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Chapter 2: Problem 50

Rank the following according to their strength as acids: Acid Ka pK A citrate _________ 4.76 B succinic acid 6.17 脳 10鈥�5 ______ C succinate 2.29 脳 10鈥�6 ______ D formic acid 1.78 脳 10鈥�4 ______ E citric acid _________ 3.13

Short Answer

Expert verified
Citric acid is strongest, followed by formic acid, succinic acid, succinate, and citrate.

Step by step solution

01

Understand Acid Strength

Acid strength is determined by the acid dissociation constant, \( K_a \). A larger \( K_a \) value indicates a stronger acid because it means the acid ionizes more in solution. Conversely, the \( pK_a \) value is inversely related to \( K_a \); a smaller \( pK_a \) implies a stronger acid.
02

Convert pK to Ka

Given pK values can be converted to \( K_a \) using the formula: \[ K_a = 10^{-pK_a} \]. For citric acid: \[ K_a = 10^{-3.13} \approx 7.41 \times 10^{-4} \]. For citrate, since no \( K_a \) is given but a \( pK_a \), we will keep \( pK_a = 4.76 \) to compare.
03

List All Ka Values

Now list all \( K_a \) values for the acids provided: - Citrate: \( K_a \) corresponds to \( pK_a = 4.76 \), \[ K_a = 10^{-4.76} \].- Succinic acid: \( K_a = 6.17 \times 10^{-5} \).- Succinate: \( K_a = 2.29 \times 10^{-6} \).- Formic acid: \( K_a = 1.78 \times 10^{-4} \).- Citric acid: \( K_a \approx 7.41 \times 10^{-4} \).
04

Rank Based on Ka Values

Arrange the acids based on their \( K_a \) values from strongest to weakest:- Citric acid \( \approx 7.41 \times 10^{-4} \)- Formic acid \( = 1.78 \times 10^{-4} \)- Succinic acid \( = 6.17 \times 10^{-5} \)- Succinate \( = 2.29 \times 10^{-6} \)- Citrate (derived \( K_a \) from \( pK_a = 4.76 \))

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Key Concepts

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

Acid Dissociation Constant
The acid dissociation constant, often denoted as \( K_a \), is a crucial measure to understand the strength of an acid. In simple terms, it tells us how well an acid releases its hydrogen ion (\( H^+ \)) when dissolved in water.

Understanding the value of \( K_a \) can help you identify how potent or strong an acid is:
  • A larger \( K_a \) value indicates a stronger acid. This is because it means the acid dissociates more completely, releasing more hydrogen ions into the solution.
  • A smaller \( K_a \) value signifies a weaker acid, as it dissociates less, releasing fewer hydrogen ions.
To use \( K_a \) effectively, always remember it reflects the degree of ionization of the acid in an aqueous solution. The more ions an acid produces, the higher its potential to lower the pH of the solution, thereby being a stronger acid. In practical chemistry, comparing \( K_a \) values helps determine which acids are stronger in a given set.
pKa Conversion
Converting between \( K_a \) and \( pK_a \) is a helpful skill when evaluating acids. The \( pK_a \) is the negative logarithm of \( K_a \). It serves as an easier way to express acidity, especially since \( K_a \) values can sometimes be tiny numbers that are cumbersome to handle.

The mathematical conversion is simple:
  • \( pK_a = -\log(K_a) \)
  • \( K_a = 10^{-pK_a} \)
This inverse relationship implies that:
  • A lower \( pK_a \) value corresponds to a higher \( K_a \), indicating a stronger acid.
  • A higher \( pK_a \) value suggests a lower \( K_a \), thus a weaker acid.
For example, citric acid has a \( pK_a \) of 3.13, which can be converted using \( K_a = 10^{-3.13} \) to see how it compares with other acids.

Understanding and converting between \( K_a \) and \( pK_a \) allows for quick and straightforward comparisons of acid strength across different substances.
Weak vs Strong Acids
Recognizing the difference between weak and strong acids is fundamental in chemistry. Here, the concepts of \( K_a \) and \( pK_a \) play essential roles.
  • **Strong acids** have a high \( K_a \) and low \( pK_a \). They dissociate almost completely in water, providing a significant amount of hydrogen ions. Common examples include hydrochloric acid (HCl) and sulfuric acid (H2SO4).
  • **Weak acids**, on the other hand, have a low \( K_a \) and high \( pK_a \). They only partially dissociate in water. Their equilibrium lies more towards the undissociated form. Acetic acid (CH3COOH) is a typical example of a weak acid.
In the given problem, the acids were ranked based on their \( K_a \), identifying which is the stronger acid. Citric acid, with a higher \( K_a \)., turned out to be stronger than the others, indicating its ability to dissociate more in solution compared to others like citrate.
  • Always seek to look at both \( K_a \) and \( pK_a \) when comparing acids to gauge their strength effectively.
  • Understanding these differences aids in practical applications, such as predicting reaction outcomes or adjusting pH in solutions.

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Most popular questions from this chapter

The amino acid glycine \(\left(\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}\right)\) has \(\mathrm{p} K\) values of \(2.35\) and \(9.78\). Indicate the structure and net charge of the molecular species that predominate at \(\mathrm{pH} 2,7\), and 10 .

Consider the following molecules and their melting points listed below. How can you account for the diff erences in melting points among these molecules of similar size? $$ \begin{array}{lcc} & \begin{array}{c} \text { Molecular weight } \\ \left(\mathrm{g} \cdot \mathbf{m o l}^{-1}\right) \end{array} & \begin{array}{c} \text { Melting } \\ \text { point }\left({ }^{\circ} \mathbf{C}\right) \end{array} \\ \hline \text { Water, } \mathrm{H}_{2} \mathrm{O} & 18.0 & 0 \\ \text { Ammonia, } \mathrm{NH}_{3} & 17.0 & -77 \\ \text { Methane, } \mathrm{CH}_{4} & 16.0 & -182 \end{array} $$

a. Water has a surface tension that is nearly three times greater than that of ethanol. Explain. b. The surface tension of water decreases with increasing temperature. Explain.

The \(\mathrm{pH}\) of blood is maintained within a narrow range \((7.35\) 7.45). Carbonic acid, \(\mathrm{H}_{2} \mathrm{CO}_{3}\), participates in blood buffering. a. Write the equations for the dissociation of the two ionizable protons. b. The \(\mathrm{p} K\) for the first ionizable proton is \(6.35\); the \(\mathrm{p} K\) for the second ionizable proton is \(10.33\). Use this information to identify the weak acid and the conjugate base present in the blood. c. Calculate the concentration of carbonic acid in a sample of blood with a bicarbonate concentration of \(24 \mathrm{mM}\) and a \(\mathrm{pH}\) of \(7.40\).

Give the conjugate base of the following acids: a. \(\mathrm{HC}_{2} \mathrm{O}_{4}^{-}\); b. \(\mathrm{HSO}_{3}^{-} ;\)c. \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\); d. \(\mathrm{HCO}_{3}^{-} ;\)e. \(\mathrm{HAsO}_{4}^{2-} ;\) f. \(\mathrm{HPO}_{4}^{2-} ;\) g. \(\mathrm{HO}_{2}^{-}\)
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