Question

Given the equilibrium: \(\mathrm{CICH}_{2} \mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} \rightleftarrows \mathrm{H}_{3} \mathrm{O}^{+}+\) \(\mathrm{ClCH}_{2} \mathrm{COO}^{-}\) exists at \(25^{\circ} \mathrm{C} . \mathrm{K}_{\mathrm{a}}=1.35 \times 10^{-3}\). (a) Determine the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration for a \(0.1 \mathrm{M}\) solution of monochloroacetic acid \(\left(\mathrm{CICH}_{2} \mathrm{COOH}\right)\) in water \(\left(\mathrm{H}_{2} \mathrm{O}\right)\). (b) Can one make the assumption that the dissociated acid is negligible with respect to the undissociated acid? (c) Calculate to what degree this solution is more acidic than 1.0 M acetic acid \(\left(\mathrm{K}_{\mathrm{a}}=1.8 \times 10^{-5}\right.\) at \(\left.25^{\circ} \mathrm{C}\right)\).

Short answer

The equilibrium concentration of H3O+ in a 0.1 M monochloroacetic acid solution is approximately 0.00367 M. The dissociated acid can be considered negligible with respect to the undissociated acid. Comparatively, the 0.1 M monochloroacetic acid solution is approximately 0.865 times as acidic as a 1.0 M acetic acid solution, meaning it is less acidic.

Step-by-step solution

Initial Concentrations

First, let's write down the initial concentrations of all components. We have a 0.1 M solution of CICH2COOH and pure H2O. The initial concentration of H3O+ and ClCH2COO- is 0 as they are not initially present in the solution. Initial Concentrations: [CICH2COOH] = 0.1 M [H2O] = constant [H3O+] = 0 M [ClCH2COO-] = 0 M

Change in Concentrations

As the reaction proceeds, some of the CICH2COOH will dissociate, giving H3O+ and ClCH2COO-. Let's assume x moles of CICH2COOH dissociate: Change in Concentrations: Δ[CICH2COOH] = -x M Δ[H3O+] = +x M Δ[ClCH2COO-] = +x M

Equilibrium Concentrations

At equilibrium, the concentrations will be: Equilibrium Concentrations: [CICH2COOH] = 0.1 - x M [H3O+] = x M [ClCH2COO-] = x M

Equilibrium Expression

Using the Ka expression and the given Ka value, we can find x: Ka = [H3O+][ClCH2COO-] / [CICH2COOH] 1.35 x 10^(-3) = (x)(x) / (0.1 - x)

Solving for x

Assuming x is small compared to 0.1, we can approximate the equation as: 1.35 x 10^(-3) = x² / 0.1 Solving for x: x = √(1.35 x 10^(-3) x 0.1) ≈ 0.00367 M So, the equilibrium concentration of H3O+ is approximately 0.00367 M. #b) Negligible Dissociated Acid?#

Comparing Concentrations

Let's compare the dissociated and undissociated concentrations: Dissociated acid (H3O+): 0.00367 M Undissociated acid (CICH2COOH): 0.1 - 0.00367 ≈ 0.0963 M Since the dissociated acid concentration is much smaller than the undissociated acid concentration, we can assume that the dissociated acid is negligible with respect to the undissociated acid. #c) Comparison with 1.0 M Acetic Acid#

Calculating Hydronium Concentration in Acetic Acid Solution

We are given that the Ka of acetic acid is 1.8 x 10^(-5). Using the equilibrium expression and the 1.0 M initial concentration, we can calculate the H3O+ concentration in the acetic acid solution: For acetic acid solution: Ka = [H3O+][CH3COO-] / [CH3COOH] 1.8 x 10^(-5) = x² / (1 - x) Assuming x is small compared to 1: 1.8 x 10^(-5) = x² / 1 Solving for x (H3O+ concentration in acetic acid solution): x = √(1.8 x 10^(-5)) ≈ 0.00424 M

Comparing H3O+ Concentrations

Now we compare the H3O+ concentrations in the monochloroacetic acid and acetic acid solutions: H3O+ in monochloroacetic acid: 0.00367 M H3O+ in acetic acid: 0.00424 M To find the degree to which the monochloroacetic acid solution is more acidic, we can find the ratio of their H3O+ concentrations: More acidic degree = (H3O+ in monochloroacetic acid) / (H3O+ in acetic acid) = 0.00367 / 0.00424 ≈ 0.865 So, the 0.1 M monochloroacetic acid solution is approximately 0.865 times as acidic as a 1.0 M acetic acid solution, which means it is less acidic.

Key concepts

Chemical Equilibrium

In the world of chemistry, chemical equilibrium represents a state where the rate of the forward reaction equals the rate of the reverse reaction. This doesn't mean that the reactants and products are equal in concentration, but that their concentrations have stabilized at a fixed ratio, unchanging over time.

For acid dissociation reactions, such as that of monochloroacetic acid in water, equilibrium is described by the acid dissociation constant (\r\(K_a\)), which is a quantifiable measure of the strength of an acid in solution. It signifies the extent to which an acid can donate protons to water, forming hydronium ions (\r\(H_3O^{+}\)). When dealing with weak acids like monochloroacetic acid, we typically make the assumption that the dissociated components are in small quantity compared to the original acid concentration, allowing for simplifications in calculations, as seen in our exercise where the \r\(x\) value was considered negligible relative to the starting concentration.

Monochloroacetic Acid

Monochloroacetic acid (\r\(ClCH_2COOH\)) is a chlorinated derivative of acetic acid and belongs to the class of carboxylic acids. In an aqueous solution, this compound can donate a proton to water, creating \r\(ClCH_2COO^{-}\) (monochloroacetate ion) and \r\(H_3O^{+}\) (hydronium ion). This behavior is a typical acid-base reaction, leading to a chemical equilibrium between the reactants and the products.

The \r\(K_a\) value is a crucial parameter in determining the acid strength, and for monochloroacetic acid, it is relatively higher than that of acetic acid, suggesting that it is a stronger acid. When calculating the degree of dissociation, we use the initial concentration and the \r\(K_a\) value to find the equilibrium concentration of the dissociated ions. Our problem highlights this process, emphasizing that although the \r\(K_a\) implies a stronger acidic nature, its lesser magnitude of ionization relative to a higher concentration of acetic acid resulted in monochloroacetic acid being less acidic.

Acid-Base Chemistry

Acid-base chemistry is a fundamental concept in chemistry that deals with the transfer of protons between species. Acids are proton donors and bases are proton acceptors. The strength of an acid or a base is typically gauged by their dissociation in water, which involves breaking of chemical bonds and the formation of new ones until an equilibrium state is reached.

In the context of our exercise, understanding acid strengths was crucial for interpreting the comparative acidity of monochloroacetic acid to acetic acid. The strength of an acid is often inferred from its \r\(K_a\) value; a higher \r\(K_a\) indicates a stronger acid. As we've seen, although the \r\(K_a\) values show monochloroacetic acid to be stronger than acetic acid, the actual concentrations of hydronium ions in solution provided the definitive measure of relative acidity, showing that a more dilute solution of a stronger acid can be less acidic than a more concentrated solution of a weaker acid.