Question

Explain why a mixture formed by mixing \(100 \mathrm{~mL}\) of \(0.100 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{COOH}\) and \(50 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{NaOH}\) will act as a buffer.

Short answer

The mixture formed by mixing 100 mL of 0.100 M CH3COOH and 50 mL of 0.100 M NaOH will act as a buffer because it contains a weak acid (CH3COOH) and its conjugate base (CH3COONa) in significant amounts with a concentration ratio of 1. This meets the buffer criteria, ensuring that the resulting mixture will effectively resist pH changes.

Step-by-step solution

Determine the moles of the initial substances

To start, calculate the moles of CH3COOH and NaOH initially present in the mixture. The number of moles can be calculated using the formula: Number of moles = volume (L) × concentration (M) For CH3COOH: Number of moles = (100 mL × 0.100 M) / 1000 = 0.0100 moles For NaOH: Number of moles = (50 mL × 0.100 M) / 1000 = 0.00500 moles

Write the balanced equation for the reaction

Now that we have the moles of the two reactants, write the balanced equation for the reaction between acetic acid (CH3COOH) and sodium hydroxide (NaOH). The equation representing this reaction is: CH3COOH(aq) + NaOH(aq) → CH3COONa(aq) + H2O(l)

Determine the limiting reactant

Since we have different amounts of the reactants (0.0100 moles of CH3COOH and 0.00500 moles of NaOH), we need to determine the limiting reactant: the reactant that is completely consumed during the reaction. Using the stoichiometry of the balanced equation (1:1), we find that 0.00500 moles of NaOH will completely react with 0.00500 moles of CH3COOH. Since we have more CH3COOH available (0.0100 moles), NaOH is the limiting reactant.

Calculate the amounts of reactants and products after the reaction

NaOH is completely consumed during the reaction. Calculate the remaining moles of CH3COOH and the moles of CH3COONa produced. For CH3COOH: Initial moles: 0.0100 moles Moines reacted: 0.00500 moles Final moles: 0.0100 - 0.00500 = 0.00500 moles For CH3COONa: Initial moles: 0 Moines formed: 0.00500 moles Final moles: 0.00500 moles

Calculate the final concentrations and check buffer criteria

Compute the final concentrations of CH3COOH and CH3COONa in the mixture, considering that the total volume of the solution is 150 mL (100 mL of acetic acid solution + 50 mL of NaOH solution). For CH3COOH: Concentration = moles / volume = 0.00500 moles / (150 mL / 1000) = 0.0333 M For CH3COONa: Concentration = moles / volume = 0.00500 moles / (150 mL / 1000) = 0.0333 M Now, check the buffer criteria: 1. The mixture contains a weak acid (CH3COOH) and its conjugate base (CH3COONa) in significant amounts. 2. The ratio of concentrations is 0.0333 M / 0.0333 M = 1, which is not extremely large or small. Since the resulting mixture meets both buffer criteria, we can conclude that it will act as a buffer.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in which the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentrations of reactants and products over time. It's essential in understanding buffer solutions, which are systems that resist changes in pH upon the addition of an acid or a base. Buffers typically consist of a weak acid and its conjugate base or a weak base and its conjugate acid, both present in significant quantities.

When a strong acid or base is added to the buffer, the chemical equilibrium shifts to counteract the pH change. This is known as Le Châtelier's principle. In the case of the acetic acid (CH3COOH) and sodium acetate (CH3COONa) buffer system, the equilibrium would adjust by consuming or releasing H+ ions, thereby stabilizing the pH.

Acid-Base Reaction

Acid-base reactions are processes in which an acid donates a proton (H+) to a base. In the exercise, acetic acid, a weak acid, donates a proton to the strong base sodium hydroxide (NaOH), forming water (H2O) and the salt sodium acetate (CH3COONa). This particular reaction is important for creating a buffer solution because it produces a conjugate acid-base pair.

The presence of this conjugate pair in a buffer solution helps maintain a stable pH. When a strong acid is introduced to the buffer, it reacts with the conjugate base (CH3COONa), and when a strong base is added, it reacts with the weak acid (CH3COOH), thus neutralizing the added substances and preventing significant shifts in pH.

Stoichiometry

Stoichiometry is the area of chemistry that relates to the quantitative relationships between the substances as they participate in various chemical reactions. Understanding stoichiometry allows us to predict the amounts of products formed from a given amount of reactants. In the exercise, the stoichiometric 1:1 ratio of the reaction between CH3COOH and NaOH indicates that one mole of CH3COOH reacts with one mole of NaOH to form one mole of CH3COONa and one mole of H2O.

By using stoichiometric calculations, we determine the moles of each reactant and the products formed. This precise calculation ensures the correct proportions are present to form a buffer solution, which is critical for the buffer's function to resist changes in pH.

Limiting Reactant

The limiting reactant in a chemical reaction is the reactant that is completely consumed first, limiting the quantity of the product that can be formed. In our exercise, NaOH is identified as the limiting reactant because it is present in a lesser amount compared to CH3COOH. As there is a 1:1 stoichiometric ratio, every mole of NaOH will react with a mole of CH3COOH until NaOH is depleted.

Identifying the limiting reactant is important for predicting the composition of the final mixture in terms of the remaining reactants and products. In the context of buffer solutions, ensuring a sufficient quantity of both a weak acid and its conjugate base is key to its ability to mitigate pH changes. As such, understanding which reactant limits the reaction and the quantities involved after the reaction is essential for predicting the efficacy of the buffer solution.