Question

What volume of 0.1M HCl solution should be added to a 500mL of 0.5M HCOOH solution in order to prepare an acid solution of pH =1.5. Ka of formic acid is 2×10−4

at 298K?

I am not sure how to proceed with this question. Iam also confused how equilibrium reaction will be

I guessed it would be HCOOH+HCl →salt
Let V be volume of HCl. At t=equilibrium, salt]=0.1V0.25−0.1V

Now, pH=pKa+log0.1V(0.25−0.1V)⇒V=2.5L
But answer is V=0.208L

Am I completely wrong somewhere? Can someone give tell me how to proceed?

NOTE:I am not asking full solution.
Just telling how to proceed is fine.

Answer 1

The problem requires using the Henderson-Hasselbalch equation to find the volume of 0.1M HCl necessary to adjust the pH of a 0.5M HCOOH solution to 1.5, considering the neutralization reaction between HCl and HCOOH and the resulting buffer solution.

Step-by-step explanation:

The question relates to an acid-base titration problem where a student is asked to calculate the volume of 0.1M HCl solution to add to a 500mL of 0.5M HCOOH (formic acid) solution to achieve a solution with a pH of 1.5.

This involves understanding the concept of pH calculations, acid dissociation constants (Ka), and buffer solutions. Since HCl is a strong acid, it will dissociate completely, neutralizing an equivalent amount of the weak acid HCOOH and forming its conjugate base, HCOO-.

The Henderson-Hasselbalch equation should be used to relate the pH, pKa, and the ratios of concentrations of the conjugate acid-base pair (HCOOH and HCOO-).

The incorrect assumption was made that the reaction proceeds to form a salt, instead of considering the neutralization of HCOOH by HCl and the resulting buffer composition.

Correcting the equation for the pH calculation and considering the neutralization of formic acid by HCl, one can solve for the correct volume of HCl needed to reach the desired pH.