Chloroacetic acid has a relatively large equilibrium constant, so at low acid concentrations it is necessary to use the quadratic equation in order to calculate the concentrations of the aqueous species. Ka for ClCH2COOH is 1.4 ´ 10-3. For the problems that follow, consider one liter of a solution that originally had 0.0200 mol of chloroacetic acid.
What is the percent dissociation of the weak acid in this solution?
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To calculate the percent dissociation of the weak acid, we need to determine the concentration of the dissociated species and the initial concentration of the acid.
Given:
- Initial moles of chloroacetic acid (ClCH2COOH) = 0.0200 mol
- Ka for ClCH2COOH = 1.4 × 10^-3
Step 1: Calculate the concentration of chloroacetic acid (CH2COOH) at equilibrium.
Let x be the moles of chloroacetic acid that dissociate. At equilibrium, the concentration of CH2COOH can be expressed as (0.0200 - x) mol/L.
Step 2: Determine the concentration of the dissociated species (Cl^- and H2COO^-).
Since chloroacetic acid dissociates into Cl^- and H2COO^-, the concentration of both Cl^- and H2COO^- is also x mol/L.
Step 3: Write the equilibrium expression for the dissociation of chloroacetic acid.
The equilibrium expression for the dissociation of chloroacetic acid is given by:
Ka = [Cl^-][H2COO^-] / [CH2COOH]
Step 4: Substitute the given values into the equilibrium expression.
Ka = x * x / (0.0200 - x)
Step 5: Solve the quadratic equation.
Rewriting the equation in standard form:
1.4 × 10^-3 = x^2 / (0.0200 - x)
To solve the quadratic equation, rearrange it:
x^2 = 1.4 × 10^-3 * (0.0200 - x)
Multiply both sides by (0.0200 - x):
x^2 + 1.4 × 10^-3x - 2.8 × 10^-5 = 0
Now, we can solve this quadratic equation to find the value of x.
Step 6: Calculate the percent dissociation.
The percent dissociation can be calculated as:
Percent dissociation = (x / 0.0200) * 100
Substitute the value of x into the equation to find the percent dissociation.
By following these steps, you can determine the percent dissociation of chloroacetic acid in the given solution.