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Chapter 14: Problem 87

Calculate the \(\mathrm{pH}\) of the following solutions. a. \(0.10 \mathrm{M} \mathrm{NaOH}\) b. \(1.0 \times 10^{-10} \mathrm{M} \mathrm{NaOH}\) c. \(2.0 \mathrm{M} \mathrm{NaOH}\)

Short Answer

Expert verified
The pH values for the given NaOH solutions are: a. 0.10 M NaOH: pH = 13 b. \(1.0 \times 10^{-10} M\) NaOH: pH = 4 c. 2.0 M NaOH: pH > 14 or 'extremely basic'

Step by step solution

01

Identify the relationship between concentration and pH

To calculate the pH of a solution, we use the formula: pH = -log[H+] In this case, we are given the concentration of NaOH, which is a strong base. Since it dissociates completely in water, it will produce an equal concentration of OH⁻ ions. We need to calculate the pOH first and then use the relationship between pH and pOH to find the pH. The relationship between pOH and pH is as follows: pH + pOH = 14 Now the task is to find the pOH for each concentration and use this relationship to calculate pH.
02

Calculate pOH for 0.10 M NaOH

For the first solution, the NaOH concentration is 0.10 M. Since NaOH dissociates completely, the OH⁻ concentration will also be 0.10 M. To find the pOH, use the pOH = -log[OH⁻]: pOH = -log(0.10) pOH = 1
03

Calculate pH for 0.10 M NaOH

Now that we have the pOH, we can find the pH by using pH + pOH = 14: pH = 14 - pOH pH = 14 - 1 pH = 13 The pH of the 0.10 M NaOH solution is 13.
04

Calculate pOH for \(1.0 \times 10^{-10} M\) NaOH

For the second solution, the concentration of NaOH is \(1.0 \times 10^{-10} M\). The OH⁻ concentration will be the same: pOH = -log(\(1.0 \times 10^{-10}\)) pOH = 10
05

Calculate pH for \(1.0 \times 10^{-10} M\) NaOH

Now, find the pH by using pH + pOH = 14: pH = 14 - pOH pH = 14 - 10 pH = 4 The pH of the \(1.0 \times 10^{-10} M\) NaOH solution is 4.
06

Calculate pOH for 2.0 M NaOH

For the third solution, the concentration of NaOH is 2.0 M. pOH = -log(2.0) pOH ≈ -0.301
07

Calculate pH for 2.0 M NaOH

Now use pH + pOH = 14 to find the pH: pH = 14 - pOH pH = 14 - (-0.301) pH ≈ 14.301 However, since the pH scale typically ranges from 0 to 14, it's more appropriate to indicate that the solution is extremely basic and should be reported as pH > 14 or "extremely basic". Here are the final pH values for each NaOH solution: a. 0.10 M NaOH: pH = 13 b. \(1.0 \times 10^{-10} M\) NaOH: pH = 4 c. 2.0 M NaOH: pH > 14 or 'extremely basic'

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Most popular questions from this chapter

Aluminum hydroxide is an amphoteric substance. It can act as either a Brønsted-Lowry base or a Lewis acid. Write a reaction showing \(\mathrm{Al}(\mathrm{OH})_{3}\) acting as a base toward \(\mathrm{H}^{+}\) and as an acid toward \(\mathrm{OH}^{-}\).

A sample containing \(0.0500 \mathrm{~mol} \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) is dissolved in enough water to make \(1.00 \mathrm{~L}\) of solution. This solution contains hydrated \(\mathrm{SO}_{4}{ }^{2-}\) and \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}{ }^{3+}\) ions. The latter behaves as an acid: $$\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}(a q) \rightleftharpoons \mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{OH}^{2+}(a q)+\mathrm{H}^{+}(a q)$$ a. Calculate the expected osmotic pressure of this solution at \(25^{\circ} \mathrm{C}\) if the above dissociation is negligible. b. The actual osmotic pressure of the solution is \(6.73\) atm at \(25^{\circ} \mathrm{C}\). Calculate \(K_{\mathrm{a}}\) for the dissociation reaction of \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\). (To do this calculation, you must assume that none of the ions goes through the semipermeable membrane. Actually, this is not a great assumption for the tiny \(\mathrm{H}^{+}\) ion.)

Trichloroacetic acid \(\left(\mathrm{CCl}_{3} \mathrm{CO}_{2} \mathrm{H}\right)\) is a corrosive acid that is used to precipitate proteins. The \(\mathrm{pH}\) of a \(0.050 \mathrm{M}\) solution of trichloroacetic acid is the same as the \(\mathrm{pH}\) of a \(0.040 \mathrm{M} \mathrm{HClO}_{4}\) solution. Calculate \(K_{\mathrm{a}}\) for trichloroacetic acid.

Calculate the concentration of all species present and the \(\mathrm{pH}\) of a \(0.020 M \mathrm{HF}\) solution.

Using your results from Exercise 129, place the species in each of the following groups in order of increasing base strength. a. \(\mathrm{OH}^{-}, \mathrm{SH}^{-}, \mathrm{SeH}^{-}\) b. \(\mathrm{NH}_{3}, \mathrm{PH}_{3}\) c. \(\mathrm{NH}_{3}, \mathrm{HONH}_{2}\)
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