The pH of the solution can be calculated using the following steps:
Write the chemical equation for the dissociation of ethanoic acid:
CH3COOH + H2O ⇌ CH3COO- + H3O+
Write the equilibrium expression for the dissociation of ethanoic acid:
Ka = [CH3COO-][H3O+] / [CH3COOH]
Since the solution is equimolar in CH3COOH and CH3COO-, we can assume that the initial concentrations of CH3COOH and CH3COO- are equal. Let's use the variable x to represent the concentration of CH3COO- and CH3COOH in mol/L.
[CH3COOH] = x mol/L [CH3COO-] = x mol/L
Since CH3COOH is a weak acid, we can assume that only a small fraction of it dissociates in water. Let's use the variable y to represent the concentration of H3O+ ions in mol/L that are produced from the dissociation of CH3COOH. From the dissociation of ethanoic acid, we know that [CH3COO-] = [H3O+].
[CH3COO-] = y mol/L [H3O+] = y mol/L
Use the equilibrium expression to solve for the concentration of H3O+ ions:
Ka = [CH3COO-][H3O+] / [CH3COOH] 1.79 x 10^-5 = y^2 / x
Solving for y in terms of x, we get:
y = sqrt(Ka * x)
Calculate the pH of the solution using the equation:
pH = -log[H3O+]
pH = -log(y)
Substituting in the value of y from Step 5, we get:
pH = -log(sqrt(Ka * x))
Simplifying, we get:
pH = -0.5 * log(Ka * x)
Substituting in the value of Ka, we get:
pH = -0.5 * log(1.79 x 10^-5 * x)
Now we can calculate the pH for the solution by substituting the value of x as it is equimolar.
pH = -0.5 * log(1.79 x 10^-5 * x)
pH = -0.5 * log(1.79 x 10^-5 * 1)
pH = -0.5 * log(1.79 x 10^-5)
pH = 4.74
Therefore, the pH of an equimolar solution of ethanoic acid and Na+CH3COO- is 4.74.