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7.4.1: Considering Acid–Base Reactions: pH

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    52369
  • It is almost certain that you have heard the term pH, it is another of those scientific terms that have made it into everyday life, yet its scientific meaning is not entirely obvious. For example: why does an increase in pH correspond to a decrease in “acidity” and why does pH change with temperature?135 How do we make sense of pH and use that information to better understand chemical systems?

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    The key idea underlying pH is that water undergoes an acid–base reaction with itself. Recall that this reaction involves the transfer of a proton from one water molecule to another. The proton is never free or “alone”; it is always bonded to an oxygen within another water molecule. Another important point about pH is that the reaction is readily reversible. Under normal conditions (room temperature), the reaction proceeds in both directions. If we look at the reaction, it makes intuitive sense that the reactants on the right (H3O+ and OH) can react together to give two H2O molecules simply because of the interaction of the positive and negative charges, and we have already seen that the forward reaction does occur. This is one of the first examples we have seen of a reaction that goes both forward and backward in the same system. As we will see, all reactions are reversible at the nanoscale (we will consider the implications of this fact in detail in the next chapter). In any sample of pure water, there are three different molecular species: water molecules (H2O), hydronium ions (H3O+), and hydroxide ions (OH), as shown in the figure above. These three species are constantly interacting with each other through the formation of relatively weak H-bonding interactions, which are constantly forming and breaking. Remember, in liquid water, the water molecules are constantly in motion and colliding with one another. Some of these collisions have enough energy to break the covalent H—O bond in water or in the hydronium ion. The result is the transfer of H+ and the formation of a new bond with either another water molecule (to form hydronium ion) or with a hydroxide ion (to form a water molecule). To get a feeling for how dynamic this process is, it is estimated that the average lifetime of an individual hydronium ion is on the order of 1 to 2 picoseconds (1 x 10–12 ps), an unimaginably short period of time. In pure water, at 25 °C, the average concentration of hydronium ions is 1 x 10–7 mol/L. We use square brackets to indicate concentration, so we write this as:

    [H3O+] = 1 x 10–7 M

    Note that this is a very, very, very small fraction of the total water molecules, given that the concentration of water molecules [H2O] in pure water is ~55.4 M.

    In pure water, every time a hydronium ion is produced, a hydroxide ion must also be formed. Therefore, in pure water at 25 °C, the following equation must be true:

    [H3O+] = [OH] = 1 x 10–7 M

    It must also be true that the product of the hydronium and hydroxide ion concentrations, [H3O+][ OH], is a constant at a particular temperature. This constant is a property of water. At 25oC, this constant is 1 x 10–14 and given the symbol Kw, 25oC. So why do we care? Because when we add an acid or a base to a solution of water at 25oC, the product of [H3O+][OH] remains the same: 1 x 10–14. We can use this fact to better understand the behavior of acids, bases, and aqueous solutions.

    For many people, dealing with negative exponents does not come naturally. Their implications and manipulations can be difficult. Believe it or not, the pH scale 136 was designed to make dealing with exponents easier, but it does require that you understand how to work with logarithms (perhaps an equally difficult task). pH is defined as:

    pH = – log [H3O+] 137

    In pure water (at 25oC),where the [H3O+]=1x10–7 M, pH=7 (pH has no units).A solution with a higher concentration of hydronium ions than pure water is acidic, and a solution with a higher concentration of hydroxyl ions is basic. This leads to the counter-intuitive fact that as acidity [H3O+] goes up, pH goes down. See for yourself: calculate the pH of a solution with a [H3O +] of 1x10–2 M (pH=2), and of 1x10–9 M (pH=9). Moreover, because it is logarithmic, a one unit change in pH corresponds to a change in [H3O+] of a factor of 10.

