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Chapter 13: Problem 15

Can the \(\mathrm{pH}\) of a solution be negative? Explain.

Short Answer

Expert verified
Yes, the pH of a solution can be negative if the molar concentration of hydrogen ions \([H^+]\) is greater than 1, which can occur in extremely acidic solutions. This is because the pH is calculated as \[pH = -\log_{10} [H^+]\], and logarithm values become negative when their argument is greater than 1.

Step by step solution

01

Understanding pH

pH is a measure of the acidity of a solution, which represents the concentration of hydrogen ions (H+) in the solution. It is defined as the negative logarithm (base 10) of the molar concentration of hydrogen ions. Mathematically, it can be expressed as: \[ pH = -\log_{10} [H^+] \] where [H^+] is the molar concentration of hydrogen ions in the solution.
02

Calculating pH

To calculate the pH of a solution, we need to find the concentration of hydrogen ions. We can then plug it into the formula mentioned above. For example, consider a solution with [H^+] = 0.01 M (mol/L). The pH of the solution can be calculated as follows: \[ pH = -\log_{10} (0.01) = 2\] In this case, the pH of the solution is 2.
03

Can pH be negative?

The pH of a solution can be negative if the molar concentration of hydrogen ions [H^+] is greater than 1. This can occur in very acidic solutions. Mathematically speaking, logarithm values become negative when their argument (input) is greater than 1. For example, if the [H^+] > 1: \[ pH = -\log_{10}([H^+]) < 0\] In this case, the pH of the solution will indeed be negative.
04

Conclusion

Yes, the pH of a solution can be negative. This occurs when the molar concentration of hydrogen ions [H^+] in the solution is greater than 1. This is often seen in extremely acidic solutions.

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Most popular questions from this chapter

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. \(6.2 \times 10^{-12} \mathrm{M} \mathrm{HNO}_{3}\)

What are the major species present in 0.015 \(M\) solutions of each of the following bases? a. KOH b. \(\mathrm{Ba}(\mathrm{OH})_{2}\) What is \(\left[\mathrm{OH}^{-}\right]\) and the \(\mathrm{pH}\) of each of these solutions?

Papaverine hydrochloride (abbreviated papH \(^{+} \mathrm{Cl}^{-} ;\) molar mass \(=378.85 \mathrm{g} / \mathrm{mol}\) ) is a drug that belongs to a group of medicines called vasodilators, which cause blood vessels to expand, thereby increasing blood flow. This drug is the conjugate acid of the weak base papaverine (abbreviated pap; \(K_{\mathrm{b}}=\) \(8.33 \times 10^{-9}\) at \(35.0^{\circ} \mathrm{C}\) ). Calculate the \(\mathrm{pH}\) of a \(30.0-\mathrm{mg} / \mathrm{mL}\) aqueous dose of papH \(^{+} \mathrm{Cl}^{-}\) prepared at \(35.0^{\circ} \mathrm{C} . K_{\mathrm{w}}\) at \(35.0^{\circ} \mathrm{C}\) is \(2.1 \times 10^{-14}\).

Consider 0.10 \(M\) solutions of the following compounds: \(\mathrm{AlCl}_{3}, \mathrm{NaCN}, \mathrm{KOH}, \mathrm{CsClO}_{4},\) and NaF. Place these solutions in order of increasing \(\mathrm{pH}\).

Codeine \(\left(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{3}\right)\) is a derivative of morphine that is used as an analgesic, narcotic, or antitussive. It was once commonly used in cough syrups but is now available only by prescription because of its addictive properties. If the \(\mathrm{pH}\) of a \(1.7 \times 10^{-3}-M\) solution of codeine is \(9.59,\) calculate \(K_{\mathrm{b}}\)
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