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Chapter 14: Problem 55

Calculate the \(\mathrm{pH}\) of each of the following solutions of a strong acid in water. a. \(0.10 \mathrm{M} \mathrm{HCl}\) c. \(1.0 \times 10^{-11} \mathrm{M} \mathrm{HCl}\) b. \(5.0 \mathrm{M} \mathrm{HCl}\)

Short Answer

Expert verified
The pH values for the given strong acid solutions are as follows: a. \(0.10 \mathrm{M} \mathrm{HCl}\): pH = 1.00 b. \(1.0 \times 10^{-11} \mathrm{M} \mathrm{HCl}\): pH = 11 c. \(5.0 \mathrm{M} \mathrm{HCl}\): pH ≈ -0.30

Step by step solution

01

Identify the concentration of hydrogen ions

Since HCl is a strong acid, it completely dissociates in water and releases an equal concentration of hydrogen ions (H+). In this case, the concentration of H+ ions is equal to the concentration of HCl: \[[\mathrm{H}^+] = 0.10 \mathrm{M}\]
02

Calculate the pH

Now we can use the pH formula to calculate the pH value: \[pH = -\log_{10}[\mathrm{H}^+] = -\log_{10}(0.10) = 1.00\] The pH of a \(0.10 \mathrm{M} \mathrm{HCl}\) solution is 1.00. b. Calculate the pH of a \(1.0 \times 10^{-11} \mathrm{M} \mathrm{HCl}\) solution
03

Identify the concentration of hydrogen ions

Since HCl is a strong acid, it completely dissociates in water, releasing an equal concentration of H+ ions. In this case, \[[\mathrm{H}^+] = 1.0 \times 10^{-11} \mathrm{M}\]
04

Calculate the pH

Now we can use the pH formula to calculate the pH value: \[pH = -\log_{10}[\mathrm{H}^+] = -\log_{10}(1.0 \times 10^{-11}) = 11\] The pH of a \(1.0 \times 10^{-11} \mathrm{M} \mathrm{HCl}\) solution is 11. c. Calculate the pH of a \(5.0 \mathrm{M} \mathrm{HCl}\) solution
05

Identify the concentration of hydrogen ions

Since HCl is a strong acid, it completely dissociates in water, releasing an equal concentration of H+ ions. In this case, \[[\mathrm{H}^+] = 5.0 \mathrm{M}\]
06

Calculate the pH

Now we can use the pH formula to calculate the pH value: \[pH = -\log_{10}[\mathrm{H}^+] = -\log_{10}(5.0) \approx -0.30\] The pH of a \(5.0 \mathrm{M} \mathrm{HCl}\) solution is approximately -0.30.

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Most popular questions from this chapter

A solution is prepared by adding \(50.0 \mathrm{~mL}\) of \(0.050 M \mathrm{HBr}\) to \(150.0 \mathrm{~mL}\) of \(0.10 \mathrm{M}\) HI. Calculate the concentrations of all species in this solution. HBr and HI are both considered strong acids.

What are the major species present in a \(0.150 \mathrm{M} \mathrm{NH}_{3}\) solution? Calculate the \(\left[\mathrm{OH}^{-}\right]\) and the \(\mathrm{pH}\) of this solution.

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.)

Consider \(50.0 \mathrm{~mL}\) of a solution of weak acid \(\mathrm{HA}=K_{\mathrm{a}}(1.00 \times\) \(10^{-6}\) ), which has a pH of \(4.000\). What volume of water must be added to make the \(\mathrm{pH}=5.000 ?\)

Calculate the percent dissociation for a \(0.22 M\) solution of chlorous acid \(\left(\mathrm{HClO}_{2}, K_{\mathrm{a}}=1.2 \times 10^{-2}\right)\)
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