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Degree of Dissociation and Its Formula With Solved Example for JEE

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Last updated date: 28th May 2024
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Introduction to Degree of Dissociation and Observed Density

The degree of dissociation ($\alpha$) of compounds, i.e. the amount to which the substance dissociates, can be calculated using the density of vapour measurement. The fraction of the total number of molecules or moles that have dissociated can be characterised as the degree of dissociation of a vapour. Unless there is a change in the number of molecules due to dissociation, thermal dissociation is not followed by a change in density or volume. Here, we will look into the general discussion about the definition as well as the formulas related to the degree of dissociation, the factors affecting it and the relationship between vapour density and degree of dissociation.

Degrees of Dissociation

The degree of association is defined as the percentage of a total number of molecules that are joined or united to form a larger molecule. The phenomenon of producing free ions carrying current that are dissociated from the percentage of solute at a certain concentration is referred to as the degree of dissociation. It is represented as $\alpha$, where $\alpha$ is the amount of substance of the reactant dissociated. 

Mathematically, it is represented as,

$\alpha=\dfrac{\text { number of moles dissociate }}{\text { number of moles present initially }}=\dfrac{\text { Percentage dissociation }}{100}$


Dissociation degrees are always in the range of 0 to 1. It is important not to count the number of individual parts when doing computations. Regardless of how many bits the substance dissociates into, only the number of units of dissociated substance should be measured. We must count groupings of pieces rather than individual pieces.


The most interesting degrees of dissociation are those that are more than 0 and less than 1. We don't need to examine the degree of dissociation if something entirely dissociates or does not disassociate at all.

Degrees of dissociation can be applied to a wide range of chemical systems. 

Degree of Dissociation Formula

The formula for determining the degree of dissociation ($\alpha$) is as follows:

$\alpha=\frac{D-d}{d}=\frac{M_{t}-M_{o}}{M_{o}}$

Where, 

D= theoretical (calculated) vapour density

d= vapour density (observed) after dissociation

Mt= theoretical (calculated) molecular mass 

Mo= Observed molecular mass after dissociation

How to Find Degree of Dissociation?

The degree of dissociation is calculated by dividing the amount of dissociated material by the total amount of the substance, which can be expressed in molecules or moles.

For example, take the help of this question.

Q. What is the degree of dissociation for a 0.25 M solution of phenol at 25oC? The dissociation constant 𝐾𝑎 is 1.6 $\times$ 10-10 M.

Ans.

$ \alpha=\dfrac{\text { number of moles dissociate }}{\text { number of moles present initially }}=\dfrac{\text { Percentage dissociation }}{100}$


Ostwald's dilution law can be used to calculate the acid dissociation constant and degree of dissociation. 

According to Ostwald's dilution equation, the acid dissociation constant is equal to the degree of dissociation squared divided by one minus the degree of dissociation times the original concentration of the acid. 

$k=\dfrac{\alpha^{2} C}{(1-\alpha)}$


Where, k is the acid dissociation constant, ($\alpha$) is the degree of dissociation and C is the concentration of the acid.

The degree of dissociation is particularly minimal for weak acids like phenol, where only a small percentage of the molecules dissociate. 

As a result, one minus the degree of dissociation is close to one. 

Ostwald's dilution equation can be simplified to K and is nearly equivalent to squared times Col for weak acids. 

We can now solve the problem.

Ostwald's dilution law,

$K_{a}=\dfrac{\alpha^{2}}{1-\alpha} C_{0}$


where, $C_{0}$ is the initial concentration

$\begin{align} &1-\alpha \cong 1 \\ &K_{a} \cong C_{0}{\alpha} \\ &\alpha \cong \sqrt{\dfrac{K_{a}}{C_{0}}} \end{align}$

Acid dissociation constant $\left(K_{a}\right)$


$K_{a}=\dfrac{\left[H^{+}\right]\left[\Lambda^{-}\right]}{[H A]}$


where, $[H A] \sim 0.25 \mathrm{M}$


$\begin{align} &\alpha=\sqrt{\dfrac{\left(1.6 \times 10^{-10} M\right)}{0.25 M}} \\ &\alpha=\sqrt{6.4 \times 10^{-10}} \\ &\alpha=2.5298 \ldots \times 10^{-5} \\ &\alpha=2.5 \times 10^{-5} \end{align}$

