Question

The concentration of acetic acid in pyrolysis oil varies between 1 and the \(8 \mathrm{wt} \%\). HAc is the most abundant acid in the oil. Can you explain the low (2-3) but hardly varying \(\mathrm{pH}\) of the oil?

Short answer

Question: Explain the low but hardly varying pH of pyrolysis oil, given that the concentration of acetic acid in it varies between 1 and 8 wt%. Answer: The pH of pyrolysis oil depends on the square root of the product of the equilibrium constant (Ka) for acetic acid and the initial concentration of acetic acid. Due to the small Ka value of acetic acid, the overall pH is low. Additionally, small changes in the concentration of acetic acid have little effect on the pH due to the square root relationship. This leads to a low but hardly varying pH of pyrolysis oil.

Step-by-step solution

Write down the equilibrium constant (Ka) for acetic acid

Acetic acid is a weak acid and its dissociation in water can be written as: HAc \(\rightleftharpoons\) H\(^+\) + Ac\(^-\) The equilibrium constant, Ka, for this reaction is given by: Ka = \(\frac{[\mathrm{H}^+][\mathrm{Ac}^-]}{[\mathrm{HAc}]}\)

Use the Ka value to determine the concentration of hydrogen ions (H\(^+\))

The Ka value for acetic acid is around \(1.75 \times 10^{-5}\). To determine the concentration of hydrogen ions (H\(^+\)), we can use the approximation that the concentration of HAc decreases by x, while the concentration of H\(^+\) and Ac\(^-\) increase by x. Then: Ka = \(\frac{(x)(x)}{([\mathrm{HAc}]_0 - x)}\) Where \([\mathrm{HAc}]_0\) is the initial concentration of HAc, and x is the concentration of H\(^+\) and Ac\(^-\) at equilibrium.

Simplify the equation and determine the relationship between the concentration of acetic acid and the pH of the oil

In most cases, x is relatively small compared to the initial concentration of acetic acid (HAc), so we can approximate that \([\mathrm{HAc}]_0\) - x \(\approx [\mathrm{HAc}]_0\). This simplifies the equation: Ka \(\approx \frac{x^2}{[\mathrm{HAc}]_0}\) Now, we can solve for x, which represents the concentration of H\(^+\) ions: x \(\approx \sqrt{Ka \times [\mathrm{HAc}]_0}\)

Calculate the pH of the solution

The pH of a solution is defined as the negative logarithm of the hydrogen ion concentration: pH = \(- \log_{10} [\mathrm{H}^+]\) Using the relationship found in step 3, we have: pH \(\approx -\log_{10} \sqrt{Ka \times [\mathrm{HAc}]_0}\)

Explain the low but hardly varying pH of pyrolysis oil

As we can see from the equation found in step 4, the pH of the oil depends on the square root of the product of the equilibrium constant (Ka) and the initial concentration of acetic acid. The value of Ka for acetic acid is very small, thus the overall pH value will be low. Moreover, since the pH value is affected by the square root of the product, small changes in the concentration of acetic acid will not have a significant impact on the pH of the oil. This explains the low but hardly varying pH of pyrolysis oil.

Key concepts

Acetic Acid Equilibrium

The chemistry of acetic acid in pyrolysis oil involves an equilibrium between the non-dissociated acetic acid molecules (HAc) and their dissociation products: hydrogen ions (H\(^+\)) and acetate ions (Ac\(^-\)). This equilibrium can be represented as follows:

\[ \text{HAc} \rightleftharpoons \text{H}^+ + \text{Ac}^- \]
The concept of equilibrium here means that the forward and backward reactions happen at the same rate once equilibrium is established, leading to a constant concentration ratio of the involved species.

In a dynamic system like this, the position of the equilibrium will determine the concentrations of each species in the mixture. This in turn influences other properties of the solution, such as pH. Understanding this equilibrium helps to explain how and why even small amounts of acetic acid can lead to significant changes in hydrogen ion concentration and thus affect the overall acidity of the pyrolysis oil.

Dissociation Constant (Ka)

The dissociation constant, Ka, is a crucial parameter in understanding the behavior of weak acids like acetic acid. It is a measure of the strength of an acid in solution, indicating how well the acid dissociates into its ions in water.

The expression for the dissociation constant of acetic acid is:\[K_a = \frac{[\text{H}^+][\text{Ac}^-]}{[\text{HAc}]} \]
This expression relates the concentrations of the products (hydrogen and acetate ions) and the reactant (acetic acid) when equilibrium is reached in a solution. For acetic acid, the Ka value is typically around \(1.75 \times 10^{-5}\).

This small Ka value suggests that only a small fraction of acetic acid molecules dissociate in water. Knowing the Ka allows us to estimate the concentration of hydrogen ions in solution, which is a significant step towards understanding the solution's pH.

Hydrogen Ion Concentration

In a solution containing acetic acid, determining the hydrogen ion concentration is essential for calculating the pH. The approximation used for weak acids considers that the concentration of hydrogen ions is equivalent to the amount of dissociated acetic acid. This is given by:\[x \approx \sqrt{K_a \times [\text{HAc}]_0} \]
Here, \([\text{HAc}]_0\) represents the initial concentration of acetic acid, and \(x\) is the concentration of hydrogen ions at equilibrium. This equation helps us conclude that the hydrogen ion concentration varies with the initial concentration of acetic acid and the Ka value.

Because x is generally small compared to \([\text{HAc}]_0\), we use the simplification in calculations, which helps in predicting the pH of the solution with reasonable accuracy for weak acids like acetic acid in pyrolysis oil.

pH Calculation

The pH of a solution is a measure of its acidity, specifically the concentration of hydrogen ions. It is calculated using the formula:

\[pH = -\log_{10} [\text{H}^+]\]
This equation implies that the pH is inversely proportional to the hydrogen ion concentration—higher concentrations lower the pH, indicating a more acidic solution.

In the case of pyrolysis oil, the pH can be determined using the hydrogen ion concentration derived from the dissociation constant and initial acetic acid concentration: \[pH \approx -\log_{10} \sqrt{K_a \times [\text{HAc}]_0}\]
This explains why pyrolysis oil, with its typical acetic acid concentration, maintains a low and stable pH. Even minor changes in acetic acid concentration do not significantly affect the pH, due to the nature of the square root dependency in the pH equation.