Question

A \(0.100 M\) solution of chloroacetic acid \(\left(\mathrm{ClCH}_{2} \mathrm{COOH}\right)\) is \(11.0 \%\) ionized. Using this information, calculate \(\left[\mathrm{ClCH}_{2} \mathrm{COO}^{-}\right],\left[\mathrm{H}^{+}\right],\) \(\left[\mathrm{ClCH}_{2} \mathrm{COOH}\right],\) and \(K_{a}\) for chloroacetic acid.

Short answer

In a $0.100 M$ chloroacetic acid solution with $11.0\%$ ionization, the concentrations of the different species are as follows: - Concentration of $\mathrm{ClCH}_{2} \mathrm{COO}^{-}$: $0.0110 M$ - Concentration of $\mathrm{H}^{+}$: $0.0110 M$ - Concentration of $\mathrm{ClCH}_{2} \mathrm{COOH}$: $0.0890 M$ The acid dissociation constant, $K_{a}$, for chloroacetic acid is $1.35 \times 10^{-3}$.

Step-by-step solution

Calculate the initial concentrations of the species

A 0.100 M solution of chloroacetic acid (ClCH2COOH) is 11.0% ionized. To find the concentrations of ClCH2COO-, H+, and ClCH2COOH in the solution, multiply the initial concentration of the chloroacetic acid by the percentage of ionization. Initial concentration of ClCH2COOH = 0.100 M Percentage of ionization = 11.0% = 0.110

Calculate the concentrations of ClCH2COO- and H+

For every mole of chloroacetic acid that ionizes, one mole of ClCH2COO- and one mole of H+ are formed. So, we can calculate the concentration of ClCH2COO- and H+ by multiplying the initial concentration of the acid by the percentage of ionization. Concentration of ClCH2COO- = Initial concentration × Percentage of ionization Concentration of ClCH2COO- = 0.100 M × 0.110 = 0.0110 M Concentration of H+ = Initial concentration × Percentage of ionization Concentration of H+ = 0.100 M × 0.110 = 0.0110 M

Calculate the concentration of ClCH2COOH

Since the solution is 11.0% ionized, 89.0% of the chloroacetic acid remains unionized. Calculate the concentration of ClCH2COOH by multiplying its initial concentration by the remaining percentage. Remaining concentration of ClCH2COOH = Initial concentration × (1 - Percentage of ionization) Remaining concentration of ClCH2COOH = 0.100 M × (1 - 0.110) = 0.100 M × 0.890 = 0.0890 M

Calculate Ka

Using the equilibrium concentrations of ClCH2COOH, ClCH2COO-, and H+, we can now determine the acid dissociation constant (Ka) using the following equilibrium expression: \(K_{a} = \frac{[\mathrm{ClCH}_{2} \mathrm{COO}^{-}][\mathrm{H}^{+}]}{[\mathrm{ClCH}_{2} \mathrm{COOH}]} \) Substituting the equilibrium concentrations and solving for Ka: \(K_{a} = \frac{(0.0110)(0.0110)}{(0.0890)} = 1.35 \times 10^{-3}\) #Conclusion# Concentration of ClCH2COO- = 0.0110 M Concentration of H+ = 0.0110 M Concentration of ClCH2COOH = 0.0890 M Ka for chloroacetic acid = 1.35 × 10⁻³

Key concepts

Chloroacetic Acid

Chloroacetic acid, represented as \(\mathrm{ClCH}_2\mathrm{COOH}\), is a derivative of acetic acid where one hydrogen atom is replaced by a chlorine atom. This substitution results in a molecule that has differing properties compared to regular acetic acid. The chlorine atom, being more electronegative than hydrogen, increases the molecule’s ability to donate protons, thus making chloroacetic acid a stronger acid than its parent compound. Understanding chloroacetic acid is vital in many industrial and chemical processes, where it is often used as a building block for more complex organic compounds. Its properties largely stem from how it interacts with water, notable in its ability to release hydrogen ions.

Ionization

Ionization refers to the process by which an atom or molecule acquires a positive or negative charge by gaining or losing electrons to form ions. In the context of acids in solution, like chloroacetic acid, ionization is the process where the acid donates protons to water molecules, thereby forming positive hydrogen ions \(\mathrm{H}^+\) and the corresponding negative base ions, in this case, chloroacetate ions \(\mathrm{ClCH}_2\mathrm{COO}^-\). Several factors affect the degree of ionization, which can include:

• The acid's intrinsic properties, such as strength and concentration.
• The presence of other ions in solution which can impact the equilibrium through the common ion effect.

Understanding ionization is crucial as it allows us to predict the behavior of acids in solutions, and to calculate important parameters, such as the concentration of ions formed when the acid is dissolved.

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction and its reverse reaction proceed at the same rate. In the case of chloroacetic acid in water, equilibrium is reached when the forward reaction (ionization of chloroacetic acid) equals the backward reaction (reforming of chloroacetic acid from ions). At this state, the concentrations of products and reactants remain constant, though they are not necessarily equal. It's important to note that chemical equilibrium is dynamic, meaning the reactions continue to occur, yet there is no net change in the concentration of reactants and products. This principle forms the basis for calculating the acid dissociation constant, \(K_a\), which quantifies the extent of ionization and provides insights into the acid strength.

Molar Concentration

Molar concentration, often denoted by \(M\) or \([ ]\), describes the amount of solute (substance being dissolved) present in a unit volume of solution. It is expressed in moles per liter (mol/L). Calculating molar concentration is a basic yet fundamental concept, which is necessary for determining how much of a substance interacts in a chemical reaction.In the case of chloroacetic acid, the initial molar concentration is given before any ionization occurs. As ionization proceeds, percentages of the acid dissociate, forming new species, such as hydrogen and chloroacetate ions. By determining the molar concentration of each species at equilibrium, meaningful conclusions can be drawn about the solution's behavior, and important constants like the acid dissociation constant, \(K_a\), can be calculated. This provides greater insight into the reaction dynamics and allows for predictions of chemical behavior under different conditions.