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    The pH scale is commonly thought of as spanning units 1–14, but in fact many of the strongest acid solutions have pH < 1. Representations of the pH scale often use colors to indicate the change in pH. This convention is used because there are many compounds that change color depending on the [H3O ] of the solution in which they are dissolved. For example, litmus138 is red when dissolved in an acidic (pH < 7) solution, and blue when dissolved in a basic (pH > 7) solution. Perhaps you have noticed that when you add lemon juice (acidic) to tea, the color changes. Do not get confused: solutions of acids and bases do not intrinsically differ in terms of color. The color change depends on the nature of molecules dissolved in the solution. Think about how changes in pH might affect molecular structure and, by extension, the interactions between molecules and light (a topic that is more extensively treated in the spectroscopy supplement).

    It is important to note that at 37oC the value of Kw is different: [H3O+][OH] = 2.5 x 10–14 and therefore the pH = 6.8. Weirdly, this does not mean that the solution is acidic, since [H3O+] = [OH]. The effect is small, but it is significant; it means that a pH of 7 does not always mean that a solution is neutral (it depends on the temperature). This is particularly important when the concept of pH is applied to physiological systems, since the body is usually not at room temperature.

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    Now let us consider what happens when we add a Brønsted–Lowry acid to water. For example, if we prepare a solution of 0.10 M HCl (where we dissolve 0.10 mol HCl(g) in enough water to make 1 liter of solution), the reaction that results (see figure) contains more hydronium ion (H3O+). Now if we measure139 the pH of the solution of 0.10 M HCl, we find that it is 1.0 pH units. If we convert back to concentration units from pH (if pH = – log [H3O+], then [H3O+] = 10–pH), we find that the concentration of H3O+ in 0.10 M HCl is 0.10 M. This makes sense, in light of our previous discussion about how HCl completely dissociates into Cl- and H+ (associated with water molecules).

    [HCl] M

    [H2O] M

    [H3O+] M

    [OH] M

    [Cl–] M

    Before reaction After Reaction

    0.10 ~0

    ~55.5 ~55.4

    1.0 x 10–7 ~1.0 x 10–1

    1.0 x 10–7 1.0 x 10–13

    0
    1.0 x 10–1

    This table gives the concentrations of all the species present both before and after the reaction. There are several things to notice about this table. Because the measured pH = 1 and we added 0.1 M (or 10-1 M) HCl, it is reasonable to assume that all the HCl dissociated and that the vast majority of the H3O+ came from the HCl. We can ignore the H3O+ present initially in the water. Why? Because it was six orders of magnitude (0.0000001)(10-7) smaller than the H+ derived from the HCl (10-1). It is rare to see pH measurements with more than three significant figures, so the H3O+ originally present in the water does not have a significant effect on the measured pH value. Although we are not generally concerned about the amount of hydroxide, it is worth noting that [H3O+][OH] remains a constant (Kw), and therefore when [H3O+] increases the [OH] decreases.

    Although a number of substances dissolve in water, not all ionize, and not all substances that ionize alter the pH. For example, NaCl ionizes completely when dissolved in water, yet the pH of this solution is still 7. The Na+ and Cl ions do not affect the pH at all. However, if we make a 1 M solution of ammonium chloride (NH4Cl), we find that its pH is around 5. Although it might not be completely obvious why the pH of this solution is 5 and the pH of a 1M NaCl solution is 7, once you know that it is (and given what you know about pH), you can determine the concentrations of H3O+, NH4+, NH3, OH and Cl present (see Chapter 8). The question is: Why are NH4Cl and HCl so different? (We consider this point in Chapter 9.)

    References

    135 In fact Kw increases with temperature due to Le Chatelier’s principle, about which we will have more to say shortly.

    136 The pH scale was first developed in 1909 by Danish biochemist Soren Sorensen.

    137 In fact, pH is better defined as pH = {H3O+}, where the { } refer to the activity of the species rather than the concentration. This is a topic better left to subsequent courses, although it is important to remember that any resulting calculations on pH using concentrations provide only approximations.

    138 Litmus is a water-soluble mixture of different dyes extracted from lichens, especially Roccella tinctoria— Wikipedia!

    139 pH is typically measured by using a pH meter that measures the differences between the electrical potential of the solution relative to some reference. As the concentration of hydronium ion increases, the voltage (potential between the solution and the reference) changes and can be calibrated and reported as pH.

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