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Chapter 17: Problem 84

Rainwater is acidic because \(\mathrm{CO}_{2}(\mathrm{g})\) dissolves in the water, creating carbonic acid, \(\mathrm{H}_{2} \mathrm{CO}_{3}\) . If the rainwater is too acidic, it will react with limestone and seashells (which are principally made of calcium carbonate, CaCO_ \(_{3} ) .\) Calculate the concentrations of carbonic acid, bicarbonate ion \(\left(\mathrm{HCO}_{3}^{-}\right)\) and carbonate ion \(\left(\mathrm{CO}_{3}^{2-}\right)\) that are in a raindrop that has a pH of 5.60 , assuming that the sum of all three species in the raindrop is \(1.0 \times 10^{-5} M .\)

Short Answer

Expert verified
In a raindrop with pH 5.60, the concentrations of carbonic acid (H₂CO₃), bicarbonate ion (HCO₃⁻), and carbonate ion (CO₃²⁻) are 8.31 × 10⁻⁶ M, 1.67 × 10⁻⁶ M, and 2.00 × 10⁻⁹ M, respectively.

Step by step solution

01

1. Write the equilibrium reactions for carbonic acid dissociation

First, let's write down the two equilibrium reactions involving carbonic acid dissociation: Reaction 1: \(H_{2}CO_{3} \rightleftharpoons H^{+} + HCO_{3}^{-}\) Reaction 2: \(HCO_{3}^{-} \rightleftharpoons H^{+} + CO_{3}^{2-}\)
02

2. Write the equilibrium constants for the reactions

The equilibrium constants for the two reactions involving carbonic acid dissociation are given as follows: Equilibrium Constant 1: \(K_{a1} = \frac{[H^{+}][HCO_{3}^{-}]}{[H_{2}CO_{3}]}\) Equilibrium Constant 2: \(K_{a2} = \frac{[H^{+}][CO_{3}^{2-}]}{[HCO_{3}^{-}]}\)
03

3. Find the concentration of H⁺ ions using the given pH

We are given the pH of rainwater as 5.60. Using the formula for pH: pH = -log([H⁺]) We can find the concentration of H⁺ ions: [H⁺] = 10^(-pH) = 10^(-5.60) = 2.51 × 10⁻⁶ M
04

4. Set up two equations using the total concentration and the equilibrium constants

We know that the sum of the three species is: [H₂CO₃] + [HCO₃⁻] + [CO₃²⁻] = 1.0 × 10⁻⁵ M Using the equilibrium constants from Step 2, we can set up two more equations: \(K_{a1} = \frac{[H^{+}][HCO_{3}^{-}]}{[H_{2}CO_{3}]}\) \(K_{a2} = \frac{[H^{+}][CO_{3}^{2-}]}{[HCO_{3}^{-}]}\) Now, let's plug in the [H⁺] value that we calculated in Step 3: \(K_{a1} = \frac{(2.51 \times 10^{-6})([HCO_{3}^{-}])}{[H_{2}CO_{3}]}\) \(K_{a2} = \frac{(2.51 \times 10^{-6})([CO_{3}^{2-}])}{[HCO_{3}^{-}]}\)
05

5. Find the values for Ka1 and Ka2 for carbonic acid

To solve the system of equations, we need the Ka1 and Ka2 values for carbonic acid. Ka1 (for H₂CO₃) = 4.45 × 10⁻⁷ Ka2 (for HCO₃⁻) = 4.69 × 10⁻¹¹
06

6. Solve the system of equations to find the concentrations

Now we have three equations and three unknowns: 1. [H₂CO₃] + [HCO₃⁻] + [CO₃²⁻] = 1.0 × 10⁻⁵ M 2. \(\frac{(2.51 \times 10^{-6})([HCO_{3}^{-}])}{[H_{2}CO_{3}]} = 4.45 \times 10^{-7}\) 3. \(\frac{(2.51 \times 10^{-6})([CO_{3}^{2-}])}{[HCO_{3}^{-}]} = 4.69 \times 10^{-11}\) Solve this system of equations to get: [H₂CO₃] = 8.31 × 10⁻⁶ M [HCO₃⁻] = 1.67 × 10⁻⁶ M [CO₃²⁻] = 2.00 × 10⁻⁹ M These are the concentrations of carbonic acid, bicarbonate ion, and carbonate ion, respectively, in a raindrop with pH 5.60.

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Most popular questions from this chapter

(a) Will \(\mathrm{Co}(\mathrm{OH})_{2}\) precipitate from solution if the \(\mathbf{p H}\) of a 0.020 M solution of \(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}\) is adjusted to 8.5? (b) Will \(\mathrm{AgIO}_{3}\) precipitate when 20 mL of 0.010 M \(\mathrm{AglO}_{3}\) is mixed with 10 mL of 0.015 \(M \mathrm{NaIO}_{3}\)? ( \(K_{s p}\) of \(\mathrm{AgIO}_{3}\) is \(3.1 \times 10^{8}\))?

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