What is the concentration of citric acid in Sprite given its pH?

The pH of flat Sprite is usually around 4.17, which gives an H⁺ concentration in the beverage of 6.76 x 10^-5 M. Citric acid, the main component of Sprite, is a triprotic acid. Given this data, we can calculate the concentration of citric acid in Sprite.

First, let’s understand what triprotic means. A triprotic acid can donate three protons (H⁺ ions) per molecule. Citric acid (C₆H₈O₇) is a weak triprotic acid, and its dissociation can be represented in three steps:

1. C₆H₈O₇ ⇌ C₆H₇O₇^– + H⁺

2. C₆H₇O₇^– ⇌ C₆H₆O₇^2- + H⁺

3. C₆H₆O₇^2- ⇌ C₆H₅O₇^3- + H⁺

Given the pH of 4.17, the concentration of H⁺ ions is 6.76 x 10^-5 M. Since citric acid is triprotic, we can assume that each molecule of citric acid contributes three H⁺ ions. Therefore, the concentration of citric acid can be approximated as one-third of the H⁺ concentration.

Concentration of citric acid = (6.76 x 10^-5 M) / 3 ≈ 2.25 x 10^-5 M

Thus, the concentration of citric acid in Sprite is approximately 2.25 x 10^-5 M.