Question

What are the major species present in 0.250 $M$ solutions of each of the following acids? Calculate the $\mathrm{pH}$ of each of these solutions. a. ${\mathrm{HOC}}_6{\mathrm{H}}_5$ b. HCN

Short answer

The major species in the 0.250 M solution of ${\mathrm{HOC}}_6{\mathrm{H}}_5$ are ${\mathrm{HOC}}_6{\mathrm{H}}_5$, ${\mathrm{H}}^{+}$, ${\mathrm{OC}}_6{\mathrm{H}}_5^{-}$, and the pH is approximately 0.60. For the 0.250 M solution of HCN, the major species are HCN, ${\mathrm{H}}^{+}$, ${\mathrm{CN}}^{-}$, and the pH is approximately 0.60.

Step-by-step solution

Write the chemical equation for ionization

When an acid reacts with water, it donates an H+ ion to the water molecule to form a hydronium ion (H3O+). The general equation is: $$\mathrm{HA}\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{A}}^{-}$$ For our problem: $${\mathrm{HOC}}_6{\mathrm{H}}_5(aq)\rightleftharpoons {\mathrm{H}}^{+}(aq)+{\mathrm{OC}}_6{\mathrm{H}}_5^{-}(aq)$$

Identify the acid dissociation constant (Ka)

Referring to the available reference data, we can find that in case of ${\mathrm{HOC}}_6{\mathrm{H}}_5$ we have the acid dissociation constant $K_a=1.6\times {10}^{-5}$.

Calculate the equilibrium concentrations using the ICE table or approximation method

Since the dissociation constant $K_a$ is quite small, we can use the approximation method by assuming the change in the concentration of the major species is negligible. Thus, the concentration of H+ will be approximately equal to the concentration of ${\mathrm{HOC}}_6{\mathrm{H}}_5$, which is $0.250$ $\mathrm{M}$.

Calculate the pH of the solution

The pH is determined using the formula pH = $-\log \left[{\mathrm{H}}^{+}\right]$. So, we have: $$pH=-\log \left(0.250\right)$$ $$pH\approx 0.60$$ The major species in the 0.250 M solution of ${\mathrm{HOC}}_6{\mathrm{H}}_5$ are ${\mathrm{HOC}}_6{\mathrm{H}}_5$, ${\mathrm{H}}^{+}$, ${\mathrm{OC}}_6{\mathrm{H}}_5^{-}$, and the pH is approximately 0.60. #b. HCN#

Write the chemical equation for ionization

The equation for the ionization of HCN is: $$\mathrm{HCN}(aq)\rightleftharpoons {\mathrm{H}}^{+}(aq)+{\mathrm{CN}}^{-}(aq)$$

Identify the acid dissociation constant (Ka)

Referring to the available reference data, we can find that for HCN, we have the acid dissociation constant $K_a=4.9\times {10}^{-10}$.

Calculate the equilibrium concentrations using the ICE table or approximation method

Since the dissociation constant $K_a$ is very small, we can use the approximation method by assuming the change in the concentration of the major species is negligible. Thus, the concentration of H+ will be approximately equal to the concentration of HCN, which is $0.250$ $\mathrm{M}$.

Calculate the pH of the solution

The pH is determined using the formula pH = $-\log \left[{\mathrm{H}}^{+}\right]$. So, we have: $$pH=-\log \left(0.250\right)$$ $$pH\approx 0.60$$ The major species in the 0.250 M solution of HCN are HCN, ${\mathrm{H}}^{+}$, ${\mathrm{CN}}^{-}$, and the pH is approximately 0.60.

Key concepts

Chemical Ionization

Chemical ionization is a process where an acid donates a proton (${\mathrm{H}}^{+}$) to a solvent, usually water, to form ions. This concept is essential when studying the behavior of acids and bases in solutions. For the acids discussed in the example, let's consider how ionization occurs.- **Phenol (${\mathrm{HOC}}_6{\mathrm{H}}_5$):** This compound ionizes in water to produce hydronium ions (${\mathrm{H}}_3{\mathrm{O}}^{+}$) and phenoxide ions (${\mathrm{OC}}_6{\mathrm{H}}_5^{-}$).- **Hydrogen cyanide (HCN):** When dissolved in water, it ionizes to form hydronium ions and cyanide ions (${\mathrm{CN}}^{-}$).Understanding the ionization reaction helps predict the concentrations of the various species in solution, which are critical for further calculations such as pH. The general form of the ionization equation is:$$\mathrm{HA}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{A}}^{-}.$$This simple representation shows the dissociation of an acid ($\mathrm{HA}$) in water.

pH Calculation

Calculating the pH of an acidic solution is a fundamental skill in chemistry. pH is a measure of acidity and is calculated using the concentration of hydrogen ions ($[{\mathrm{H}}^{+}]$) in the solution.- **Formula:** The pH is calculated with the formula: $$\text{pH}=-\log ([{\mathrm{H}}^{+}]).$$- **Example Calculation:** For a 0.250 M solution of an acid like phenol, after assuming full ionization, you can calculate $\mathrm{pH}=-\log (0.250)$, getting an approximate pH value of 0.60.The pH scale ranges from 0 to 14, with lower values indicating more acidic solutions. A pH of 0.60 is extremely acidic, reflecting a high concentration of hydrogen ions.

Acid Dissociation Constant

The acid dissociation constant ($K_a$) is a quantitative measure of an acid's strength in solution. It tells us how well an acid can donate its proton to the water.### Understanding $K_a$- **Smaller $K_a$ Values:** These indicate a weaker acid, as less ionization occurs.- **Larger $K_a$ Values:** These suggest a stronger acid, meaning more ionization.For example:- **Phenol:** Has a $K_a=1.6\times {10}^{-5}$, meaning it's a relatively weak acid.- **Hydrogen cyanide:** With $K_a=4.9\times {10}^{-10}$, it is an even weaker acid compared to phenol.Knowing $K_a$ helps in predicting how much of the acid will ionize and is critical for accurate pH calculations and understanding acid behavior in chemical reactions.