What IS the original molarity of a solution of formic acid (HCOOH) whose pH is 3.26 at equilibrium?
The Correct Answer and Explanation is:
To find the original molarity of a solution of formic acid (HCOOH) with a pH of 3.26 at equilibrium, we need to use the acid dissociation constant (Ka) for formic acid and apply the ICE (Initial, Change, Equilibrium) method.
Step 1: Write the dissociation equation
Formic acid is a weak acid and partially ionizes:
HCOOH ⇌ H⁺ + HCOO⁻
Step 2: Use the pH to find H+H⁺H+
pH = 3.26
H+H⁺H+ = 10^(–pH) = 10^(–3.26) ≈ 5.50 × 10⁻⁴ M
Step 3: Use the Ka of formic acid
Ka of formic acid = 1.8 × 10⁻⁴
Let the initial concentration of HCOOH be C
At equilibrium:
- H+H⁺H+ = HCOO−HCOO⁻HCOO− = 5.50 × 10⁻⁴ M
- HCOOHHCOOHHCOOH = C – 5.50 × 10⁻⁴
Using the Ka expression:
Ka = H+H⁺H+HCOO−HCOO⁻HCOO− / HCOOHHCOOHHCOOH
1.8 × 10⁻⁴ = (5.50 × 10⁻⁴)² / (C – 5.50 × 10⁻⁴)
Solve for C:
1.8 × 10⁻⁴ = (3.03 × 10⁻⁷) / (C – 5.50 × 10⁻⁴)
Multiply both sides by (C – 5.50 × 10⁻⁴):
1.8 × 10⁻⁴(C – 5.50 × 10⁻⁴) = 3.03 × 10⁻⁷
Expand the left side:
1.8 × 10⁻⁴C – 9.9 × 10⁻⁸ = 3.03 × 10⁻⁷
Add 9.9 × 10⁻⁸ to both sides:
1.8 × 10⁻⁴C = 3.03 × 10⁻⁷ + 9.9 × 10⁻⁸ = 3.999 × 10⁻⁷
Now divide both sides:
C = (3.999 × 10⁻⁷) / (1.8 × 10⁻⁴) ≈ 2.22 × 10⁻³ M
Final Answer:
The original molarity of formic acid is 0.00222 M
Explanation (300 words):
To determine the original molarity of a formic acid solution with a pH of 3.26, we must understand the relationship between pH, hydrogen ion concentration, and the dissociation behavior of weak acids. The pH value indicates how acidic a solution is and can be converted into the hydrogen ion concentration by using the formula H+H⁺H+ = 10^(–pH). For a pH of 3.26, this gives approximately 5.50 × 10⁻⁴ M.
Formic acid is a weak acid that does not completely ionize in water. It partially dissociates into hydrogen ions and formate ions. The acid dissociation constant (Ka) quantifies how much of the acid dissociates at equilibrium. For formic acid, Ka is 1.8 × 10⁻⁴. Using the ICE method, we let the initial concentration of the acid be C. At equilibrium, the amount that has dissociated is equal to the concentration of hydrogen ions, which is also equal to the concentration of formate ions.
We then plug these values into the Ka expression, solving for C, the initial concentration of the acid. After doing algebraic manipulation, we find that C is equal to 0.00222 M. This means that to produce a pH of 3.26 at equilibrium, the solution must have originally contained formic acid at a concentration of about 2.22 millimoles per liter. This demonstrates how the behavior of weak acids in solution can be quantified through equilibrium chemistry and pH calculations.
