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Calculate the hydrogen ion concentration for solutions with these \(\mathrm{pH}\) values: (a) \(2.42,\) (b) 11.21 (d) 15.00 . (c) 6.96

Short Answer

Expert verified
(a) \([H^+] \approx 3.80 \times 10^{-3}\), (b) \([H^+] \approx 6.17 \times 10^{-12}\), (c) \([H^+] \approx 1.10 \times 10^{-7}\), (d) \([H^+] \approx 1.00 \times 10^{-15} \text{ mol/L}\).

Step by step solution

01

Understanding pH and concentration

The pH of a solution is the negative logarithm (base 10) of the hydrogen ion concentration, denoted as \( [H^+] \). The relationship is expressed as the formula: \( \text{pH} = -\log_{10}([H^+]) \). To find the hydrogen ion concentration, we need to rearrange this formula to solve for \([H^+]\).
02

Rearranging formula to find [H+]

The rearranged formula is \( [H^+] = 10^{-\text{pH}} \). This formula will allow us to calculate the hydrogen ion concentration from a given pH value. We will apply this formula to each pH value provided.
03

Calculating [H+] for pH = 2.42

Plug the value \(2.42\) into the equation: \( [H^+] = 10^{-2.42} \). By calculating this expression, we find \( [H^+] \approx 3.80 \times 10^{-3} \text{ mol/L} \).
04

Calculating [H+] for pH = 11.21

Using the formula with \(11.21\), calculate: \( [H^+] = 10^{-11.21} \). This gives us \( [H^+] \approx 6.17 \times 10^{-12} \text{ mol/L} \).
05

Calculating [H+] for pH = 15.00

For \(pH = 15.00\), use the formula: \( [H^+] = 10^{-15.00} \). This results in \( [H^+] \approx 1.00 \times 10^{-15} \text{ mol/L} \).
06

Calculating [H+] for pH = 6.96

Substitute \(6.96\) into the formula: \( [H^+] = 10^{-6.96} \). This calculation leads to \( [H^+] \approx 1.10 \times 10^{-7} \text{ mol/L} \).

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Key Concepts

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

Hydrogen Ion Concentration
In chemistry, the concentration of hydrogen ions \( [H^+] \)in a solution is crucial for determining the pH level. The hydrogen ion concentration is measured in moles per liter (mol/L), and it indicates how acidic or basic a solution is.
An increase in hydrogen ions generally leads to a decrease in pH value, creating a more acidic solution. Conversely, a lower concentration results in a higher pH, indicating a basic solution.
Calculating the concentration of hydrogen ions involves using the mathematical relationship between pH and \( [H^+] \). Knowing this parameter can signal how a solution will behave chemically, which can be essential in fields such as biochemistry, medicine, and environmental science. Tools like the equation \( [H^+] = 10^{-\text{pH}} \) allow scientists and students to calculate the hydrogen ion concentration quickly, aiding in understanding chemical reactions and processes.
Logarithmic Relationship
The concept of pH is fundamentally a logarithmic relationship. This means that pH is related to hydrogen ion concentration with a base-10 logarithm. In mathematical terms, pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration, or \( \text{pH} = -\log_{10}([H^+]) \).
This logarithmic nature implies significant changes due to small variations in hydrogen ion concentration.
For every unit change in pH, there is a tenfold change in \([H^+]\). For instance:
  • A change from pH 4 to pH 3 means the hydrogen ion concentration increases tenfold.
  • A shift from pH 8 to pH 7 marks a tenfold decrease in hydrogen ion concentration.
Understanding this is crucial because it shows how sensitive chemical reactions can be to small changes in pH. It also helps explain why pH values range from 0 to 14, capturing an immense array of \([H^+]\) levels in a comprehensible scale.
Acidic and Basic Solutions
Solutions are categorized as acidic or basic (alkaline) based on their pH values:
  • Acidic solutions have a pH less than 7. They contain a higher concentration of hydrogen ions, making them more likely to donate protons in chemical reactions.
  • Neutral solutions, like pure water, have a pH of exactly 7. Here, the hydrogen ion and hydroxide ion concentrations are balanced.
  • Basic solutions, or alkaline solutions, have a pH greater than 7. These solutions have a lower concentration of hydrogen ions and are more prone to accept protons.
The distinction between acidic and basic is crucial in understanding how substances interact. For instance, acids may react vigorously with metals, while bases might not.
By comprehending the nature of acid and base solutions, one can predict and control the outcomes of chemical processes effectively. This understanding is key in many industries, such as pharmaceuticals and environmental engineering, to ensure safety and effectiveness.

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Most popular questions from this chapter

About half of the hydrochloric acid produced annually in the United States ( 3.0 billion pounds) is used for metal pickling. This process involves the removal of metal oxide layers from metal surfaces to prepare them for coating. (a) Write the overall and net ionic equations for the reaction between iron(III) oxide, which represents the rust layer over iron, and HCl. Identify the Brónsted acid and base. (b) Hydrochloric acid is also used to remove scale (which is mostly \(\mathrm{CaCO}_{3}\) ) from water pipes. Hydrochloric acid reacts with calcium carbonate in two stages; the first stage forms the bicarbonate ion, which then reacts further to form carbon dioxide. Write equations for these two stages and for the overall reaction. (c) Hydrochloric acid is used to recover oil from the ground. It dissolves rocks (often \(\mathrm{CaCO}_{3}\) ) so that the oil can flow more easily. In one process, a 15 percent (by mass) HCl solution is injected into an oil well to dissolve the rocks. If the density of the acid solution is \(1.073 \mathrm{~g} / \mathrm{mL},\) what is the \(\mathrm{pH}\) of the solution?

Describe this reaction according to the Lewis theory of acids and bases: $$ \mathrm{AlCl}_{3}(s)+\mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{AlCl}_{4}^{-}(a q) $$

Classify each of these species as a weak or strong base: (a) LiOH, (b) \(\mathrm{CN}^{-}\) (c) \(\mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{ClO}_{4}^{-},\) (e) \(\mathrm{NH}_{2}\).

In terms of orbitals and electron arrangements, what must be present for a molecule or an ion to act as a Lewis acid (use \(\mathrm{H}^{+}\) and \(\mathrm{BF}_{3}\) as examples)? What must be present for a molecule or ion to act as a Lewis base (use \(\mathrm{OH}^{-}\) and \(\mathrm{NH}_{3}\) as examples)?

Define pOH. Write an equation relating \(\mathrm{pH}\) and \(\mathrm{pOH}\).

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