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Chapter 13: Problem 58

Calculate the \(\mathrm{pH}\) of each of the following solutions containing a strong acid in water. a. \(2.0 \times 10^{-2} M \mathrm{HNO}_{3}\) b. \(4.0 \mathrm{M} \mathrm{HNO}_{3}\) c. \(6.2 \times 10^{-12} \mathrm{M} \mathrm{HNO}_{3}\)

Short Answer

Expert verified
In summary, the pH values of the given HNO\(_3\) solutions are as follows: a. \(2.0 \times 10^{-2} M \mathrm{HNO}_{3} \Rightarrow pH \approx 1.70\) b. \(4.0 \mathrm{M} \mathrm{HNO}_{3} \Rightarrow pH \approx 0.398\) c. \(6.2 \times 10^{-12} \mathrm{M} \mathrm{HNO}_{3} \Rightarrow pH \approx 11.21\)

Step by step solution

01

Identify the concentration of hydronium ions

Since HNO\(_{3}\) is a strong acid and we can assume 100% dissociation in water, the concentration of H\(_{3}\)O\(^{+}\) ions will be equal to the given concentration of HNO\(_3\). So, \(\mathrm{[H_{3}O^{+}]} = 2.0 \times 10^{-2} \mathrm{M}\).
02

Calculate pH

Now, substitute the concentration of H\(_{3}\)O\(^{+}\) in the pH formula: \(pH = -\log (2.0 \times 10^{-2})\) After calculating the value, we get: \(pH \approx 1.70\) #b. Calculating pH for 4.0 M HNO₃ solution#
03

Identify the concentration of hydronium ions

For 4.0 M HNO\(_3\), the concentration of H\(_{3}\)O\(^{+}\) ions will be equal to the given concentration of HNO\(_3\). So, \(\mathrm{[H_{3}O^{+}]} = 4.0 \mathrm{M}\).
04

Calculate pH

Substitute the concentration of H\(_{3}\)O\(^{+}\) in the pH formula: \(pH = -\log (4.0)\) After calculating the value, we get: \(pH \approx 0.398\) #c. Calculating pH for 6.2 x 10⁻¹² M HNO₃ solution#
05

Identify the concentration of hydronium ions

For 6.2 x 10⁻¹² M HNO\(_3\), the concentration of H\(_{3}\)O\(^{+}\) ions will be equal to the given concentration of HNO\(_3\). So, \(\mathrm{[H_{3}O^{+}]} = 6.2 \times 10^{-12} \mathrm{M}\).
06

Calculate pH

Substitute the concentration of H\(_{3}\)O\(^{+}\) in the pH formula: \(pH = -\log (6.2 \times 10^{-12})\) After calculating the value, we get: \(pH \approx 11.21\) In summary, the pH values of the given HNO\(_3\) solutions are as follows: a. \(2.0 \times 10^{-2} M \mathrm{HNO}_{3} \Rightarrow pH \approx 1.70\) b. \(4.0 \mathrm{M} \mathrm{HNO}_{3} \Rightarrow pH \approx 0.398\) c. \(6.2 \times 10^{-12} \mathrm{M} \mathrm{HNO}_{3} \Rightarrow pH \approx 11.21\)

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Most popular questions from this chapter

Consider \(0.25 \mathrm{M}\) solutions of the following salts: \(\mathrm{NaCl}\), RbOCI, KI, Ba(CIO_{ } _ { 2 } \text { , and } \mathrm { NH } _ { 4 } \mathrm { NO } _ { 3 } \text { . For each salt, indicate } whether the solution is acidic, basic, or neutral.

Write out the stepwise \(K_{\mathrm{a}}\) reactions for citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right)\) a triprotic acid.

A typical aspirin tablet contains 325 mg acetylsalicylic acid \(\left(\mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4}\right) .\) Calculate the \(\mathrm{pH}\) of a solution that is prepared by dissolving two aspirin tablets in enough water to make one cup \((237 \mathrm{mL})\) of solution. Assume the aspirin tablets are pure acetylsalicylic acid, \(K_{\mathrm{a}}=3.3 \times 10^{-4}\)

A sample containing 0.0500 mole of \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) is dissolved in enough water to make 1.00 L of solution. This solution contains hydrated \(\mathrm{SO}_{4}^{2-}\) and \(\mathrm{Fe}^{3+}\) 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 go through the semipermeable membrane. Actually, this is not a great assumption for the tiny \(\mathrm{H}^{+}\) ion.)

The pH of a 0.063-M solution of hypobromous acid (HOBr but usually written HBrO) is 4.95. Calculate \(K_{\mathrm{a}}\).
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