The degree of dissociation, alpha, of an acid, HA, is defined by the relationship: alpha= [(A-)/[(A-)+ (HA)]. Calculate the degree of dissociation for acetic acid (pK=4.76) at 0.1 M
To calculate the degree of dissociation (alpha) for acetic acid (HA), you will need to use the acid dissociation constant (pK) and the initial concentration of the acid (HA).
The acid dissociation constant (pK) is a measure of the strength of an acid. For acetic acid, the pK value is given as 4.76.
The degree of dissociation (alpha) is defined by the equation:
alpha = [(A-) / [(A-) + (HA)]]
In this equation, (A-) represents the concentration of the dissociated form (acetate ions) and (HA) represents the concentration of the undissociated form (acetic acid).
Given that the initial concentration of acetic acid (HA) is 0.1 M, we can now calculate the degree of dissociation.
Step 1: Calculate the concentrations of (A-) and (HA).
Since the degree of dissociation (alpha) is unknown, let's assume x as the concentration of (A-).
Therefore, the concentration of (A-) can be written as x M.
The concentration of (HA) will be the initial concentration minus the concentration of (A-).
So, the concentration of (HA) can be written as (0.1 - x) M.
Step 2: Substitute the concentrations into the equation for alpha.
alpha = [(A-) / [(A-) + (HA)]]
alpha = [x / (x + (0.1 - x))]
Simplifying the equation:
alpha = x / (0.1)
Step 3: Calculate the value of x.
To find the value of x, we need to consider the equilibrium condition.
The equilibrium expression for acetic acid dissociation is given as:
HA ⇌ H+ + (A-)
Based on this, we can set up an equilibrium expression and solve for x.
Ka = [H+] * [A-] / [HA]
Since the Ka value is related to the pK value, we can rewrite the equation as:
10^(-pK) = (x) * (x) / (0.1 - x)
Simplifying and rearranging the equation, we get:
10^(-4.76) = x^2 / (0.1 - x)
Now we need to solve this equation to find the value of x. This can be done using numerical methods or by using approximate techniques such as the quadratic formula.
Once you find the value of x, you can substitute it back into the equation for alpha to calculate the degree of dissociation (alpha).
Note: The calculation might require a calculator or software program that can handle equations and numerical calculations.