronium ion concentration, denoted as \([H_3O^+]\), describes how many hydronium ions are present in a solution. This concentration is typically expressed in moles per liter (M), which tells us the amount of hydronium ions in a specific volume of solution. The concept of hydronium ions is central to understanding the acidity of a solution because they result from the combination of a hydrogen ion \(H^+\) with a water molecule (H2O).
The more hydronium ions present in a solution, the more acidic it is. Conversely, fewer hydronium ions suggest a less acidic, or more basic, solution. Hydronium ion concentration is crucial in calculating the pH of a solution, as it directly relates to the acidity or basicity of a given solution.
The Role of Logarithmic Scale in pH
The pH scale is a logarithmic scale utilized to measure the acidity or basicity of a solution. Unlike a linear scale, where change is uniform, a logarithmic scale indicates units of tenfold differences. This means each whole-number shift in pH represents a tenfold change in the concentration of hydrogen ions.
The formula \( \text{pH} = -\log_{10}(\mathrm{[H_3O^+]}) \) uses this logarithmic understanding. By applying the negative logarithm to the hydronium ion concentration, we determine the pH, translating complex ion concentrations into the simple pH scale (ranging from 0 to 14).
  • For instance, a pH of 3 is ten times more acidic than a pH of 4.
  • This logarithmic nature allows large variations in ion concentration to be represented in a compact and comprehensible manner.
Understanding the logarithmic scale is essential for interpreting pH correctly and appreciating the broad range of acidity and basicity captured by it.
Basics of Acid-Base Chemistry
Acid-base chemistry revolves around the interaction of acids and bases and how they balance each other in a solution. Acids are substances that increase the concentration of hydrogen ions (or hydronium ions) in a solution, while bases decrease it by providing hydroxide ions (OH-) or by accepting hydrogen ions.
The concept of \( \text{pH} \) itself is a reflection of acid-base chemistry, as it quantifies the balance between these ions in a solution.
  • A pH less than 7 indicates an acidic solution. This means the solution has a higher concentration of hydronium ions compared to pure water.
  • A pH higher than 7 indicates a basic or alkaline solution, signifying more hydroxide ions present.
  • A pH of 7 suggests a neutral solution, which is notably the pH of pure water at 25掳C.
Recognizing how hydronium and hydroxide ions interact and neutralize one another is crucial in understanding the fundamentals of acid-base reactions. Additionally, this knowledge is pivotal in fields such as chemistry, biology, environmental science, and medicine, where pH often plays a key role in processes and reactions.

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Most popular questions from this chapter

A solution contains \(0.675 \mathrm{~g}\) of ethylamine, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\), per \(100.0 \mathrm{~mL}\) of solution. Electrical conductivity measurements at \(20^{\circ} \mathrm{C}\) show that \(0.98 \%\) of the ethylamine has reacted with water. Write the equation for this reaction. Calculate the \(\mathrm{pH}\) of the solution.

Self-contained environments, such as that of a space station, require that the carbon dioxide exhaled by people be continuously removed. This can be done by passing the air over solid alkali hydroxide, in which carbon dioxide reacts with hydroxide ion. What ion is produced by the addition of \(\mathrm{OH}^{-}\) ion to \(\mathrm{CO}_{2}\) ? Use the Lewis concept to explain this.

A solution of lye (sodium hydroxide, \(\mathrm{NaOH}\) ) has a hydroxide-ion concentration of \(0.050 M\). What is the \(\mathrm{pH}\) at \(25^{\circ} \mathrm{C}\) ?

A wine was tested for acidity, and its \(\mathrm{pH}\) was found to be \(3.85\) at \(25^{\circ} \mathrm{C}\). What is the hydronium-ion concentration?

The nitride ion and the amide ion, \(\mathrm{NH}_{2}^{-}\), have greater attractions for the hydronium ion than the hydroxide ion does. Write the equations for the reactions that occur when calcium nitride and sodium amide are added to water (each gives \(\mathrm{NH}_{3}\) ). Which is the stronger base, the nitride ion or the amide ion? Why? What is the meaning of the statement that the hydroxide ion is the strongest base that can exist in water?
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