/*! 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 5 A. Are there any \(\mathrm{H}_{3... [FREE SOLUTION] | 91Ó°ÊÓ

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A. Are there any \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions present in pure water at neutral \(\mathrm{pH}\) (i.e., at \(p H=7.0) ?\) If \(s 0,\) how are they formed? B. If they exist, what is the ratio of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions to \(\mathrm{H}_{2} \mathrm{O}\) molecules at neutral pH? (Hint: the molecular weight of water is \(18,\) and 1 liter of water weighs 1 kg.

Short Answer

Expert verified
Yes, hydronium ions exist in pure water. The ratio of \( ext{H}_3 ext{O}^+\) to \( ext{H}_2 ext{O}\) is approximately \\(1.8 \times 10^{-9}\\).

Step by step solution

01

Understanding Pure Water at Neutral pH

In pure water at neutral pH (pH = 7.0), there are \( ext{H}_2 ext{O}\) molecules in equilibrium. This equilibrium involves a self-ionization process where water molecules (\( ext{H}_2 ext{O}\)) dissociate into hydroxide ions (\( ext{OH}^-\)) and hydronium ions (\( ext{H}_3 ext{O}^+\)). This means that hydronium ions \(\text{H}_3\text{O}^+\) are indeed present in pure water at neutral pH.
02

Formation of Hydronium Ions

The formation of hydronium ions is a result of the self-ionization of water. This is represented by the chemical equation: \( ext{2 H}_2 ext{O} ightleftharpoons ext{OH}^- + ext{H}_3 ext{O}^+\). Both ions are present at a very low concentration due to this dissociation, which occurs naturally in water.
03

Calculating the Concentration of \\(\text{H}_3\text{O}^+\\) Ions

At neutral pH (pH = 7), the concentration of hydronium ions (\([\text{H}_3\text{O}^+]\)) in water is \(10^{-7}\, ext{mol/L}\). This concentration results from the relationship \([\text{H}^+] = 10^{-\text{pH}}\)\, where pH = 7 in this scenario.
04

Calculating the Number of Water Molecules in 1 Liter

Since the molecular weight of water is 18 g/mol, 1 liter of water (1000 g) contains \(\frac{1000}{18}\approx 55.56\) moles of \(\text{H}_2 ext{O}\). Each mole contains \(6.022 \times 10^{23}\) molecules (Avogadro's number), so \( \approx 3.34 \times 10^{25}\) water molecules are present in 1 liter.
05

Determining the Ratio of \\(\text{H}_3\text{O}^+\\) Ions to \\(\text{H}_2\text{O}\\) Molecules

With \(10^{-7}\, ext{mol/L}\) of hydronium ions and approximately \(3.34 \times 10^{25}\) water molecules per liter, the number of hydronium ions is \(10^{-7} imes 6.022 \times 10^{23} \approx 6.022 \times 10^{16}\). The ratio of \(\text{H}_3\text{O}^+\) ions to \(\text{H}_2\text{O}\) molecules is \(\frac{6.022 \times 10^{16}}{3.34 \times 10^{25}}\), which simplifies to \(\approx 1.8 \times 10^{-9}\).

