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Chapter 13: Problem 97

Which of the following is/are true about a \(0.10 \mathrm{M}\) solution of a strong acid, HY? (a) \(\left[\mathrm{Y}^{-}\right]=0.10 \mathrm{M}\) (b) \([\mathrm{HY}]=0.10 \mathrm{M}\) (c) \(\left[\mathrm{H}^{+}\right]=0.10 \mathrm{M}\) (d) \(\mathrm{pH}=1.0\) (c) \(\left[\mathrm{H}^{+}\right]+\left[\mathrm{Y}^{-}\right]=0.20 \mathrm{M}\)

Short Answer

Expert verified
(a) [Y⁻] = 0.10 M (b) [HY] = 0.10 M (c) [H⁺] = 0.10 M (d) pH = 1.0 (e) [H⁺] + [Y⁻] = 0.20 M Answer: (a), (c), (d), and (e) are true.

Step by step solution

01

Understand the behavior of strong acids in solution

Strong acids, such as HY, are acids that completely dissociate in water. That means that for a strong acid, its hydrogen ion (H+) concentration is equal to its initial molarity, and its conjugate base ion (Y-) concentration is also equal to the initial molarity of the acid.
02

Analyze statement (a)

(a) \([\mathrm{Y}^{-}]=0.10 \mathrm{M}\) Since HY is a strong acid, it dissociates completely, meaning the concentration of Y⁻ ions in the solution is equal to the initial concentration of HY. In this case, the statement is true.
03

Analyze statement (b)

(b) \([\mathrm{HY}]=0.10 \mathrm{M}\) After dissociation, the concentration of the undissociated HY molecules should essentially be zero. The statement is false.
04

Analyze statement (c)

(c) \([\mathrm{H}^{+}]=0.10 \mathrm{M}\) As HY is a strong acid, its hydrogen ion concentration, \([\mathrm{H}^{+}]\), is equal to its initial molarity (0.10 M). This statement is true.
05

Analyze statement (d)

(d) \(\mathrm{pH}=1.0\) pH is calculated using the formula \(\mathrm{pH}=-\log_{10}\left([\mathrm{H}^{+}]\right)\). Since \([\mathrm{H}^{+}]=0.10 \mathrm{M}\): \(\mathrm{pH}=-\log_{10}(0.10)\) \(\mathrm{pH}=1.0\) The statement is true.
06

Analyze statement (e)

(e) \([\mathrm{H}^{+}]+[\mathrm{Y}^{-}]=0.20 \mathrm{M}\) Since both the hydrogen ion and Y- ion concentrations are equal to the initial concentration of HY (0.10 M), their sum is: \(0.10 \mathrm{M} + 0.10 \mathrm{M} = 0.20 \mathrm{M}\) The statement is true.
07

Conclusion

Based on our analysis, the following statements about the 0.10 M solution of the strong acid, HY, are true: (a) \([\mathrm{Y}^{-}]=0.10 \mathrm{M}\) (c) \([\mathrm{H}^{+}]=0.10 \mathrm{M}\) (d) \(\mathrm{pH}=1.0\) (e) \([\mathrm{H}^{+}]+[\mathrm{Y}^{-}]=0.20 \mathrm{M}\)

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Most popular questions from this chapter

Write the overall chemical equation and calculate \(K\) for the complete ionization of oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\)

Uric acid, \(\mathrm{HC}_{5} \mathrm{H}_{3} \mathrm{O}_{3} \mathrm{~N}_{4}\), can accumulate in the joints. This accumulation causes severe pain and the condition is called gout. \(K_{\mathrm{a}}\) for uric acid is \(5.1 \times 10^{-6} .\) For a \(0.894 M\) solution of uric acid, calculate (a) \(\left[\mathrm{H}^{+}\right]\) (b) \(\left[\mathrm{OH}^{-}\right]\) (c) \(\mathrm{pH}\) (d) \% ionization

Caproic acid, \(\mathrm{HC}_{6} \mathrm{H}_{11} \mathrm{O}_{2}\), is found in coconut oil and is used in making artificial flavors. A solution is made by dissolving \(0.450 \mathrm{~mol}\) of caproic acid in enough water to make \(2.0 \mathrm{~L}\) of solution. The solution has \(\left[\mathrm{H}^{+}\right]=1.7 \times\) \(10^{-3} M\). What is \(K_{\mathrm{a}}\) for caproic acid?

Consider the following six beakers. All have \(100 \mathrm{~mL}\) of aqueous \(0.1 \mathrm{M}\) solutions of the following compounds: beaker A has HI beaker B has \(\mathrm{HNO}_{2}\) beaker \(\mathrm{C}\) has \(\mathrm{NaOH}\) beaker \(\mathrm{D}\) has \(\mathrm{Ba}(\mathrm{OH})_{2}\) beaker \(\mathrm{E}\) has \(\mathrm{NH}_{4} \mathrm{Cl}\) beaker \(\mathrm{F}\) has \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\)

Find \(\left[\mathrm{H}^{+}\right]\) and the \(\mathrm{pH}\) of the following solutions. (a) \(1.75 \mathrm{~L}\) of a \(37.5 \%\) (by mass) solution \((d=1.00 \mathrm{~g} / \mathrm{mL})\) of \(\mathrm{HCl} .\) What is the \(\mathrm{pH}\) of \(0.175 \mathrm{~L}\) of the same solution? (b) A solution made up of \(22 \mathrm{~g}\) of \(\mathrm{HBr}\) dissolved in enough water to make \(479 \mathrm{~mL}\) of solution. What is the \(\mathrm{pH}\) if the same mass of \(\mathrm{HBr}\) is dissolved in enough water to make \(47.9 \mathrm{~mL}\) of solution?
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