Water autoionization and Kw
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- Water can undergo autoionization to form H3O+H, start subscript, 3, end subscript, O, start superscript, plus, end superscript and OH−O, H, start superscript, minus, end superscript ions.
- The equilibrium constant for the autoionization of water, KwK, start subscript, w, end subscript, is 10−1410, start superscript, minus, 14, end superscript at 25∘C25, space, degree, C.
- In a neutral solution, [H3O+]=[OH−]open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket, equals, open bracket, O, H, start superscript, minus, end superscript, close bracket
- In an acidic solution, [H3O+]>[OH−]open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket, is greater than, open bracket, O, H, start superscript, minus, end superscript, close bracket
- In a basic solution, [OH−]>[H3O+]open bracket, O, H, start superscript, minus, end superscript, close bracket, is greater than, open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket
For aqueous solutions at 25 C the following relationship are always true.
∘C25, space, degree, C, the following relationships are always true:∘C25, space, degree, C, the following relationships are always true:∘C25, space, degree, C, the following relationships are always true:∘C25, space, degree, C, the following relationships are always true:25\,^\circ\text{C25
25, space, degree, C
∘C25, space, degree, C, the following relationships are always true:∘C25, space, degree, C, the following relationships are always true:∘C25, space, degree, C, the following relationships are always true:∘C25, space, degree, C, the following relationships are always true:25\,^\circ\text{C25
25, space, degree, C
Kw=[H3O+][OH−]=10−14K, start subscript, w, end subscript, equals, open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket, open bracket, O, H, start superscript, minus, end superscript, close bracket, equals, 10, start superscript, minus, 14, end superscriptpH+pOH=14p, H, plus, p, O, H, equals, 14
- The contribution of the autoionization of water to [H3O+]open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket and [OH−]open bracket, O, H, start superscript, minus, end superscript, close bracketbecomes significant for extremely dilute acid and base solutions.
Autoionization of water
Since acids and bases react with each other, this implies that water can react with itself! While that might sound strange, it does happen−minuswater molecules exchange protons with one another to a very small extent. We call this process the autoionization, or self-ionization, of water.
The proton exchange can be written as the following balanced equation:
H2O(l)+H2O(l)⇌H3O+(aq)+OH−(aq)
One water molecule is donating a proton and acting as a Bronsted-Lowry acid, while another water molecule accepts the proton, acting as a Bronsted-Lowry base. This results in the formation of hydronium and hydroxide ions in a 1:11, colon, 1molar ratio. For any sample of pure water, the molar concentrations of hydronium, H3O+H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, and hydroxide, OH−O, H, start superscript, minus, end superscript, must be equal:
[H3O+]=[OH−] in pure water
The autoionization constant, KwK, start subscript, w, end subscript
The expression for the autoionization constant is
Kw=[H3O+][OH−](Eq. 1)K, start subscript, w, end subscript, equals, open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket, open bracket, O, H, start superscript, minus, end superscript, close bracket, space, space, left parenthesis, E, q, point, space, 1, right parenthesis
Remember that when writing equilibrium expressions, the concentrations of solids and liquids are not included. Therefore, our expression for KwK, start subscript, w, end subscript does not include the concentration of water, which is a pure liquid.
We can calculate the value of KwK, start subscript, w, end subscript at 25∘C25, space, degree, C using [H3O+]open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket, which is related to the pHp, H of water. At 25∘C25, space, degree, C, the pHp, H of pure water is 77. Therefore, we can calculate the concentration of hydronium ions in pure water:
[H3O+]=10−pH=10−7 M at 25∘Copen bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket, equals, 10, start superscript, minus, p, H, end superscript, equals, 10, start superscript, minus, 7, end superscript, space, M, space, space, a, t, space, 25, space, degree, C
In the last section, we saw that hydronium and hydroxide form in a 1:11, colon, 1 molar ratio during the autoionization of pure water. We can use that relationship to calculate the concentration of hydroxide in pure water at 25∘C25, degree, C:
[OH−]=[H3O+]=10−7 M at 25∘Copen bracket, O, H, start superscript, minus, end superscript, close bracket, equals, open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket, equals, 10, start superscript, minus, 7, end superscript, space, M, space, space, a, t, space, 25, space, degree, C
This is a little tough to visualize, but 10−710, start superscript, minus, 7, end superscript is an extremely small number! Within a sample of water, only a small fraction of the water molecules will be in the ionized form.
