Final answer:
To calculate the pH of a solution of ethylammonium bromide, we need to consider the equilibrium between the weak base ethylamine and its conjugate acid ethylammonium ion. The pKb value of ethylamine is 3.19. Using the percent ionization, we can calculate the concentration of hydroxide ion and then convert it to pH.
Step-by-step explanation:
To calculate the pH of a solution of ethylammonium bromide, we need to consider the equilibrium between the weak base ethylamine and its conjugate acid ethylammonium ion. The pKb value of ethylamine is given as 3.19. To calculate the pH, we need to find the concentration of hydroxide ion, which is equal to the concentration of ethylamine that ionizes. Since ethylamine is a weak base, we can assume that the extent of ionization is small. Therefore, we can use the percent ionization given in the question, which is 5.4%, to calculate the concentration of ethylamine that ionizes.
We can assume that the concentration of ethylamine that ionizes is equal to the initial concentration of ethylamine multiplied by the percent ionization. In this case, the initial concentration of ethylammonium bromide is 0.49 M. Therefore, the concentration of ethylamine that ionizes is 0.049 x 0.054 = 0.002646 M.
To convert this concentration to the concentration of hydroxide ion, we can assume that for every molecule of ethylamine that ionizes, one hydroxide ion is produced. Therefore, the concentration of hydroxide ion is also 0.002646 M. To calculate the pH, we can use the equation: pH = 14 - pOH. Since the concentration of hydroxide ion is given, we can calculate the pOH as -log[OH-] = -log(0.002646) = 2.579. Therefore, the pH is 14 - 2.579 = 11.421.