Problem 32 - Chemistry: An Atoms-Focused Approach

Question

What is the pH at \(25^{\circ} \mathrm{C}\) of a solution that results from mixing equal volumes of a \(0.05 M\) solution of acetic acid and a \(0.025 M\) solution of sodium hydroxide?

Step-by-Step Solution

Answer

Answer: The pH of the mixed solution is approximately 4.74.

Step 1: Write down the balanced chemical equation

The first step is to write down the balanced chemical equation for the reaction between acetic acid (CH3COOH) and sodium hydroxide (NaOH). CH3COOH + NaOH -> CH3COONa + H2O The equation shows that acetic acid reacts with sodium hydroxide to form sodium acetate (CH3COONa) and water.

Step 2: Calculate the moles of reactants

To find the concentration of ions after the reaction, we need to calculate the moles of the reactants (acetic acid and sodium hydroxide) in the solution. As equal volumes of the two solutions are mixed, let's assume the volume of each solution is V. Moles of acetic acid = M (concentration) x V (volume) = 0.05 M x V = 0.05V Moles of sodium hydroxide = M (concentration) x V (volume) = 0.025 M x V = 0.025V

Step 3: Determine the limiting reactant and calculate moles of products

From the balanced equation, we can see that one mole of acetic acid reacts with one mole of sodium hydroxide. However, in our case, the moles of acetic acid are more than the moles of sodium hydroxide, so sodium hydroxide is the limiting reactant. The moles of acetic acid and sodium hydroxide react in a 1:1 ratio, so the moles of sodium acetate produced is 0.025V. The moles of remaining acetic acid is 0.05V - 0.025V = 0.025V.

Step 4: Calculate concentrations of products and remaining reactant

Now, the total volume of the solution after mixing is 2V. To find the concentration of species in the solution, we can use the formula: Concentration = Moles/V, where V is the total volume of the solution. Concentration of sodium acetate (CH3COONa) = 0.025V / 2V = 0.0125 M Concentration of acetic acid (CH3COOH) = 0.025V / 2V = 0.0125 M

Step 5: Calculate the pH of the mixed solution

We can use the equation for acetic acid ionization to help us find pH. CH3COOH (aq) <-> CH3COO- + H+ Since acetic acid is a weak acid, we can use the Ka expression: Ka = (molar concentration of CH3COO-)(molar concentration of H+)/(molar concentration of CH3COOH) For acetic acid, Ka = 1.8 x 10^-5 The concentration of CH3COO- and CH3COOH is the same in the solution, let's denote it as x: 1.8 x 10^-5 = (x)(H+)/((0.0125-x)) As x is very small in comparison to 0.0125, we can simplify the equation as: 1.8 x 10^-5 = (x)(H+)/0.0125 To find H+ concentration, we can solve for H+: H+ = (1.8 x 10^-5)(0.0125)/x Finally, to find the pH, we use the equation pH = -log(H+): pH = -log((1.8 x 10^-5)(0.0125)/x) The pH of the mixed solution is approximately 4.74.