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Chapter 17: Problem 114

What is the \(\mathrm{pH}\) at \(25^{\circ} \mathrm{C}\) of water saturated with \(\mathrm{CO}_{2}\) at a partial pressure of \(111.5 \mathrm{kPa}\) ? The Henry's law constant for \(\mathrm{CO}_{2}\) at \(25^{\circ} \mathrm{C}\) is $3.1 \times 10^{-4} \mathrm{~mol} / \mathrm{L}-\mathrm{kPa}$.

Short Answer

Expert verified
The pH of water saturated with CO₂ at a partial pressure of 111.5 kPa and a temperature of 25°C is approximately 4.44.

Step by step solution

01

Determine the dissolved CO₂ concentration using Henry's Law constant

Using Henry's Law constant, we can calculate the concentration of CO₂ dissolved in water: \[ C_{CO_{2}} = k_{H} \times P \] where \(C_{CO_{2}}\) is the concentration of CO₂, \(k_{H}\) is Henry's Law constant, and \(P\) is the partial pressure of CO₂. \[ C_{CO_{2}} = (3.1 \times 10^{-4} \, \mathrm{mol/L/kPa}) \times (111.5 \, \mathrm{kPa}) \] \[ C_{CO_{2}} = 0.034565 \, \mathrm{mol/L} \]
02

Write the dissolution and formation equation of carbonic acid

The dissolution of CO₂ in water and the subsequent formation of carbonic acid (H₂CO₃) can be represented as follows: \[ CO_{2} \, (g) + H_{2}O \, (l) \rightleftharpoons H_{2}CO_{3} \, (aq) \]
03

Write the ionization equation of carbonic acid

The ionization of carbonic acid (H₂CO₃) into hydrogen ions (H⁺) and bicarbonate ions (HCO₃⁻) can be represented as follows: \[ H_{2}CO_{3} \, (aq) \rightleftharpoons H^{+} \, (aq) + HCO_{3}^{-} \, (aq) \]
04

Calculate the hydrogen ion concentration using the equilibrium constant

The equilibrium constant (Ka1) for the ionization of carbonic acid is \(4.45 \times 10^{-7}\). Using this equilibrium constant, we can calculate the concentration of hydrogen ions (H⁺): \[ K_{a1} = \frac{[H^{+}][HCO_{3}^{-}]}{[H_{2}CO_{3}]} \] Assuming that the concentration of H⁺ and HCO₃⁻ ions is the same (since they both come from the ionization of one molecule of H₂CO₃) and using the concentration of H₂CO₃ obtained in step 1, we can solve for the H⁺ concentration: \[ 4.45 \times 10^{-7} = \frac{[H^{+}]^{2}}{0.034565} \] \[ [H^{+}]^{2} = (4.45 \times 10^{-7}) \times 0.034565 \] \[ [H^{+}] = \sqrt{(4.45 \times 10^{-7}) \times 0.034565} = 3.59 \times 10^{-5} \, \mathrm{mol/L} \]
05

Calculate the pH

Now that we have the concentration of hydrogen ions (H⁺), we can calculate the pH using the following equation: \[ pH = -\log{[H^{+}]} \] \[ pH = -\log{(3.59 \times 10^{-5})} = 4.44 \] So, the pH of water saturated with CO₂ at a partial pressure of 111.5 kPa and a temperature of 25°C is approximately 4.44.

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Most popular questions from this chapter

Write the expression for the solubility-product constant for each of the following ionic compounds: $\mathrm{BaCrO}_{4}, \mathrm{CuS}, \mathrm{PbCl}_{2}\( and \)\mathrm{LaF}_{3} .$

For each of the following slightly soluble salts, write the net ionic equation, if any, for reaction with a strong acid: (a) MnS, (b) \(\mathrm{PbF}_{2}\), (c) \(\mathrm{AuCl}_{3}\) (d) \(\mathrm{Hg}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) (e) CuBr.

Compare the titration of a strong, monoprotic acid with a strong base to the titration of a weak, monoprotic acid with a strong base. Assume the strong and weak acid solutions initially have the same concentrations. Indicate whether the following statements are true or false. (a) More base is required to reach the equivalence point for the strong acid than the weak acid. \((\mathbf{b})\) The \(\mathrm{pH}\) at the beginning of the titration is lower for the weak acid than the strong acid. \((\mathbf{c})\) The \(\mathrm{pH}\) at the equivalence point is 7 no matter which acid is titrated.

Suggest how the cations in each of the following solution mixtures can be separated: (a) \(\mathrm{Na}^{+}\) and $\mathrm{Cd}^{2+},(\mathbf{b}) \mathrm{Cu}^{2+}\( and \)\mathrm{Mg}^{2+},(\mathbf{c}) \mathrm{Pb}^{2+}$ and \(\mathrm{Al}^{3+},(\mathbf{d}) \mathrm{Ag}^{+}\) and \(\mathrm{Hg}^{2+} .\)

You are asked to prepare a \(\mathrm{pH}=3.00\) buffer starting from $2.00 \mathrm{~L}\( of \)0.025 \mathrm{M}$ solution of benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\) and any amount you need of sodium benzoate $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COONa}\right) .(\mathbf{a})\( What is the \)\mathrm{pH}$ of the benzoic acid solution prior to adding sodium benzoate? (b) How many grams of sodium benzoate should be added to prepare the buffer? Neglect the small volume change that occurs when the sodium benzoate is added.
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