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Key Concepts

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

Hydronium Ions Formation
In pure water, hydronium ions (\(\text{H}_3\text{O}^+\)) are indeed present, even in neutral conditions. The presence of these ions is due to a fascinating process known as autoionization or self-ionization. During this process, two water molecules interact in such a way that one water molecule donates a proton (\(\text{H}^+\)) to another water molecule. This exchange transforms one water molecule into a hydronium ion and the other into a hydroxide ion (\(\text{OH}^-\)). As a result, hydronium ions and hydroxide ions are present at equal and very low concentrations in pure water, contributing to its natural acidic and basic balance.
Self-Ionization of Water
Pure water undergoes a simple, yet critical chemical reaction known as self-ionization. This reaction is expressed by the equation:\[2 \text{H}_2\text{O} \rightleftharpoons \text{OH}^- + \text{H}_3\text{O}^+\]This equation indicates that two water molecules can reversibly form a hydroxide ion and a hydronium ion. This self-ionization process occurs spontaneously in pure water and is a key reason why pure water has a neutral pH. The balance between hydronium and hydroxide ions signifies that the water is neither too acidic nor too basic, maintaining a pH value of exactly 7.0.
Concentration Calculation
At neutral pH 7, the concentration of hydronium ions in pure water is an intriguing concept. It is known to be \(10^{-7} \,\text{mol/L}\).This can be calculated by understanding the relationship:\[[\text{H}^+] = 10^{-\text{pH}}\]Given that pH equates to 7 in pure water, substituting we derive:\( [\text{H}_3\text{O}^+] = 10^{-7} \,\text{mol/L}\).This low concentration reflects the tiny, yet constant level of ionization occurring in water, necessary for equilibrium in such a neutral solution as water.
Molecular Weight of Water
The molecular weight of water is a basic but vital measure in chemistry, pegged at 18 g/mol. This measurement aids us in determining the number of bonds and atoms within a molecule. For water, each molecule contains two hydrogen atoms and one oxygen atom.When calculating the number of molecules in a given volume, such as 1 liter of water weighing 1000 grams, the molecular weight guides us to find out how many moles that liter contains. By dividing the weight (in grams) by the molecular weight, \( \frac{1000\,\text{g}}{18\,\text{g/mol}} \approx 55.56\,\text{mol} \),we understand that about 55.56 moles of water is present. In terms of actual \(\text{H}_2\text{O}\) molecules, by applying Avogadro’s number \(6.022 \times 10^{23}\), we ascertain there are approximately \(3.34 \times 10^{25}\) \(\text{H}_2\text{O}\) molecules in a liter of water.

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Most popular questions from this chapter

To gain a better feeling for atomic dimensions, assume that the page on which this question is printed is made entirely of the polysaccharide cellulose, whose molecules are described by the formula \(\left(\mathrm{C}_{n} \mathrm{H}_{2 n} \mathrm{O}_{n}\right),\) where \(n\) can be a quite large number and is variable from one molecule to another. The atomic weights of carbon, hydrogen, and oxygen are \(12,1,\) and \(16,\) respectively, and this page weighs \(5 \mathrm{g}\) A. How many carbon atoms are there in this page? B. In cellulose, how many carbon atoms would be stacked on top of each other to span the thickness of this page (the size of the page is \(21.2 \mathrm{cm} \times 27.6 \mathrm{cm},\) and it is \(0.07 \mathrm{mm}\) thick)? C. Now consider the problem from a different angle. Assume that the page is composed only of carbon atoms. A carbon atom has a diameter of \(2 \times 10^{-10} \mathrm{m}(0.2 \mathrm{nm}) ;\) how many carbon atoms of \(0.2 \mathrm{nm}\) diameter would it take to span the thickness of the page? D. Compare your answers from parts \(\mathrm{B}\) and \(\mathrm{C}\) and explain any differences.

A carbon atom contains six protons and six neutrons. A. What are its atomic number and atomic weight? B. How many electrons does it have? C. How many additional electrons must it add to fill its outermost shell? How does this affect carbon's chemical behavior? D. Carbon with an atomic weight of 14 is radioactive. How does it differ in structure from nonradioactive carbon? How does this difference affect its chemical behavior?

In principle, there are many different, chemically diverse ways in which small molecules can be linked to form polymers. For example, the small molecule ethene \(\left(\mathrm{CH}_{2}=\mathrm{CH}_{2}\right)\) is used commercially to make the plastic polyethylene \(\left(\ldots-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\right.\) \(\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\ldots .\) ). The individual subunits of the three major classes of biological macromolecules, however, are all linked by similar reaction mechanisms, i.e., by condensation reactions that eliminate water. Can you think of any benefits that this chemistry offers and why it might have been selected in evolution?

The elements oxygen and sulfur have similar chemical properties because they both have six electrons in their outermost electron shells. Indeed, both elements form molecules with two hydrogen atoms, water \(\left(\mathrm{H}_{2} \mathrm{O}\right)\) and hydrogen sulfide \(\left(\mathrm{H}_{2} \mathrm{S}\right)\). Surprisingly, at room temperature, water is a liquid, yet \(\mathrm{H}_{2} \mathrm{S}\) is a gas, despite sulfur being much larger and heavier than oxygen. Explain why this might be the case.

A. Describe the similarities and differences between van der Waals attractions and hydrogen bonds. B. Which of the two bonds would form (a) between two hydrogens bound to carbon atoms, (b) between a nitrogen atom and a hydrogen bound to a carbon atom, and (c) between a nitrogen atom and a hydrogen bound to an oxygen atom?

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