Question

What are the major species present in 0.250\(M\) solutions of each of the following acids? Calculate the pH of each of these solutions. a. \(\mathrm{HNO}_{2}\) b. \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\left(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)\)

Short answer

The major species present and the pH values of the solutions are: a. HNO2 solution: Major species are HNO2, H+, and NO2-. The pH is 2.07. b. CH3CO2H (HC2H3O2) solution: Major species are HC2H3O2, H+, and C2H3O2-. The pH is 2.67.

Step-by-step solution

Write the acid dissociation equation and expressions for Ka

For both acids, the general acid dissociation equation is: \[HA \rightleftharpoons H^+ + A^-\] The expressions for Ka will be: \[K_a = \frac{[H^+][A^-]}{[HA]}\]

Find the Ka values for the given acids

Look up the Ka values for each acid in a table or textbook. The Ka values are: a. HNO2: Ka = 4.5 x 10^-4 b. CH3CO2H (also known as HC2H3O2): Ka = 1.8 x 10^-5

Set up equilibrium expressions

Write the equilibrium expressions for the acid dissociations and Ka using the given initial concentrations: a. HNO2: \[[H^+] = x\] \[[NO_2^-] = x\] \[[HNO_2] = 0.250 - x\] 4.5 x 10^-4 = \(\frac{x^2}{0.250-x}\) b. CH3CO2H (HC2H3O2): \[[H^+] = x\] \[[C_2H_3O_2^-] = x\] \[[HC_2H_3O_2] = 0.250 - x\] 1.8 x 10^-5 = \(\frac{x^2}{0.250-x}\)

Solve for the H+ concentration

In both cases, since Ka is small, we can assume x << 0.250. This simplifies the denominators to 0.250: a. Solving for x in the HNO2 case: 4.5 x 10^-4 = \(\frac{x^2}{0.250}\) x = 0.00849 (approximately) = [H+] b. Solving for x in the CH3CO2H case: 1.8 x 10^-5 = \(\frac{x^2}{0.250}\) x = 0.00212 (approximately) = [H+]

Calculate the pH

Use the formula pH = -log[H+] to calculate the pH of each solution: a. pH (HNO2 solution) = -log(0.00849) = 2.07 b. pH (CH3CO2H solution) = -log(0.00212) = 2.67 The major species present and the pH values of the solutions are: a. HNO2 solution: Major species are HNO2, H+, and NO2-. The pH is 2.07. b. CH3CO2H (HC2H3O2) solution: Major species are HC2H3O2, H+, and C2H3O2-. The pH is 2.67.

Key concepts

pH Calculation

Calculating the pH of an acid solution is an important step in understanding its acidity.
To calculate pH, we use the formula:

Here, \[H^+] \] is the concentration of hydrogen ions in the solution. For example, if you have calculated \[H^+] = 0.00849 M \] for a solution, the pH would be \(-\log(0.00849)\), which is approximately 2.07. This tells us the acidity level.
Lower pH values mean higher acidity. Remember, pH is a logarithmic scale, so each whole number represents a tenfold difference in ion concentration.

Equilibrium Expressions

Equilibrium expressions are a way to write out the balance of chemicals in a reaction.
For an acid dissociating in water, the expression is set up as:

• \[HA \rightleftharpoons H^+ + A^-\]
• \[K_a = \frac{[H^+][A^-]}{[HA]}\]

Here, \[K_a\] is the acid dissociation constant, and \[HA\], \[H^+\], and \[A^-\] represent concentrations of the acid, hydrogen ions, and conjugate base.
Understanding equilibrium helps determine the changes in concentration of each species as the reaction proceeds.

Ka Values

\[K_a\] values are crucial in determining the strength of an acid. It's a constant that reflects the extent to which an acid dissociates in water.
High \[K_a\] values indicate stronger acids because they dissociate more completely. For instance, \[K_a = 4.5 \times 10^{-4}\] for \text{HNO}_2\ indicates a partially dissociating acid.
By using \[K_a\] in calculations like \[(\text{e.g. } \frac{x^2}{0.250-x} = K_a)\]\, we can predict concentrations of different species at equilibrium.

Acid-Base Chemistry

Acid-base chemistry involves understanding how acids and bases interact with water and each other.
An acid donates \[H^+\] ions, and a base accepts them. In a solution like \[\text{HNO}_2\], \[\text{HNO}_2\] donates \[H^+\], forming \[\text{NO}_2^-\].
Recognizing major species, such as the acid, \[H^+\], and the conjugate base, helps us understand reactions in a solution. Acid-base reactions are reversible, and their study involves equilibrium and \[K_a\] values to predict behavior in various conditions.