![a) What is the change in pH when [OH-] increases by a factor of 10? b) What is the change in [H3O+] when the pH decreases by 3 units?](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1778234477485-e7758970e3916205.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 determine the changes in pH and [H_3O^+]: a) What is the change in pH when [OH^-] increases by a factor of 10? Step 1: Define the initial and final concentrations of [OH^-]. Let the initial hydroxide ion concentration be [OH^-]_1. The final hydroxide ion concentration is [OH^-]_2 = 10 × [OH^-]_1. Step 2: Relate pOH to [OH^-]. The pOH is defined as pOH = -[OH^-]. Initial pOH: pOH_1 = -[OH^-]_1 Final pOH: pOH_2 = -(10 × [OH^-]_1) = -( 10 + [OH^-]_1) = -1 - [OH^-]_1 = pOH_1 - 1. So, the pOH decreases by 1 unit. Step 3: Relate pH to pOH. At 25^ C, pH + pOH = 14. Initial pH: pH_1 = 14 - pOH_1 Final pH: pH_2 = 14 - pOH_2 = 14 - (pOH_1 - 1) = 14 - pOH_1 + 1 = pH_1 + 1. Step 4: Calculate the change in pH. The change in pH is pH = pH_2 - pH_1 = (pH_1 + 1) - pH_1 = 1. The pH increases by 1 unit. The change in pH is: pH increases by 1 unit b) What is the change in [H_3O^+] when the pH decreases by 3 units? Step 1: Define the initial and final pH values. Let the initial pH be pH_1. The final pH is pH_2 = pH_1 - 3. Step 2: Relate [H_3O^+] to pH. The hydronium ion concentration is related to pH by the formula [H_3O^+] = 10^-pH. Initial [H_3O^+]: [H_3O^+]_1 = 10^-pH_1 Final [H_3O^+]: [H_3O^+]_2 = 10^-pH_2 = 10^-(pH_1 - 3) Step 3: Simplify the expression for the final [H_3O^+]. [H_3O^+]_2 = 10^-pH_1 + 3 = 10^-pH_1 × 10^3 Substitute [H_3O^+]_1 = 10^-pH_1: [H_3O^+]_2 = [H_3O^+]_1 × 1000 The change in [H_3O^+] is: increases by a factor of 1000 3 done, 2 left today. You're making progress.