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Chapter 14: Problem 167

Phosphoric acid is a common ingredient in traditional cola drinks. It is added to provide the drinks with a pleasant tart taste. Assuming that in cola drinks the concentration of phosphoric acid is \(0.007 M,\) calculate the \(\mathrm{pH}\) of this solution.

Short Answer

Expert verified
The pH of the cola drink solution containing 0.007 M phosphoric acid is approximately 2.20.

Step by step solution

01

Write the dissociation expression for phosphoric acid

Phosphoric acid, H₃PO₄, is a triprotic weak acid which means it can release three hydrogen ions. However, for simplicity, we'll consider only the first dissociation step: H₃PO₄ <--> H⁺ + H₂PO₄⁻ Now, write the acid dissociation constant expression, Ka₁, for this reaction: Ka₁ = \(\frac{[H⁺][H₂PO₄⁻]}{[H₃PO₄]}\)
02

Set up the reaction's equilibrium concentrations

Let x represent the amount of H₃PO₄ that dissociates. At equilibrium, we'll have the following concentrations: [H₃PO₄] = 0.007 M - x [H⁺] = x [H₂PO₄⁻] = x We can rewrite the acid dissociation constant expression using these concentrations: Ka₁ = \(\frac{x^2}{0.007 - x}\)
03

Make an approximation to simplify the equation

Since phosphoric acid is a weak acid and doesn't dissociate much, we can make the approximation that x << 0.007. This allows us to simplify the equation as follows: Ka₁ ≈ \(\frac{x^2}{0.007}\)
04

Solve for the concentration of H₃O⁺ ions

The Ka₁ value of phosphoric acid is 7.1 × 10⁻³. Now, we can solve for x: 7.1 × 10⁻³ ≈ \(\frac{x^2}{0.007}\) x² = 7.1 × 10⁻³ × 0.007 x = √(7.1 × 10⁻³ × 0.007) x ≈ 0.00634 M The concentration of H₃O⁺ ions (or H⁺ ions) is approximately 0.00634 M.
05

Calculate the pH of the solution

Now that we have the concentration of H₃O⁺ ions, we can find the pH using the formula: pH = -log₁₀[H₃O⁺] pH ≈ -log₁₀(0.00634) pH ≈ 2.20 The pH of the cola drink solution containing 0.007 M phosphoric acid is approximately 2.20.

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