Final answer:
To calculate the pH of a 0.670 M solution of Ca(NO₂)₂, we can use the expression pH = -log[H+]. By considering the hydrolysis reaction of NO₂¯ and the given equilibrium constant (Ka), we can calculate the concentration of H+ ions. Finally, we can apply the pH expression to find the pH of the solution.
Step-by-step explanation:
The pH of a solution can be calculated using the expression pH = -log[H+]. In this case, we need to find the concentration of H+ ions in a 0.670 M solution of Ca(NO₂)₂. The compound Ca(NO₂)₂ dissociates into Ca²+ ions and NO₂¯ ions. Since NO₂¯ is the conjugate base of a weak acid, HNO₂, we can assume that it acts as a weak base. Therefore, we can use the expression for the hydrolysis of a weak base to find the concentration of H+ ions. The hydrolysis reaction is: NO₂¯ + H₂O ⟷ HNO₂ + OH¯. The equilibrium expression for this reaction is given by Kw/Ka = [H+][OH¯]/[NO₂¯].
Using the given equilibrium constant (Ka) for HNO₂ as 4.5 × 10⁻⁴, we can substitute the values into the equation and solve for [H+]. Since [OH¯] is negligible compared to [H+], we can omit it from the equation. We can calculate [NO₂¯] as the concentration of Ca(NO₂)₂ (0.670 M) multiplied by the number of NO₂¯ ions per Ca(NO₂)₂ unit, which is 2. Finally, we can plug in the known values and solve for [H+], giving us [H+] = (√(Kw/Ka)) * √([NO₂¯]).
Once we have the value for [H+], we can calculate the pH using the expression pH = -log[H+].