Question

Acetylene has an acid ionization constant \(\left(\mathrm{K}_{\mathrm{A}}\right)\) of \(\sim 10^{-22}\). (a) Calculate the concentration of acetylide ion expected to be present in a \(14 \mathrm{M}\) solution of potassium hydroxide that is \(0.01 \mathrm{M}\) in acetylene (assuming ideal solutions). (b) Outline a practical method (or methods) that you think might be suitable to determine an approximate experimental value of \(\mathrm{K}_{\mathrm{A}}\) for acetylene, remembering that water has \(\mathrm{K}_{\mathrm{A}}\) of about \(10^{-14}\). (c) Would you expect \(\mathrm{H}-\mathrm{C} \equiv \mathrm{N}\) to be a stronger acid than \(\mathrm{H}-\mathrm{C} \equiv \mathrm{C}-\mathrm{H}\) ? Why?

Short answer

(a) The concentration of acetylide ions in the solution is approximately \(10^{-24} M\). (b) Possible methods to determine the experimental value of Ka for acetylene include potentiometric titration and spectrophotometry. These methods may need to be adapted or combined due to the low Ka value of acetylene. (c) H-C≡N (hydrogen cyanide) is likely to be a stronger acid than H-C≡C-H (acetylene) because its conjugate base (cyanide ion) is more stabilized than the acetylide ion.

Step-by-step solution

(a) Calculate the concentration of acetylide ion)

To solve this problem, we first need to write the equilibrium expression for the ionization of acetylene in the presence of potassium hydroxide: \(HC \equiv CH + KOH \rightleftharpoons HC \equiv CK^- + H_2O\) From the given Ka, we know that: \(Ka \approx 10^{-22} = \frac{[HC \equiv CK^-]}{[HC \equiv CH]}\) Given that the initial concentration of acetylene is 0.01 M, we can represent the change in concentration at equilibrium as follows: - Decrease in [acetylene] = +x - Increase in [acetylide ion] = -x Therefore, at equilibrium: - [acetylene] = 0.01-x - [acetylide ion] = x Now, we can plug these values into the Ka expression and solve for x (the concentration of acetylide ion): \(10^{-22}=\frac{x}{0.01-x}\) Assuming that x is much smaller than 0.01, we can approximate the equation to: \(10^{-22}=\frac{x}{0.01}\) Solving for x, we get: \(x \approx 10^{-24}\) So, the concentration of acetylide ions in the solution is approximately \(10^{-24} M\).

(b) Suggest practical methods to determine Ka)

One possible method to determine the experimental value of Ka for acetylene would be to use a technique called "potentiometric titration." This involves measuring the pH change during the titration of a weak acid (acetylene in this case) with a strong base (for example, sodium hydroxide). By measuring the change in potential (voltage) as the base is added to the acid, we can plot a titration curve and find the half-equivalence point. At the half-equivalence point, the pH of the solution equals the pKa of the weak acid (in our case, acetylene). Another possible method is to use "spectrophotometry." This involves measuring the absorption of light at various wavelengths by the acetylene solution at different concentrations. By constructing a calibration curve, we can determine the concentration of acetylide ions at equilibrium, and thereby calculate the Ka value for acetylene. These methods may need to be adapted or combined to accurately measure the very low Ka value of acetylene (since water has a Ka of around \(10^{-14}\)).

(c) Compare the acidity of H-C≡N and H-C≡C-H)

We are asked to compare the acidity of two molecules: H-C≡N (hydrogen cyanide) and H-C≡C-H (acetylene). The acidity of a molecule depends on the stability of the conjugate base that is formed when the molecule loses a proton (H+). In general, a more stable conjugate base indicates a stronger acid. Let's examine the conjugate bases of both molecules: - H-C≡N: The conjugate base is C≡N- (cyanide ion). The negative charge is distributed across two electronegative atoms (C and N), which provides a high degree of stabilization. - H-C≡C-H: The conjugate base is C≡C-H- (acetylide ion). The negative charge is localized on a less electronegative carbon atom. Comparing the two conjugate bases, we can conclude that the cyanide ion is more stabilized than the acetylide ion. Therefore, H-C≡N (hydrogen cyanide) is likely to be a stronger acid than H-C≡C-H (acetylene).

Key concepts

Acid Ionization Constant

Understanding the acid ionization constant, or Ka, is crucial when studying the acidity of different substances. It represents the strength of an acid in solution and is defined as the equilibrium constant for the ionization of the acid. This constant is particularly important for weak acids like acetylene, which partially ionize in solution. For acetylene, the Ka is approximately \(10^{-22}\), signifying it's a rather weak acid with a low tendency to donate its protons to form acetylide ions.

When assessing acidity, a low Ka value indicates a weak acid that doesn't ionize significantly in solution, meaning the concentration of hydrogen ions, H+, generated is also low. In contrast, a higher Ka value corresponds to a strong acid that fully dissociates in solution. The value of Ka is often expressed in terms of pKa, which is the negative logarithm of Ka, and provides a more convenient way to compare acid strengths — the lower the pKa, the stronger the acid.

Concentration of Acetylide Ion

The concentration of acetylide ion in a solution is a direct reflection of an acid's ionization behavior. For acetylene, this concentration is derived from its reaction with a strong base like potassium hydroxide. Using the acid ionization constant (Ka), we can predict the concentration of the acetylide ion at equilibrium. For acetylene reacting with KOH, the resulting concentration of acetylide ions is found to be negligibly small, around \(10^{-24} M\).

This calculation assumes that the concentration of acetylene decreases by a negligible amount compared to its initial concentration and therefore can be approximated without significantly affecting the result. Knowing the concentration of the acetylide ion is crucial for various analytic procedures and provides insight into the extent of the reaction between acetylene and the hydroxide ion.

Potentiometric Titration

Potentiometric titration is a method that can be used to determine the acid ionization constant of a weak acid like acetylene. This analytical technique involves adding a strong base, such as sodium hydroxide, to the acid solution and measuring the pH at various points throughout. One pays close attention to the half-equivalence point, where the number of moles of acid equals the moles of base, thus neutralizing half of the acid.

At this point, the observed pH is equal to the pKa of the weak acid, which is another representation of the strength of the acid. Potentiometric titration delivers high precision in determining the pKa and requires careful calibration of the pH electrode and meticulous procedural execution. Despite the minute concentration of acetylene's ionization, with the right experimental setup and conditions, even such low Ka values can be approached and calculated.

Spectrophotometry

Spectrophotometry is another powerful tool for characterizing the ionization of acids like acetylene. This technique involves measuring the intensity of light absorbed by a solution at various wavelengths. The absorbance is related to the concentration of the absorbing species in the solution, according to Beer-Lambert's law. For weak acids like acetylene that produce a conjugate base capable of absorbing light, spectrophotometry can be used to quantify the concentration of the acetylide ion.

By establishing a calibration curve that correlates absorbance with known concentrations of the acetylide ion, we can deduce the concentration in an unknown sample and thus determine the Ka. This method can be particularly effective when the absorbance changes are significant and can be detected by the instrument, even for species present in minuscule concentrations. Both potentiometric titration and spectrophotometry provide a means of gauging the true acid ionization constant of a compound, making them invaluable in the field of analytical chemistry.