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Chapter 14: Problem 48

A solution with a pH of 10 is 100 times more basic than a solution with \(\mathrm{pH}\) 8. Explain.

Short Answer

Expert verified
A solution with pH 10 is 100 times more basic than one with pH 8 because the pH scale is logarithmic.

Step by step solution

01

Understand pH Scale

The pH scale measures how acidic or basic a solution is, ranging from 0 to 14. A pH value below 7 indicates an acidic solution, while a pH value above 7 indicates a basic solution.
02

Calculate the Difference in pH

To compare the basicity of two solutions, note the difference in their pH values. Here, the difference between pH 10 and pH 8 is: 10 - 8 = 2.
03

Relate pH Difference to Basicity

The pH scale is logarithmic, meaning each whole number pH change represents a tenfold change in H鈦� ion concentration. Therefore, a difference of 2 pH units means the solution with pH 10 is \(10^2 = 100\) times more basic than the solution with pH 8.

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Key Concepts

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

acidic solution
An acidic solution is one where the pH is less than 7. pH is a measure that indicates the concentration of hydrogen ions (H鈦�) in the solution. The lower the pH, the higher the concentration of H鈦� ions, making the solution more acidic. Examples of acidic solutions include lemon juice, vinegar, and stomach acid. These solutions often taste sour and can be corrosive.
basicity
Basicity refers to the ability of a solution to accept hydrogen ions. Solutions with pH values higher than 7 are considered basic or alkaline. The higher the pH, the lower the concentration of H鈦� ions, making the solution more basic. Common basic solutions include baking soda, bleach, and soap. These solutions tend to feel slippery and can neutralize acids.
logarithmic scale
The pH scale is a logarithmic scale, which means that each whole number change in pH represents a tenfold change in hydrogen ion concentration. For instance, a pH change from 4 to 5 means the H鈦� ion concentration decreases by a factor of 10. Because of this logarithmic nature, small numerical changes in pH can represent large changes in acidity or basicity. This is why pH 10 is 100 times more basic than pH 8, as explained by the formula: \text(pH difference) \(10^{\text(difference)}\)\
H鈦� ion concentration
The concentration of H鈦� ions in a solution is what determines its pH. More H鈦� ions mean a more acidic solution (lower pH), while fewer H鈦� ions correspond to a more basic solution (higher pH). Accurate measurement and understanding of H鈦� ion concentration are crucial in chemistry because they affect how substances interact. For example, enzymes in our bodies work best at specific pH levels, relying on precise H鈦� ion concentrations.

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Most popular questions from this chapter

For each of the following: \((14.2,14.3)\) 1\. \(\mathrm{HNO}_{3}\) 2\. HF a. Write the formula for the conjugate base. b. Write the \(K_{\mathrm{a}}\) expression. c. Which is the weaker acid?

Calculate the volume, in milliliters, of a \(0.215 \mathrm{M} \mathrm{NaOH}\) solution that will completely neutralize each of the following: (14.8) a. \(3.80 \mathrm{~mL}\) of a \(1.25 \mathrm{M} \mathrm{HNO}_{3}\) solution b. \(8.50 \mathrm{~mL}\) of a \(0.825 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}\) solution

Consider the buffer system of nitrous acid, \(\mathrm{HNO}_{2}\), and its salt, \(\mathrm{NaNO}_{2}\). $$ \mathrm{HNO}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftarrows \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{NO}_{2}^{-}(a q) $$ a. The purpose of this buffer system is to: 1\. maintain \(\left[\mathrm{HNO}_{2}\right]\) 2\. maintain \(\left[\mathrm{NO}_{2}\right]\) 3\. maintain \(\mathrm{pH}\) b. The weak acid is needed to: 1\. provide the conjugate base 2\. neutralize added \(\mathrm{OH}^{-}\) 3\. provide the conjugate acid c. If \(\mathrm{H}_{3} \mathrm{O}^{+}\) is added, it is neutralized by: 1\. the salt 2\. \(\mathrm{H}_{2} \mathrm{O}\) 3\. \(\mathrm{OH}^{-}\) d. When \(\mathrm{OH}^{-}\) is added, the equilibrium shifts in the direction of the: 1\. reactants 2\. products 3\. does not change

What is meant by the phrase "A strong acid has a weak conjugate base"?

Calculate the \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) of each aqueous solution with the following [OH ]: a. coffee, \(1.0 \times 10^{-9} \mathrm{M}\) b. soap, \(1.0 \times 10^{-6} \mathrm{M}\) c. cleanser, \(2.0 \times 10^{-5} \mathrm{M}\) d. lemon juice, \(4.0 \times 10^{-13} \mathrm{M}\)
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