Chapter 6: Problem 23
pH of \(10^{-6} \mathrm{M}\) HCl(aq.) is : (a) just less than 6 (b) exactly equal to 6 (c) just greater than 6 (d) just less than 7
Short Answer
Expert verified
The pH of a 10^{-6} M HCl solution is exactly equal to 6.
Step by step solution
01
Understanding the pH scale
The pH of a solution is a measure of its acidity or basicity, defined as the negative logarithm (base 10) of the hydrogen ion concentration. The formula to calculate it is pH = -log[H+]. In pure water or neutral solutions at 25 degrees Celsius, the concentration of hydrogen ions (H+) is 1 x 10^-7 M, which gives a pH of 7. Acidic solutions have higher H+ concentrations and pH values less than 7, while basic solutions have lower H+ concentrations and pH values greater than 7.
02
Calculating the hydrogen ion concentration
To find the pH of the HCl solution, first determine the concentration of hydrogen ions. Since HCl is a strong acid, it dissociates completely in water. Therefore, the concentration of H+ ions in a 10^-6 M HCl solution is also 10^-6 M.
03
Calculating the pH of the HCl solution
Apply the pH formula: pH = -log[H+]. Substituting the given concentration, pH = -log(10^-6). The logarithm of 10^-6 is -6, so pH = -(-6) = 6.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Acid and Base
Understanding the nature of acids and bases is crucial in chemistry, as it helps us predict the behavior of substances in a solution. An acid is defined as a substance that increases the hydrogen ion (H+) concentration when dissolved in water, while a base does the opposite, reducing the H+ concentration. The strength of an acid or base is often determined by its ability to dissociate in water. Strong acids, like hydrochloric acid (HCl), dissociate completely, releasing all of their hydrogen ions into the solution. Weak acids, on the other hand, only partially dissociate, leading to a mixture of ions and un-dissociated acid molecules. The pH scale, ranging from 0 to 14, succinctly represents the acidity or basicity of a solution, with 7 being neutral.
For instance, lemon juice, with a pH less than 7, is acidic, while baking soda solution, with a pH greater than 7, is basic.
For instance, lemon juice, with a pH less than 7, is acidic, while baking soda solution, with a pH greater than 7, is basic.
Hydrogen Ion Concentration
The hydrogen ion concentration in a solution is a direct measure of its acidity. It is represented by [H+] and is reported in moles per liter (M). As we've seen with the HCl example, the concentration of H+ ions dictates the pH value. In neutral conditions, such as pure water at 25°C, [H+] is 1 x 10^-7 M, which is derived from the self-ionization of water. In acidic solutions, [H+] is greater than 1 x 10^-7 M, while in basic solutions, it is less. For precise pH calculation, we must precisely measure or calculate the [H+] of the solution, which becomes straightforward for strong acids and bases that have known dissociation properties.
Logarithm in Chemistry
Logarithms are critical in chemistry for several calculations, the pH being a prime example. A logarithm tells us what power a number (called the base) must be raised to produce another number. In pH calculation, the base is 10, and it reflects the inverse relationship between the concentration of hydrogen ions and the pH value. The negative sign in the pH formula \( pH = -\log[H+] \) indicates this inverse nature; as the [H+] increases, the pH decreases, indicating higher acidity. By using logarithms, we can represent very large or small numbers, like [H+], in a manageable way, making comparisons and computations far easier in the realm of chemistry.
Strong Acid Dissociation
When strong acids dissolve in water, they dissociate completely into ions. This is known as strong acid dissociation, a key concept when dealing with chemical reactions and pH calculations. Since the dissociated hydrogen ions from strong acids directly contribute to the acidity of the solution, knowing that the dissociation is complete simplifies the process of finding the pH. In the example of HCl, a strong acid, the concentration of H+ ions equals the initial concentration of HCl, because it splits into H+ and Cl- ions completely. Therefore, we can quickly calculate the pH of a 10^-6 M HCl(aq.) solution by understanding the concept of strong acid dissociation. The complete dissociation leads to a clear relationship—every molecule of HCl contributes a hydrogen ion to the solution, reflecting a 1:1 ratio in concentration.