Autoionization of Water and pH

We saw previously that water acts as a base when it reacts with HCl and as an acid when it reacts with NH3  

Water is amphoteric, it can act as either an acid or a base. Even when pure, water acts as an acid and a base with itself, a process called autoionization  

The equilibrium constant for this reaction is the product of the concentration of the two ions  

This equilibrium constant is caUed the ion product constant for water (X ) (sometimes called the dissociation constant for water). At 25 °C, K = 1.0 X lO . In pure water, since H2O is the only source of these ions, the concentrations of and OH are equal, and the solution is neutral. Since the concentrations are equal, we can easily calculate them from 

An acidic solution contains an acid that creates additional H30 ions, causing [H30 ] to increase. However, the ion product constant still applies  

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A full calculation of the pH of amphoteric ion salts is complicated. To determine the H" concentration, we must take into account the acid and base equilibria, the autoionization of water, and the charge and material balance—five equations in all for the five unknown concentrations ([H ], [OH ], [CO3 ], [HCO3], and [H2CO3]). With a few approximations, however, it can be shown that the pH of an amphoteric salt can be approximated by... 

A sample of vinegar contains 40.0 g of acetic acid (CH3-COOH) per liter of solution. Suppose 1.00 mL is removed and diluted to 1.00 L, and 1.00 mL of that solution is removed and diluted to 1.00 L. Calculate the pH of the resulting solution. [Hint This is a sufficiently dilute solution that the autoionization of water cannot be neglected.)... 

The fu-st step is to identify all the species present in solntion that may affect its pH. Because weak acids ionize to a small extent, at eqnilibrinm the major species present are nonionized HF and some H+ and F ions. Another major species is H2O, but its very small (1.0 X 10 " ) means that water is not a significant contributor to the H+ ion concentration. Therefore, unless otherwise stated, we will always ignore the H+ ions produced by the autoionization of water. Note that we need not be concerned with the OH ions that are also present in solution. The OH concentration can be determined from Equation (15.2) after we have calculated [H+]. 

Comment In both parts (a) and (b), we have neglected the contribution of the autoionization of water to [H ] and [OH ] because 1.0 X 10 M is so small compared with 1.7 X 10 M and 4.6 X 10 M. Also, the calculated pH values may differ slightly from the actual values due to the nonideality of the solution. This wiU be most pronounced in the Ba(OH)2 solution because it is less dilute and because a Ba " ion is highly charged and will interact strongly with other ions in the solution. 

In the previous calculations, we have assumed that the autoionization of water made a negligible contribution to the OH and concentrations, relative to the contribution from the added acid or base. This is true as long as the solution of acid or base is not very dilute. To see this, consider a 1.0 X 10 M in HCl solution at 25°C. Ignoring the autoionization of water, we would calculate the pH assuming that all the [HsO ] in solution comes from the complete ionization of the strong acid HCl ... 

The pH of dilute solutions of weak and strong bases for which the autoionization of water cannot be ignored can be determined by the same procedures used to derive Equations 11.25 and 11.26 for acids. The corresponding equations for dilute weak and strong bases are identical to Equations 11.25 and 11.26, except that is replaced with and jc represents [OH ]. 

A Review of Strong Electroiytes 18-2 The Autoionization of Water 18-3 The pH and pOH Scales 18-4 Ionization Constants for Weak Monoprotic Adds and Bases 18-5 Poly protic Adds 18-6 Solvolysis... 

In biological and medical applications, it is often necessary to study the autoionization of water at 37°C instead of 25°C. Given that K for water is 2.5 X 10 at 37°C, calculate the pH of pure water at this temperature. 

Because strong acids, by definition, completely ionize in solution, and because we can (in nearly all cases) ignore the contribution of the autoionization of water, the concentration of in a strong acid solution is equal to the concentration of the strong acid. For example, a 0.10 M HCl solution has an H30 concenfration of 0.10 M and a pH of 1.00. 

Finding the [OH ] and pH of a strong base solution is relatively straightforward, as shown in Example 15.11. As we did in calculating the [HjO ] in strong acid solutions, we can neglect the contribution of the autoionization of water to the [OH ] and focus solely on the strong base itself. 

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