/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 58 Calculate the \(\mathrm{pH}\) of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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 HNO鈧� 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鈦宦孤� M HNO鈧� solution#
05

Identify the concentration of hydronium ions

For 6.2 x 10鈦宦孤� 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. \(6.2 \times 10^{-12} \mathrm{M} \mathrm{HNO}_{3} \Rightarrow pH \approx 11.21\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Strong Acids
When we talk about strong acids, we refer to their complete dissociation in water. Strong acids like nitric acid (HNO鈧�) dissociate 100%, providing a straightforward calculation for hydronium ions concentration. This means every molecule of HNO鈧� breaks apart into its ions, specifically hydrogen ions (H鈦�), which immediately become hydronium ions (H鈧僌鈦�) when they interact with water. This characteristic makes strong acids easy to work with for pH calculations, since the concentration of the acid is equal to its hydronium ion concentration.

Key strong acids include:
  • Hydrochloric acid (HCl)
  • Nitric acid (HNO鈧�)
  • Sulfuric acid (H鈧係O鈧�)
These acids are used in various industries and laboratory settings due to their reactivity and predictability in aqueous solutions.
Hydronium Ion Concentration
The concept of hydronium ion concentration is fundamental in understanding acidity in solutions. When a strong acid like nitric acid dissolves in water, it releases hydrogen ions that form hydronium ions (H鈧僌鈦�). This concentration of hydronium ions directly affects the pH of the solution.

Mathematically, if the concentration of the strong acid in solution is known, the hydronium ion concentration can be given as:

  • \[[H鈧僌鈦篯 = [ ext{concentration of strong acid}]\]

It鈥檚 important to note that for very dilute solutions, such as \(6.2 \times 10^{-12} M HNO鈧僜), the contribution of hydronium ions from the water itself can affect the pH, leading to interesting results where the pH might appear neutral or even basic as in the present case.

Logarithmic Functions in pH Calculations
Logarithmic functions play a crucial role in calculating the pH of a solution. The pH scale is logarithmic, not linear, which means each whole number change on the pH scale represents a tenfold change in hydronium ion concentration. The formula to calculate pH is derived from the base-10 logarithm of the hydronium ion concentration:

  • \[pH = -\log [H鈧僌鈦篯\]
The negative sign in the formula is because we want a scale where higher concentrations of hydronium ions (and thus more acidic solutions) correspond to lower pH values.

When calculating, for example, the pH of a solution with hydronium ions concentration \(2.0 \times 10^{-2} M\),

Using the formula:

  • \[pH = -\log(2.0 \times 10^{-2})\]Resulting in \(pH \approx 1.70\).
This illustrates how logarithmic functions simplify expressions involving large ranges of ion concentrations into a more practical and manageable scale.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

At \(25^{\circ} \mathrm{C},\) a saturated solution of benzoic acid \(\left(K_{a}=6.4 \times\right.\) \(10^{-5}\) ) has a pH of \(2.80 .\) Calculate the water solubility of benzoic acid in moles per liter.

For solutions of the same concentration, as acid strength increases, indicate what happens to each of the following (increases, decreases, or doesn't change). a. \(\left[\mathrm{H}^{+}\right]\) b. \(\mathrm{pH}\) c. \(\left[\mathrm{OH}^{-}\right]\) d. pOH \(\mathbf{e} . K_{\mathrm{a}}\)

Quinine \(\left(\mathrm{C}_{20} \mathrm{H}_{24} \mathrm{N}_{2} \mathrm{O}_{2}\right)\) is the most important alkaloid derived from cinchona bark. It is used as an antimalarial drug. For quinine, \(\mathrm{p} K_{\mathrm{b}_{1}}=5.1\) and \(\mathrm{p} K_{\mathrm{b}_{2}}=9.7\left(\mathrm{p} K_{\mathrm{b}}=-\log K_{\mathrm{b}}\right) .\) Only 1 g quinine will dissolve in \(1900.0 \mathrm{mL}\) of solution. Calculate the \(\mathrm{pH}\) of a saturated aqueous solution of quinine. Consider only the reaction \(\mathrm{Q}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{QH}^{+}+\mathrm{OH}^{-}\) described by \(\mathrm{p} K_{\mathrm{b}_{1}},\) where \(\mathrm{Q}=\) quinine.

Rank the following 0.10 \(M\) solutions in order of increasing pH. a. HI, HF, NaF, NaI b. \(\mathrm{NH}_{4} \mathrm{Br}, \mathrm{HBr}, \mathrm{KBr}, \mathrm{NH}_{3}\) c. \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3} \mathrm{NO}_{3}, \mathrm{NaNO}_{3}, \mathrm{NaOH}, \mathrm{HOC}_{6} \mathrm{H}_{5}, \mathrm{KOC}_{6} \mathrm{H}_{5}\) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}, \mathrm{HNO}_{3}\)

A \(2.14-\mathrm{g}\) sample of sodium hypoiodite is dissolved in water to make 1.25 L of solution. The solution \(\mathrm{pH}\) is \(11.32 .\) What is \(K_{\mathrm{b}}\) for the hypoiodite ion?
See all solutions

Recommended explanations on Chemistry Textbooks

Inorganic Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemical Analysis

Read Explanation

Chemistry Branches

Read Explanation

Kinetics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.