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Chapter 16: Problem 32

Deuterium oxide (\(\mathrm{D}_{2} \mathrm{O},\) where \(\mathrm{D}\) is deuterium, the hydrogen-2 isotope) has an ion-product constant, \(K_{w}\) , of \(8.9 \times 10^{-16}\) at \(20^{\circ} \mathrm{C}\). Calculate \(\left[\mathrm{D}^{+}\right]\) and \(\left[\mathrm{OD}^{-}\right]\) for pure (neutral) \(\mathrm{D}_{2} \mathrm{O}\) at this temperature.

Short Answer

Expert verified
In pure (neutral) D2O at \(20^{\circ} \mathrm{C}\), the concentrations of D+ and OD- ions are equal and can be calculated using the given ion-product constant, \(K_w = 8.9 \times 10^{-16}\). By solving for their concentrations, we find that \([\mathrm{D}^+] = [\mathrm{OD}^-] = 2.98 \times 10^{-8} \ \mathrm{M}\) at this temperature.

Step by step solution

01

Write down the expression for the ion-product constant, \(K_w\), for D2O

The ion-product constant, \(K_w\), for water (H2O) is given by the product of the concentrations of H+ and OH- ions. Similarly, for deuterium oxide (D2O), the ion-product constant is the product of the concentrations of D+ and OD- ions: \[K_w = [\mathrm{D}^+][\mathrm{OD}^-]\]
02

Determine the conditions for pure (neutral) D2O

In pure (neutral) D2O, the concentrations of its ions, D+ and OD-, are equal. Let's denote the concentration of D+ and OD- as x: \[[\mathrm{D}^+] = [\mathrm{OD}^-] = x\]
03

Substitute the given value of \(K_w\) and conditions for pure D2O into the ion-product constant expression

We know that \(K_w = 8.9 \times 10^{-16}\) at \(20^{\circ} \mathrm{C}\). Substituting the given value of \(K_w\) and the conditions for pure D2O into the ion-product constant expression, we get: \[8.9 \times 10^{-16} = x^2\]
04

Solve for x, the concentration of D+ and OD- ions

To find the concentration of D+ and OD- ions (x), we need to solve the equation obtained in step 3: \[x^2 = 8.9 \times 10^{-16}\] Taking the square root of both sides: \[x = \sqrt{8.9 \times 10^{-16}}\] \[x = 2.98 \times 10^{-8}\]
05

Write down the final answer

We found that x = 2.98 x 10^{-8}. Since we denoted the concentrations of D+ and OD- ions as x, and they are equal in pure D2O, the final answer is: \[[\mathrm{D}^+] = [\mathrm{OD}^-] = 2.98 \times 10^{-8} \ \mathrm{M}\]

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Most popular questions from this chapter

Predict the products of the following acid-base reactions, and predict whether the equilibrium lies to the left or to the right of the reaction arrow: (a) \(\mathrm{O}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\) (b) \(\mathrm{CH}_{3} \mathrm{COOH}(a q)+\mathrm{HS}^{-}(a q)\) (c) \(\mathrm{NO}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\)

Calculate the \(\mathrm{pH}\) of each of the following strong acid solutions: \((\mathbf{a}) 8.5 \times 10^{-3} \mathrm{M} \mathrm{HBr},(\mathbf{b}) 1.52 \mathrm{g}\) of \(\mathrm{HNO}_{3}\) in 575 \(\mathrm{mL}\) of solution, \((\mathbf{c}) 5.00 \mathrm{mL}\) of 0.250 \(\mathrm{M} \mathrm{ClO}_{4}\) diluted to 50.0 \(\mathrm{mL}\) (d) a solution formed by mixing 10.0 \(\mathrm{mL}\) of 0.100 \(\mathrm{M} \mathrm{HBr}\) with 20.0 \(\mathrm{mL}\) of 0.200 \(\mathrm{M} \mathrm{HCl} .\)

Indicate whether each of the following statements is true or false. For each statement that is false, correct the statement to make it true. (a) In general, the acidity of binary acids increases from left to right in a given row of the periodic table. (b) In a series of acids that have the same central atom, acid strength increases with the number of hydrogen atoms bonded to the central atom. (c) Hydrotelluric acid \(\left(\mathrm{H}_{2} \mathrm{Te}\right)\) is a stronger acid than \(\mathrm{H}_{2} \mathrm{S}\) because Te is more electronegative than \(\mathrm{S} .\)

(a) Using dissociation constants from Appendix D, determine the value for the equilibrium constant for each of the following reactions. \((\mathrm{i}) \mathrm{HCO}_{3}^{-}(a q)+\mathrm{OH}^{-}(a q) \rightleftharpoons \mathrm{co}_{3^{-}(a q)}+\mathrm{H}_{2} \mathrm{O}(l)\) (ii) \(\mathrm{NH}_{4}^{+}(a q)+\mathrm{CO}_{3}^{2-}(a q) \rightleftharpoons \mathrm{NH}_{3}(a q)+\mathrm{HCO}_{3}^{-}(a q)\) (b) We usually use single arrows for reactions when the for- ward reaction is appreciable \((K\) much greater than 1\()\) equilibrium is never established. If we follow this convention, which of these equilibria might be written with a single arrow?

Identify the Bronsted-Lowry acid and the Bronsted-Lowry base on the left side of each of the following equations, and also identify the conjugate acid and conjugate base of each on the right side: (a) \(\mathrm{NH}_{4}^{+}(a q)+\mathrm{CN}^{-}(a q) \rightleftharpoons \mathrm{HCN}(a q)+\mathrm{NH}_{3}(a q)\) (b) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{N}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\) \(\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{NH}^{+}(a q)+\mathrm{OH}^{-}(a q)\) (c)\(\mathrm{HCOOH}(a q)+\mathrm{PO}_{4}^{3-}(a q) \rightleftharpoons\) \(\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\mathrm{HCOO}^{-}(a q)+\mathrm{HPO}_{4}^{2-}(a q)\)
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