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Degree of Dissociation (α) | chemca

Chemical Equilibrium

Degree of Dissociation ($\alpha$)

Calculating the extent of breakdown of molecules in reversible reactions.

By chemca Team • Updated Jan 2026

The **Degree of Dissociation** (represented by the Greek symbol alpha, $\alpha$) is the fraction of the total number of moles of a reactant that has dissociated (broken down) into products at equilibrium.

$$ \alpha = \frac{\text{Number of moles dissociated}}{\text{Initial number of moles}} $$

Range: $0 \le \alpha \le 1$
Percent Dissociation = $\alpha \times 100\%$

1. Calculation in Equilibrium

Let's consider the dissociation of $PCl_5$ in a closed vessel of total pressure $P$.

$$ PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g) $$

Stage	$PCl_5$	$PCl_3$	$Cl_2$	Total Moles
Initial Moles	1	0	0	1
At Equilibrium	$1 - \alpha$	$\alpha$	$\alpha$	$1 + \alpha$

The partial pressure of a gas is its mole fraction $\times$ Total Pressure ($P$). $$ p_{PCl_5} = \frac{1-\alpha}{1+\alpha}P, \quad p_{PCl_3} = \frac{\alpha}{1+\alpha}P, \quad p_{Cl_2} = \frac{\alpha}{1+\alpha}P $$

Expression for $K_p$

$$ K_p = \frac{p_{PCl_3} \cdot p_{Cl_2}}{p_{PCl_5}} = \frac{\alpha^2 P}{1 - \alpha^2} $$

2. Relation with Vapor Density

During dissociation, the number of moles increases, which causes the observed molar mass (and vapor density) of the mixture to decrease.

$D$: Theoretical (Initial) Vapor Density = $\frac{\text{Molar Mass of Reactant}}{2}$
$d$: Observed (Equilibrium) Vapor Density
$n$: Number of moles of products formed from 1 mole of reactant.

$$ \alpha = \frac{D - d}{d(n - 1)} $$

Also related to Molar Mass: $\alpha = \frac{M_{theoretical} - M_{observed}}{M_{observed}(n-1)}$

3. Factors Affecting $\alpha$

1. Dilution (Volume)

For reactions where moles increase (e.g., $PCl_5$), increasing volume (lowering pressure) increases $\alpha$ to produce more moles.

2. Temperature

For Endothermic reactions, increasing T increases $\alpha$. For Exothermic reactions, increasing T decreases $\alpha$.

3. Concentration

Adding an inert gas at constant pressure increases volume, thus increasing $\alpha$ for dissociation reactions.

4. Van't Hoff Factor ($i$)

In solution chemistry, the degree of dissociation connects to the Van't Hoff factor ($i$), which measures the effect on colligative properties.

$$ i = 1 + (n - 1)\alpha $$

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