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Chapter 16: Problem 44

Calculate the pH of each of the following strong acid solutions: $(\mathbf{a}) 0.0178 \mathrm{M} \mathrm{HNO}_{3},(\mathbf{b}) 0.500 \mathrm{~g}$ of \(\mathrm{HClO}_{3}\) in \(5.00 \mathrm{~L}\) of solution, \((\mathbf{c}) 5.00 \mathrm{~mL}\) of $2.00 \mathrm{M} \mathrm{HCl}\( diluted to \)0.500 \mathrm{~L}$, (d) a mixture formed by adding \(75.0 \mathrm{~mL}\) of \(0.010 \mathrm{M} \mathrm{HCl}\) to \(125 \mathrm{~mL}\) of \(0.020 \mathrm{M} \mathrm{HBr}\).

Short Answer

Expert verified
The pH values for the given strong acid solutions are as follows: a) \(pH = 1.75\) b) \(pH = 2.93\) c) \(pH = 1.70\) d) \(pH = 1.79\)

Step by step solution

01

Calculate [H+] for 0.0178 M HNO3 solution

For strong acids, [H+] = the molarity of the acid: [H+] = 0.0178 M #Solution a: Calculate pH#
02

Calculate pH

Using the formula pH = -log[H+]: pH = -log(0.0178) pH = 1.75 #Solution b: Calculate moles of HClO3 #
03

Calculate moles of HClO3

HClO3 has a molar mass of 84.46 g/mol. 0.500 g HClO3 * (1 mol / 84.46 g) = 0.00592 mol #Solution b: Calculate [H+] (concentration)#
04

Calculate [H+] (concentration)

[H+] is equal to the moles of HClO3 per liter: [H+] = 0.00592 mol / 5.00 L [H+] = 0.00118 M #Solution b: Calculate pH#
05

Calculate pH

Using the formula pH = -log[H+]: pH = -log(0.00118) pH = 2.93 #Solution c: Calculate new concentration of HCl after dilution#
06

Calculate new concentration of HCl after dilution

M1V1 = M2V2 \[M2 = \frac{(2.00 M)(0.00500 L)}{0.500 L}\] M2 = 0.0200 M #Solution c: Calculate [H+] (concentration)#
07

Calculate [H+] (concentration)

In strong acid, [H+] = concentration of acid [H+] = 0.0200 M #Solution c: Calculate pH#
08

Calculate pH

Using the formula pH = -log[H+]: pH = -log(0.0200) pH = 1.70 #Solution d: Calculate combined moles of HCl and HBr#
09

Calculate combined moles of HCl and HBr

Moles of HCl = (0.010 M)(0.075 L) = 0.00075 mol Moles of HBr = (0.020 M)(0.125 L) = 0.00250 mol Total moles = 0.00075 + 0.00250 = 0.00325 mol #Solution d: Calculate combined volume of solution#
10

Calculate combined volume of solution

Total volume = 75.0 mL + 125 mL = 200 mL = 0.200 L #Solution d: Calculate [H+] (concentration)#
11

Calculate [H+] (concentration)

[H+] = total moles / total volume [H+] = 0.00325 mol / 0.200 L [H+] = 0.01625 M #Solution d: Calculate pH#
12

Calculate pH

Using the formula pH = -log[H+]: pH = -log(0.01625) pH = 1.79 Final pH values: a) 1.75 b) 2.93 c) 1.70 d) 1.79

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Most popular questions from this chapter

The odor of fish is due primarily to amines, especially methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)\). Fish is often served with a wedge of lemon, which contains citric acid. The amine and the acid react forming a product with no odor, thereby making the less-than-fresh fish more appetizing. Using data from Appendix \(D\), calculate the equilibrium constant for the reaction of citric acid with methylamine, if only the first proton of the citric acid \(\left(K_{a 1}\right)\) is important in the neutralization reaction.

Calculate the percent ionization of propionic acid $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOH}\right)$ in solutions of each of the following concentrations \(\left(K_{a}\right.\) isgiven in AppendixD): (a) \(0.250 M,(\mathbf{b}) 0.0800 M\) (c) \(0.0200 \mathrm{M}\)

Predict whether aqueous solutions of the following compounds are acidic, basic, or neutral: $(\mathbf{a}) \mathrm{NH}_{4} \mathrm{Br},(\mathbf{b}) \mathrm{FeCl}_{3},$ (c) \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) (e) \(\mathrm{NaHC}_{2} \mathrm{O}_{4}\). (d) \(\mathrm{KClO}_{4}\),

Identify the Brønsted-Lowry acid and the BrønstedLowry base on the left side of each equation, and also identify the conjugate acid and conjugate base of each on the right side. $$ \begin{array}{l} \text { (a) } \mathrm{HBrO}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{BrO}^{-}(a q) \\\ \text { (b) } \mathrm{HSO}_{4}^{-}(a q)+\mathrm{HCO}_{3}^{-}(a q) \rightleftharpoons \mathrm{SO}_{4}^{2-}(a q)+\mathrm{H}_{2} \mathrm{CO}_{3}(a q) \\ \text { (c) } \mathrm{HSO}_{3}^{-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \end{array} $$

Identify the Lewis acid and Lewis base among the reactants in each of the following reactions: (a) $\mathrm{Fe}\left(\mathrm{ClO}_{4}\right)_{3}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons$ $$ \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}(a q)+3 \mathrm{ClO}_{4}^{-}(a q) $$ (b) $\mathrm{CN}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{HCN}(a q)+\mathrm{OH}^{-}(a q)$ (c) $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}(g)+\mathrm{BF}_{3}(g) \rightleftharpoons\left(\mathrm{CH}_{3}\right)_{3} \mathrm{NBF}_{3}(s)$ (d) $\mathrm{HIO}(l q)+\mathrm{NH}_{2}^{-}(l q) \rightleftharpoons \mathrm{NH}_{3}(l q)+\mathrm{IO}^{-}(l q)$ (lg denotes liquid ammonia as solvent)
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