Now that we know [OH−]open bracket, O, H, start superscript, minus, end superscript, close bracket and [H3O+]open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket, we can use these values in our equilibrium expression to calculate KwK, start subscript, w, end subscript at 25∘C25, degree, C:
Kw=(10−7)×(10−7)=10−14 at 25∘C
Relationship between the autoionization constant, pHp, H, and pOHp, O, H
The fact that KwK, start subscript, w, end subscript is equal to 10−1410, start superscript, minus, 14, end superscript at 25∘C25, space, degree, C leads to an interesting and useful new equation. If we take the negative logarithm of both sides of Eq. 1E, q, point, space, 1 in the previous section, we get the following:
−logKw=−log([H3O+][OH−])=−(log[H3O+]+log[OH−])=−log[H3O+]+(−log[OH−])=pH+pOH
We can abbreviate −logKwminus, log, K, start subscript, w, end subscript as pKwp, K, start subscript, w, end subscript, which is equal to 1414 at 25∘C25, space, degree, C:
pKw=pH+pOH=14 at 25∘C(Eq. 2)p, K, start subscript, w, end subscript, equals, p, H, plus, p, O, H, equals, 14, space, space, a, t, space, 25, space, degree, C, space, space, left parenthesis, E, q, point, space, 2, right parenthesis
Therefore, the sum of pHp, H and pOHp, O, H will always be 1414 for any aqueous solution at 25∘C25, space, degree, C. Keep in mind that this relationship will not hold true at other temperatures, because KwK, start subscript, w, end subscript is temperature dependent!
Definitions of acidic, basic, and neutral solutions
We have seen that the concentrations of H3O+H, start subscript, 3, end subscript, O, start superscript, plus, end superscript and OH−O, H, start superscript, minus, end superscript are equal in pure water, and both have a value of 10−7 M10, start superscript, minus, 7, end superscript, space, M at 25∘C25, space, degree, C. When the concentrations of hydronium and hydroxide are equal, we say that the solution is neutral. Aqueous solutions can also be acidic or basic depending on the relative concentrations of H3O+H, start subscript, 3, end subscript, O, start superscript, plus, end superscript and OH−O, H, start superscript, minus, end superscript.
- In a neutral solution, [H3O+]=[OH−]open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket, equals, open bracket, O, H, start superscript, minus, end superscript, close bracket
- In an acidic solution, [H3O+]>[OH−]open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket, is greater than, open bracket, O, H, start superscript, minus, end superscript, close bracket
- In a basic solution, [OH−]>[H3O+]
Autoionization and Le Chatelier's principle
We also know that in pure water, the concentrations of hydroxide and hydronium are equal. Most of the time, however, we are interested in studying aqueous solutions containing other acids and bases. In that case, what happens to [H3O+]open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket and [OH−]open bracket, O, H, start superscript, minus, end superscript, close bracket?The moment we dissolve other acids or bases in water, we change [H3O+]open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracketand/or [OH−]open bracket, O, H, start superscript, minus, end superscript, close bracket such that the product of the concentrations is no longer is equal to KwK, start subscript, w, end subscript. That means the reaction is no longer at equilibrium. In response, Le Chatelier's principle tells us that the reaction will shift to counteract the change in concentration and establish a new equilibrium.For example, what if we add an acid to pure water? While pure water at 25∘C25, space, degree, Chas a hydronium ion concentration of 10−7M10, start superscript, minus, 7, end superscript, space, M, the added acid increases the concentration of H3O+H, start subscript, 3, end subscript, O, start superscript, plus, end superscript. In order to get back to equilibrium, the reaction will favor the reverse reaction to use up some of the extra H3O+H, start subscript, 3, end subscript, O, start superscript, plus, end superscript. This causes the concentration of OH−O, H, start superscript, minus, end superscript to decrease until the product of [H3O+]open bracket, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, close bracket and [OH−]open bracket, O, H, start superscript, minus, end superscript, close bracket is once again equal to 10−1410, start superscript, minus, 14, end superscript.Once the reaction reaches its new equilibrium state, we know that:- [H+]>[OH−]open bracket, H, start superscript, plus, end superscript, close bracket, is greater than, open bracket, O, H, start superscript, minus, end superscript, close bracket because the added acid increased [H+]open bracket, H, start superscript, plus, end superscript, close bracket. Thus, our solution is acidic!
- [OH−]<10−7Mopen bracket, O, H, start superscript, minus, end superscript, close bracket, is less than, 10, start superscript, minus, 7, end superscript, space, M because favoring the reverse reaction decreased [OH−]open bracket, O, H, start superscript, minus, end superscript, close bracketto get back to equilibrium.
The important thing to remember is that any aqueous acid-base reaction can be described as shifting the equilibrium concentrations for the autoionization of water. This is really useful, because that means we can apply Eq. 1 and Eq. 2to all aqueous acid-base reactions, not just pure water!
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