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Chapter 13: Problem 75

The \(\mathrm{pH}\) of a household ammonia cleaning solution is \(11.68\). How many grams of ammonia are needed in a 1.25-L solution to give the same pH?

Short Answer

Expert verified
Answer: Approximately 0.102 grams of ammonia are needed to prepare a 1.25 L solution with a pH of 11.68.

Step by step solution

01

Calculate the concentration of \(\mathrm{OH^-}\) ions from the given pH value

Using the relationship between pH, pOH, and the ion product constant for water (\(K_\mathrm{w}\)), we can find the \(\mathrm{OH^-}\) concentration. \(pH + pOH = 14\) To find the pOH, subtract the given pH value from 14: \(pOH = 14 - pH = 14 - 11.68 = 2.32\) Now, we can determine the concentration of \(\mathrm{OH^-}\): \([\mathrm{OH^{-}}] = 10^{-pOH} = 10^{-2.32} \approx 4.79 \times 10^{-3} \mathrm{M}\)
02

Find the concentration of ammonia \(\mathrm{NH_3}\)

The ammonia cleaning solution contains a weak base, ammonium hydroxide (\(\mathrm{NH_4OH}\)), that ionizes as follows: \(\mathrm{NH_4OH} \rightarrow \mathrm{NH_3} + \mathrm{OH^-}\) The concentration of \(\mathrm{NH_3}\) can be approximated as the concentration of \(\mathrm{OH^-}\), after considering the ionization reaction. So, \([\mathrm{NH_{3}}] \approx 4.79 \times 10^{-3} \mathrm{M}\)
03

Calculate the mass of ammonia required for 1.25 L of the solution

To find the mass of ammonia needed, we will use the molarity formula: mass = molarity \(\times\) volume \(\times\) molar mass \(\text{mass }(\mathrm{NH_3}) = [\mathrm{NH_3}] \times V \times \text{ Molar Mass }(\mathrm{NH_3})\) \(\text{mass }(\mathrm{NH_3}) = (4.79 \times 10^{-3}\mathrm{M})(1.25 \mathrm{L})(17.03 \frac{\mathrm{g}}{\mathrm{mol}})\) \(\text{mass }(\mathrm{NH_3}) \approx 0.102 \mathrm{g}\) Therefore, approximately 0.102 grams of ammonia are needed to prepare 1.25 L of a solution with a pH of 11.68.

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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, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\)

Rank the following solutions in order of increasing \(\left[\mathrm{H}^{+}\right]\). \(\begin{array}{llll}0.1 & M \mathrm{HBr}, & 0.1 \mathrm{M} \mathrm{HF}, & 0.1 \mathrm{MHCHO}_{2} & 0.1 \mathrm{MHCN}\end{array}\)

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 the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of solutions with the following \(\left[\mathrm{H}^{+}\right]\). Classify each as acidic or basic. (a) \(1.0 \mathrm{M}\) (b) \(1.7 \times 10^{-4} \mathrm{M}\) (c) \(6.8 \times 10^{-8} \mathrm{M}\) (d) \(9.3 \times 10^{-11} M\)

WEB Give the formula of the conjugate base of (a) \(\mathrm{HCO}_{3}^{-}\) (b) \(\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)(\mathrm{OH})_{3}^{-}\) (c) \(\mathrm{HNO}_{2}\) (d) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}_{2}\) (e) \(\mathrm{H}_{2} \mathrm{SO}_{3}\)
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