Relation Between Vapour Density and Degree of Dissociation

$\begin{align} A(g) & \leftrightarrow &n B(g) \\c & &0 \\ c(1-\alpha) & & n c \alpha \end{align}$ 

$\begin{align}\dfrac{\text{Initial vapour density}}{\text { vapour density at equillibrium }} & =\dfrac{\text { total moles of gases at equillibrium }}{\text { initial moles of gaseous reaction }} \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\dfrac{D}{d} & =\dfrac{c[1+\alpha(n-1)]}{c} \\ \text { Therefore, } ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\alpha & =\dfrac{(D-d)}{(n-1) d} \end{align}$

Where n represents the number of moles of gaseous product given by 1 mol of gaseous reactant.

Knowing, D, d and n the degree of dissociation can be calculated.


Factors Affecting Degree of Dissociation

There are four factors on which degree of dissociation affect:

  1. Dilution: Under typical dilution, the value of ($\alpha$) is nearly 1 for strong electrolytes and less than 1 for weak electrolytes.

  2. Temperature: As the temperature of a solution rises, the degree of dissociation of an electrolyte also increases.

  3. The Electrolyte's Composition: The degree of dissociation is inversely proportional to the solution's concentration and weight, but directly proportional to the solution's dilution and the amount of solvent contained in the solution.

(i) a strong electrolyte with a concentration of 100 percent 

(ii) Electrolyte that is weak: 100 percent 

  1. The Nature of the Solvent: The degree of dissociation is also affected by the nature of the solvent, whether it is polar or nonpolar.

 

Conclusion

The fraction of a mole of the reactant that dissociates is known as the degree of dissociation. It is represented by the symbol ($\alpha$). The degree of dissociation refers to the extent to which the dissociation occurs. It can also be described as the formation of current-carrying free ions that dissociate from a percentage of the solute at a given temperature. It is more precisely defined as the number of solute particles per mole that disintegrate into ions, radicals, smaller molecules, or compounds.

A strong acid and a strong base will have a degree of dissociation very near to 1. In weaker acids and bases, the degree of dissociation is lower. The degree of dissociation also depends on several factors like dilution, temperature, the nature of the solvent and the composition of the electrolyte.

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FAQs on Degree of Dissociation and Its Formula With Solved Example for JEE

1. What is the degree of ionisation?

The fraction of the total amount of a weak acid or base that exists in the ionised form can be characterised as the degree of ionisation. It is represented by the Greek letter ($\alpha$). The equilibrium constant can be used to calculate the degree of ionisation of a weak acid or base.

An equation that can be used to relate ($\alpha$) and Ka or Kb is as follows:

$\begin{align} &K_{\alpha}=c \alpha^{2} \\ &\text { or, } \alpha^{2}=\dfrac{K_{\alpha}}{c} \\ &\text { or, } \alpha=\sqrt{\dfrac{K_{\alpha}}{c}} \end{align}$


Where, $K_{\alpha}$ is the acid dissociation constant

$\alpha$ is the degree of ionisation and 

c is the concentration.

Knowing an acid's dissociation constant and the concentration of weak acids allows us to assess its degree of ionisation.

2. What is the difference between ionisation and dissociation?

Difference between ionisation and dissociation is as follows: 

  • Ionisation is the process by which atoms or molecules are charged positively or negatively, whereas dissociation is the breakdown of a molecule into smaller particles such as ions, atoms or molecules.

  • Ionisation is known as the formation of ions, and dissociation is the formation of small constituents from larger ones.

  • When an atom or molecule gains or loses an electron, ionisation occurs, whereas dissociation occurs with the addition of solvent and the energy is released in the form of heat.

  • Ionisation always forms atoms in the end, but dissociation forms atoms, ions or molecules that are smaller than the starting materials.

  • Ionisation is irreversible whereas dissociation is a reversible reaction.