Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Chapter 14: Problem 64
Calculate the percent dissociation for a \(0.22 M\) solution of chlorous acid \(\left(\mathrm{HClO}_{2}, K_{\mathrm{a}}=1.2 \times 10^{-2}\right)\)
Short Answer
Expert verified
The percent dissociation for a \(0.22 M\) solution of chlorous acid (HClO鈧�) is approximately 20.9%.
Step by step solution
01
Set up the equilibrium expression
Write the equilibrium expression for the dissociation of chlorous acid, HClO鈧�, which is a weak acid. The dissociation reaction of HClO鈧� can be represented as:
HClO鈧� (aq) 鈬� H鈦� (aq) + ClO鈧傗伝 (aq)
Set up an equilibrium expression using the equilibrium constant, Ka:
Ka = \(\frac{[H^{+}][ClO_{2}^{-}]}{[HClO_{2}]}\)
02
Define the change in concentration
Let x represent the change in concentration of H鈦� and ClO鈧傗伝 ions. Since HClO鈧� dissociates into H鈦� and ClO鈧傗伝, we know that for every mole of HClO鈧� that dissociates, one mole of H鈦� and one mole of ClO鈧傗伝 are produced.
Initial concentrations:
[HClO鈧俔 = 0.22 M
[H鈦篯 = 0
[ClO鈧傗伝] = 0
Change in concentrations:
[HClO鈧俔 = -x
[H鈦篯 = +x
[ClO鈧傗伝] = +x
Equilibrium concentrations:
[HClO鈧俔 = 0.22 - x
[H鈦篯 = x
[ClO鈧傗伝] = x
03
Substitute equilibrium concentrations into the Ka expression
Now substitute the equilibrium concentrations into the Ka expression:
\(1.2\times10^{-2} = \frac{x^{2}}{(0.22-x)}\)
Since Ka is relatively large, we can assume that x is small compared to 0.22. This allows us to simplify the equation as:
\(1.2\times10^{-2} = \frac{x^{2}}{0.22}\)
04
Solve for x
To find the value of x, we need to solve the simplified equation:
\(x^{2} = 1.2\times10^{-2}\times0.22\)
Now, take the square root of both sides:
\(x = \sqrt{1.2\times10^{-2}\times0.22}\)
Calculating, we get:
\(x \approx 0.046\)
The value of x represents the concentration of H鈦� ions (and ClO鈧傗伝 ions) at equilibrium.
05
Calculate percent dissociation
Now that we have the concentration of H鈦� ions at equilibrium (x), we can calculate the percent dissociation using the following formula:
Percent dissociation = \(\frac{[H^{+}\; at\; equilibrium]}{[initial\; concentration\; of\; HClO_{2}]}\times 100\)
Percent dissociation = \(\frac{0.046}{0.22} \times 100\)
Calculating, we get:
Percent dissociation 鈮� 20.9%
Thus, the percent dissociation for a 0.22 M solution of chlorous acid (HClO鈧�) is approximately 20.9%.
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with 91影视!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Weak Acid Dissociation
When we talk about weak acid dissociation, it refers to the process where a weak acid partially ionizes in solution. Unlike strong acids, which completely dissociate into ions, weak acids only break apart a little. This means:
- The weak acid and its dissociated ions remain in equilibrium.
- The formula for a weak acid dissociation looks something like this: \[ \text{HA }(\text{aq}) \rightleftharpoons \text{ H}^{+}(\text{aq}) + \text{ A}^{-}(\text{aq}) \]
- Chlorous acid \( \text{HClO}_2 \) dissociates similarly, releasing \( \text{H}^+ \) and \( \text{ClO}_2^- \) ions.
Equilibrium Expression
An equilibrium expression is used to describe this balance between the reactants and products in a chemical reaction at equilibrium. For weak acids:
- The equilibrium expression is derived from the balanced equation of the dissociation.
- For chlorous acid, the expression is: \[ K_{a} = \frac{[\text{H}^{+}][\text{ClO}_{2}^{-}]}{[\text{HClO}_{2}]} \]
- This expression helps us understand the relationship between the concentrations of the acid and its ions.
Acid Dissociation Constant
The acid dissociation constant, \( K_a \), is a numerical value that describes how well an acid dissociates in water. It indicates:
- The strength of the acid; larger \( K_a \) values mean a stronger acid.
- For chlorous acid, \( K_a \) is given as \( 1.2 \times 10^{-2} \), showing it dissociates more than many other weak acids.
- This value is essential in setting up the equilibrium expression and calculating the concentrations of the ions at equilibrium.
Initial Concentration
Initial concentration refers to the starting amount of the acid before any dissociation has occurred. In the context of our problem:
- The initial concentration of chlorous acid is \( 0.22 \text{ M} \).
- It's the baseline from which changes in concentration of ions are measured.
- As the reaction proceeds, the initial concentration decreases as some of the acid dissociates into ions.
