Question

The ${10}^4\mathrm{Ka}$ values for the acids acetic, hydrofluoric, formic and nitrous are $6.7,4.5,1.8$ and $0.18$ but not in the correct order. The correct acid strengths arc (1) $\mathrm{HF}=0.18,{\mathrm{HNO}}_2=1.8,\mathrm{HCOOH}=4.5$, ${\mathrm{CH}}_3\mathrm{COOH}=6.7$ (2) $\mathrm{HF}=6.7,{\mathrm{HNO}}_2=4.5,\mathrm{HCOOH}=1.8,{\mathrm{CH}}_3\mathrm{COOH}$ $=0.18$ (3) $\mathrm{HF}=1.8,{\mathrm{HNO}}_2=0.18,\mathrm{HCOOH}=4.5$, ${\mathrm{CH}}_3\mathrm{COOH}=6.7$ (4) $\mathrm{HF}=6.7,{\mathrm{HNO}}_2=0.18,\mathrm{HCOOH}=4.5$ ${\mathrm{CH}}_3\mathrm{COOH}=1.8$

Short answer

Option (1) is correct: HF=0.18, HNO2=1.8, HCOOH=4.5, CH3COOH=6.7.

Step-by-step solution

Understanding the Problem

Given the 10^4 Ka values for four acids: acetic, hydrofluoric, formic, and nitrous, determine the correct matching of the acids with their dissociation constants. The possible Ka values are 6.7, 4.5, 1.8, and 0.18.

Knowing the relationship of Ka and acid strength

The strength of an acid is directly proportional to its Ka value. A higher Ka value indicates a stronger acid, as it means the acid dissociates more in solution.

Arrange the given Ka values in increasing order

Order the Ka values from smallest to largest to help determine the weakest to strongest acids:- 0.18 (weakest)- 1.8- 4.5- 6.7 (strongest)

Assign Ka values to the acids based on known strengths

Using known information about the acids' strengths:- Hydrofluoric acid (HF) is the weakest among the given acids.- Nitrous acid (HNO2) is stronger than HF but weaker than formic acid.- Formic acid (HCOOH) is stronger than HNO2 but weaker than acetic acid.- Acetic acid (CH3COOH) is the strongest among the given acids.

Match Ka values to correct acids

Based on the known strengths:- HF (Hydrofluoric acid): 0.18- HNO2 (Nitrous acid): 1.8- HCOOH (Formic acid): 4.5- CH3COOH (Acetic acid): 6.7

Identify the correct option

After matching, find the option that corresponds to these assignments. The correct answer matches option (1) (1) HF=0.18, HNO2=1.8, HCOOH=4.5, CH3COOH=6.7

Key concepts

Ka values

The term 'Ka' stands for the acid dissociation constant, a value that expresses the extent to which an acid dissociates into its base form and protons in a solution. Essentially, the Ka value provides insight into the strength of an acid.
Higher Ka values signify stronger acids because they dissociate more readily in solution.
For example, if we compare two acids, the one with the higher Ka value will be the stronger acid due to its higher tendency to release protons. Understanding Ka values is crucial in determining the relative strengths of different acids.

Ka values are often given in scientific notation for convenience. For instance, a Ka value of 0.18 represents $1.8\times {10}^{-1}$. When comparing Ka values, it's important to observe these exponents closely because they significantly impact the strength of the acid. In our exercise, the values are 6.7, 4.5, 1.8, and 0.18, meaning that we have to compare these numbers to identify the acid strengths correctly.

Acid Dissociation

Acid dissociation is the process by which an acid releases hydrogen ions (H+) when dissolved in water. This release, or dissociation, results in the formation of conjugate base and protons.
The general equation representing acid dissociation is:
$$HA\rightleftharpoons H^{+}+A^{-}$$

In this equation, HA represents the acid, H+ is the proton, and A- is the conjugate base. The extent of this dissociation is determined by the acid's Ka value. The higher the Ka value, the more the acid dissociates.
Understanding this dissociation process is fundamental to solving problems related to acid strength.

In the context of the provided exercise, you have to pair the given Ka values with the respective acids to determine their strengths based on how much they dissociate.

Acid Strength Hierarchy

The hierarchy of acid strength depends on their ability to donate protons (H+). The more an acid dissociates in water to release protons, the stronger the acid.
Here's a simple way to remember:

• Weak acids dissociate slightly.
• Strong acids dissociate completely or almost completely.

In our exercise, we have four acids to compare: acetic acid, hydrofluoric acid, formic acid, and nitrous acid.
According to their known properties:

• Hydrofluoric acid (HF) is the weakest.
• Nitrous acid (HNO2) is stronger than HF but weaker than formic acid (HCOOH).
• Formic acid (HCOOH) is stronger than HNO2 but weaker than acetic acid (CH3COOH).
• Acetic acid (CH3COOH) is the strongest among them.

By knowing this hierarchy, we can effectively match the given Ka values to the respective acids based on their strength.

Chemistry Problem Solving

Solving chemistry problems often involves a step-by-step approach:

• Understanding the problem statement and identifying given data.
• Using relevant chemical principles or equations.
• Applying known relationships, such as the relationship between Ka values and acid strengths.
• Operating methodically to find the solution.

In the given exercise, we start by arranging the provided Ka values in ascending order to identify which acids are weakest and which are strongest.
We then use the known hierarchy of the acids' strengths to make an educated match between these values and the names of the acids.
Finally, by reviewing these matches, we identify that the correct order is: HF=0.18, HNO2=1.8, HCOOH=4.5, CH3COOH=6.7.
This structured approach ensures that each step is clear and logical, making it easier to solve complex problems effectively.