Question

A chemistry student wants to buffer a solution with a pH of 4.5. The student adds 0.1 mol of a weak acid buffer to 0.1 mol of a conjugate base. Taking the pKa value of the buffer into consideration, determine how much stronger an acid in the same buffer system would need to be added to the solution to shift the pH from 4.5 to 4.0, assuming temperature and pressure are constant.

Answer 1

To solve this problem, we will use the Henderson-Hasselbalch equation:pH = pKa + log  [A-]/[HA] where pH is the desired pH of the solution, pKa is the acid dissociation constant of the weak acid, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid.First, we need to find the pKa value of the weak acid. Since the initial pH is 4.5 and the concentrations of the weak acid and its conjugate base are equal  0.1 mol each , we can write:4.5 = pKa + log  0.1/0.1 4.5 = pKa + log  1 4.5 = pKaNow, we want to find the new concentrations of the weak acid and its conjugate base needed to achieve a pH of 4.0. We can write the Henderson-Hasselbalch equation for the new pH:4.0 = 4.5 + log  [A-]/[HA] -0.5 = log  [A-]/[HA] To find the ratio of [A-]/[HA], we can use the inverse log function  10^x :10^-0.5  = [A-]/[HA]0.316 = [A-]/[HA]Since we want to add a stronger acid to the solution, we will increase the concentration of the weak acid [HA] and decrease the concentration of the conjugate base [A-]. Let's assume we add x mol of the stronger acid to the solution:[HA] = 0.1 + x[A-] = 0.1 - xNow, we can substitute these values into the equation:0.316 =  0.1 - x  /  0.1 + x To solve for x, we can multiply both sides by  0.1 + x :0.316  0.1 + x  = 0.1 - x0.0316 + 0.316x = 0.1 - xNow, we can add x to both sides and subtract 0.0316 from both sides:1.316x = 0.0684Finally, we can divide both sides by 1.316 to find the value of x:x = 0.0684 / 1.316x  0.052 molTherefore, the student would need to add approximately 0.052 mol of a stronger acid to the solution to shift the pH from 4.5 to 4.0.