![Calculate the equilibrium concentration of hydrogen ions, [H^+], from the given pH.](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1775611375998-5eb9c06ec0af89d7.png&w=3840&q=75)
This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Here's how to calculate the initial concentration of the weak acid HA: Step 1: Calculate the equilibrium concentration of hydrogen ions, [H^+], from the given pH. The formula for pH is: pH = -_10[H^+] Rearranging to solve for [H^+]: [H^+] = 10^-pH Given pH = 3.4: [H^+] = 10^-3.4 [H^+] ≈ 3.98 × 10^-4 M Step 2: Write the dissociation equilibrium for the weak acid HA and set up an ICE table. The dissociation of a weak acid HA is: HA(aq) H^+(aq) + A^-(aq) Let C_0 be the initial concentration of HA. | | HA | H^+ | A^- | | :---------- | :----------: | :----------: | :----------: | | Initial (I) | C_0 | 0 | 0 | | Change (C) | -x | +x | +x | | Equilibrium (E) | C_0 - x | x | x | From Step 1, we know that at equilibrium, [H^+] = x = 3.98 × 10^-4 M. Therefore, [A^-] = x = 3.98 × 10^-4 M. Step 3: Write the acid dissociation constant (K_a) expression and substitute the equilibrium concentrations. The K_a expression is: K_a = ([H^+][A^-])/([HA]) Substitute the equilibrium concentrations from the ICE table: K_a = ((x)(x))/(C_0 - x) = (x^2)/(C_0 - x) Given K_a = 1.7 × 10^-5 and x = 3.98 × 10^-4 M: 1.7 × 10^-5 = (3.98 × 10^-4)^2C_0 - (3.98 × 10^-4) Step 4: Solve for the initial concentration, C_0. Rearrange the equation to solve for C_0: K_a (C_0 - x) = x^2 K_a C_0 - K_a x = x^2 K_a C_0 = x^2 + K_a x C_0 = (x^2 + K_a x)/(K_a) C_0 = (x^2)/(K_a) + x Substitute the values: C_0 = (3.98 × 10^-4)^21.7 × 10^-5 + (3.98 × 10^-4) C_0 = 1.58404 × 10^-71.7 × 10^-5 + 3.98 × 10^-4 C_0 = 0.00931788 + 0.000398 C_0 = 0.00971588 M Rounding to two significant figures (based on the given pH and K_a values): C_0 ≈ 0.0097 M The initial concentration of the weak acid HA is 0.0097 M.