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Chapter 16: Problem 32

Deuterium oxide \(\left(\mathrm{D}_{2} \mathrm{O},\right.\) 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
The concentrations of \(\mathrm{D}^+\) and \(\mathrm{OD}^-\) ions for pure \(\mathrm{D}_{2} \mathrm{O}\) at \(20^{\circ} \mathrm{C}\) are approximately \(2.98 \times 10^{-8}\,\text{M}\).

Step by step solution

01

Write down the ion-product constant expression for \(\mathrm{D}_{2} \mathrm{O}\)

The ion-product constant expression is given by: \[K_{w} = [\mathrm{D}^+][\mathrm{OD}^-]\] As \(\mathrm{D}_{2} \mathrm{O}\) is neutral, the concentration of \(\mathrm{D}^+\) ions is equal to \(\mathrm{OD}^-\) ions. Therefore, we can simplify the equation by replacing both concentrations with a single variable, say \(x\). \[K_{w} = x^2\] Now, we are given the value of \(K_{w} = 8.9 \times 10^{-16}\) and we can plug this value into the equation and solve for \(x\).
02

Solve for \(x\)

We have the equation: \[8.9 \times 10^{-16} = x^2\] To solve for \(x\), we take the square root of both sides of the equation: \[x = \sqrt{8.9 \times 10^{-16}}\] Calculating this value, we get: \[x \approx 2.98 \times 10^{-8}\]
03

Determine the concentrations of \(\mathrm{D}^+\) and \(\mathrm{OD}^-\)

Now that we have found the value of \(x\), we can determine the concentration of \(\mathrm{D}^+\) and \(\mathrm{OD}^-\) ions. As we noted earlier, the concentration of \(\mathrm{D}^+\) ions is equal to the concentration of \(\mathrm{OD}^-\) ions. \[[\mathrm{D}^+] = [\mathrm{OD}^-] = x \] Therefore, the concentrations of \(\mathrm{D}^+\) and \(\mathrm{OD}^-\) ions are approximately \(2.98 \times 10^{-8}\,\text{M}\).

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Most popular questions from this chapter

The volume of an adult's stomach ranges from about 50 \(\mathrm{mL}\) when empty to \(1 \mathrm{~L}\) when full. If the stomach volume is \(400 \mathrm{~mL}\) and its contents have a pH of 2 , how many moles of \(\mathrm{H}^{+}\) does the stomach contain? Assuming that all the \(\mathrm{H}^{+}\) comes from \(\mathrm{HCl}\), how many grams of sodium hydrogen carbonate will totally neutralize the stomach acid?

What is the boiling point of a \(0.10 \mathrm{M}\) solution of \(\mathrm{NaHSO}_{4}\) if the solution has a density of $1.002 \mathrm{~g} / \mathrm{mL}$ ?

Calculate the pH of each of the following solutions \(\left(K_{a}\right.\) and \(K_{b}\) values are given in Appendix D): (a) \(0.150 \mathrm{M}\) propionic acid $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOH}\right)$ (b) \(0.250 \mathrm{M}\) hydrogen chromate ion \(\left(\mathrm{HCrO}_{4}^{-}\right),(\mathbf{c}) 0.750 \mathrm{M}\) pyridine \(\left(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}\right)\)

If a neutral solution of water, with \(\mathrm{pH}=7.00,\) is cooled to \(10^{\circ} \mathrm{C},\) the pH rises to \(7.27 .\) Which of the following three statements is correct for the cooled water: (i) \(\left[\mathrm{H}^{+}\right]>\left[\mathrm{OH}^{-}\right]\) (ii) \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{OH}^{-}\right], \mathrm{or}\) (iii) \(\left[\mathrm{H}^{+}\right]<\left[\mathrm{OH}^{-}\right] ?\)

Determine the \(\mathrm{pH}\) of each of the following solutions \(\left(K_{a}\right.\) and \(K_{b}\) values are given in Appendix D): (a) \(0.095 \mathrm{M}\) hypochlorous acid, \((\mathbf{b}) 0.0085 \mathrm{M}\) hydrazine, (c) \(0.165 \mathrm{M}\) hydroxylamine.
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