Final answer:
To find the ratio of H₂PO₄⁻ to H₃PO₄ at pH 3, use the Henderson-Hasselbalch equation and the pKa1 value of 2.12. Solving for the ratio gives a result of approximately 7.6 to 1.
Step-by-step explanation:
To determine the ratio of H₂PO₄⁻ to H₃PO₄ at a pH of 3, we utilize the acid dissociation constant (Ka) and the Henderson-Hasselbalch equation which is given by pH = pKa + log([A⁻]/[HA]). The pH is given as 3, and the Ka for the dissociation of H₃PO₄ to H₂PO₄⁻ is related to its pKa1, which is 2.12.
Using the equation: 3 = 2.12 + log([H₂PO₄⁻]/[H₃PO₄]), we solve for the ratio [H₂PO₄⁻]/[H₃PO₄]. This results in log([H₂PO₄⁻]/[H₃PO₄]) = 3 - 2.12, which gives us a ratio of approximately 7.6. Thus, at a pH of 3, the ratio of H₂PO₄⁻ to H₃PO₄ is approximately 7.6 to 1.