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Chapter 2: Problem 5

A. Are there \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions present in pure water at neutral \(\mathrm{pH}\) (i.e., at \(\mathrm{pH}\) \(=7.0) ?\) If \(s o,\) 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 \(1 \mathrm{kg} .\).

Short Answer

Expert verified
Yes, \(\mathrm{H}_3\mathrm{O}^+\) ions exist, with a ratio of approximately \(1.8 \times 10^{-9}\).

Step by step solution

01

Understanding the Existence of Hydronium Ions

In pure water at neutral pH (pH = 7), water undergoes a self-ionization process where a small fraction of water molecules dissociates into hydronium ions \(\mathrm{H}_{3}\mathrm{O}^{+}\) and hydroxide ions \(\mathrm{OH}^{-}\). The reaction can be expressed as:\[2\, \mathrm{H}_2\mathrm{O}(l) \rightleftharpoons \mathrm{H}_3\mathrm{O}^+(aq) + \mathrm{OH}^-(aq)\] As the pH of neutral water is 7, the concentration of \(\mathrm{H}_3\mathrm{O}^+\) ions is equal to \(10^{-7}\, \mathrm{mol/L}\).
02

Calculating the Total Number of Water Molecules in 1 Liter

Using the molecular weight of water (18 g/mol), 1 liter of water, weighing 1000 g, contains \[\frac{1000\, \mathrm{g}}{18\, \mathrm{g/mol}} = 55.56\, \mathrm{mol/L}\] of water molecules. Therefore, one liter of water contains \[55.56 \times 6.022 \times 10^{23} = 3.34 \times 10^{25}\] water molecules, where \(6.022 \times 10^{23}\) is Avogadro's number.
03

Calculating the Ratio of Hydronium Ions to Water Molecules

Given that the concentration of \(\mathrm{H}_3\mathrm{O}^+\) ions is \(10^{-7}\, \mathrm{mol/L}\):- The number of \(\mathrm{H}_3\mathrm{O}^+\) ions in 1 liter is \(10^{-7}\times 6.022 \times 10^{23} = 6.022 \times 10^{16}\) ions.The ratio of \(\mathrm{H}_3\mathrm{O}^+\) ions to \(\mathrm{H}_2\mathrm{O}\) molecules is then \[\frac{6.022 \times 10^{16}}{3.34 \times 10^{25}} \approx 1.8 \times 10^{-9}\]

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Key Concepts

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

Self-Ionization of Water
Water, even in its pure form, has a fascinating ability to undergo a process called self-ionization. This process involves a small percentage of naturally occurring water molecules to break apart or dissociate. During this dissociation, one molecule transfers a proton to another, resulting in the formation of a hydronium ion (\(\mathrm{H}_3\mathrm{O}^+\)) and a hydroxide ion (\(\mathrm{OH}^-\)). This reaction can be represented as:
  • \(2\, \mathrm{H}_2\mathrm{O}(l) \rightleftharpoons \mathrm{H}_3\mathrm{O}^+(aq) + \mathrm{OH}^-(aq)\)
Although this reaction may seem straightforward, it is important to note that it is reversible and both types of ions coexist in equilibrium. This is the reason why even pure water can conduct a slight electrical current.
Neutral pH
The concept of pH is a simplified scale that measures the acidity or basicity of a solution. A neutral pH means a balance, typically found at pH 7. At this point, the concentration of hydronium ions \(\left(\mathrm{H}_3\mathrm{O}^+\right)\) in the solution is exactly equal to that of hydroxide ions \(\left(\mathrm{OH}^-\right)\).
In pure water, at neutral pH, the concentration of these ions is \(1 \times 10^{-7}\, \mathrm{mol/L}\). This balanced presence of ions is key to the neutrality of water, where neither acidic nor basic characteristics dominate. Because pH 7 is the midpoint on the pH scale, it underscores the idea that pure water is neither acidic nor alkaline.
Water Molecules
Water molecules, chemically represented as \(\mathrm{H}_2\mathrm{O}\), consist of two hydrogen atoms bonded to one oxygen atom. The molecular weight of water is 18 grams per mole. This property is vital because it helps us understand how many water molecules are present in a given quantity of water. For example, in a liter of water weighing approximately 1000 grams, there are about 55.56 moles of water.
  • The number of molecules can be calculated using Avogadro's number, \(6.022 \times 10^{23}\), which tells us there are approximately \(3.34 \times 10^{25}\) water molecules in a single liter.
These numbers are crucial for comparing the amounts of different particles in water, such as calculating the ratio of hydronium ions to water molecules, emphasizing how incredibly vast the structure of water is, even at its purest.

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Most popular questions from this chapter

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. How many different molecules composed of (a) two, (b) three, and (c) four amino acids, linked together by peptide bonds, can be made from the set of 20 naturally occurring amino acids? B. Assume you were given a mixture consisting of one molecule each of all possible sequences of a smallish protein of molecular mass 4800 daltons. If the average molecular mass of an amino acid is, say, 120 daltons, how much would the sample weigh? How big a container would you need to hold it? C. What does this calculation tell you about the fraction of possible proteins that are currently in use by living organisms (the average molecular mass of proteins is about 30,000 daltons)?

Why do you suppose only L-amino acids and not a random mixture of the \(\mathrm{L}\) - and \(\mathrm{D}\) -forms of each amino acid are used to make proteins?

Which of the following statements are correct? Explain your answers. A. Proteins are so remarkably diverse because each is made from a unique mixture of amino acids that are linked in random order. B. Lipid bilayers are macromolecules that are made up mostly of phospholipid subunits. C. Nucleic acids contain sugar groups. D. Many amino acids have hydrophobic side chains. E. The hydrophobic tails of phospholipid molecules are repelled from water. F. DNA contains the four different bases \(A, G, U,\) and \(C\).

Which of the following statements are correct? Explain your answers. A. An atomic nucleus contains protons and neutrons. B. An atom has more electrons than protons. C. The nucleus is surrounded by a double membrane. D. All atoms of the same element have the same number of neutrons. E. The number of neutrons determines whether the nucleus of an atom is stable or radioactive. F. Both fatty acids and polysaccharides can be important energy stores in the cell. G. Hydrogen bonds are weak and can be broken by thermal energy, yet they contribute significantly to the specificity of interactions between macromolecules.
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