To understand the autoionization reaction of liquid water. To recognize the partnership among pH, pOH, and (pK_w).

You are watching: Write the expression for the ion-product constant for water, kw.


As you learned previously acids and bases can be identified in numerous various methods (Table (PageIndex1)). Respeak to that the Arrhenius meaning of an acid is a substance that dissociates in water to develop (H^+) ions (protons), and also an Arrhenius base is a substance that dissociates in water to create (OH^−) (hydroxide) ions. According to this view, an acid–base reactivity requires the reaction of a proton with a hydroxide ion to form water. Although Brønsted and Lowry characterized an acid similarly to Arrhenius by describing an acid as any kind of substance that have the right to donate a proton, the Brønsted–Lowry interpretation of a base is much more general than the Arrhenius meaning. In Brønsted–Lowry terms, a base is any kind of substance that can accept a proton, so a base is not limited to simply a hydroxide ion. This indicates that for eincredibly Brønsted–Lowry acid, tbelow exists a corresponding conjugate base with one fewer proton. Consequently, all Brønsted–Lowry acid–base reactions actually involve two conjugate acid–base pairs and the carry of a proton from one substance (the acid) to another (the base). In comparison, the Lewis meaning of acids and also bases, focuses on accepting or donating pairs of electrons quite than protons. A Lewis base is an electron-pair donor, and a Lewis acid is an electron-pair acceptor.

Table (PageIndex1): Definitions of Acids and Bases DefinitionAcidsBases
Arrhenius (H^+) donor (OH^−) donor
Brønsted–Lowry (H^+) donor (H^+) acceptor
Lewis electron-pair acceptor electron-pair donor

Since this chapter faces acid–base equilibria in aqueous solution, our conversation will use generally the Brønsted–Lowry interpretations and nomenclature. Remember, however, that all three interpretations are just different methods of looking at the exact same type of reaction: a proton is an acid, and also the hydroxide ion is a base—no issue which definition you use. In exercise, thedesigningfairy.comists tend to use whichever definition is most advantageous to make a particular suggest or understand a provided system. If, for example, we describe a base as having one or even more lone pairs of electrons that deserve to accept a proton, we are ssuggest combining the Lewis and Brønsted–Lowry definitions to emphasize the characteristic properties of a base.


Acid–Base Properties of Water

Respeak to that bereason of its extremely polar framework, liquid water have the right to act as either an acid (by donating a proton to a base) or a base (by utilizing a lone pair of electrons to accept a proton). For example, once a solid acid such as HCl dissolves in water, it dissociates into chloride ions ((Cl^−)) and also proloads ((H^+)). The proton, in turn, reacts through a water molecule to develop the hydronium ion ((H_3O^+)):

In this reaction, (HCl) is the acid, and also water acts as a base by accepting an (H^+) ion. The reaction in Equation ef16.3.1a is often created in a less complicated form by rerelocating (H_2O) from each side:

< HCl_(aq) ightarrow H^+_(aq) + Cl^-_(aq) label16.3.1b>

In Equation ef16.3.1b, the hydronium ion is stood for by (H^+), although free (H^+) ions perform not exist in liquid water as this reactivity demonstrates:

< H^+_(aq) + H_2O_(l) ightarrow H_3O^+_(aq)>

Water deserve to likewise act as an acid, as presented in Equation ef16.3.2. In this equilibrium reactivity, (H_2O) donates a proton to (NH_3), which acts as a base:

Water is thus termed amphiprotic, interpretation that it can behave as either an acid or a base, relying on the nature of the other reactant. Notice that Equation ( ef16.3.2) is an equilibrium reaction as shown by the double arrow and also for this reason has actually an equilibrium consistent associated through it.


The Ion-Product Constant of Liquid Water

Due to the fact that water is amphiprotic, one water molecule can react via an additional to create an (OH^−) ion and also an (H_3O^+) ion in an autoionization process:

<2H_2O_(l) ightleftharpoons H_3O^+_(aq)+OH^−_(aq) label16.3.3>

The equilibrium consistent (K) for this reactivity have the right to be written as follows:

(1)^2= label16.3.4>

wright here (a) is the task of a varieties. Since water is the solvent, and the solution is assumed to be dilute, the task of the water is approximated by the activity of pure water, which is identified as having actually a value of 1. The activity of each solute is approximated by the molarity of the solute. In this reaction, one water molecule acts as an acid and one water molecule acts as a base. Therefore, this reaction actually have the right to be designated as the (K_a) of water and as the (K_b) of water. It is many common, however, to designate this reaction and the associated regulation of mass activity as the (K_w) of water:

label16.3.5>

When pure liquid water is in equilibrium through hydronium and hydroxide ions at 25 °C, the concentrations of the hydronium ion and also the hydroxide ion are equal:

< = = 1.003 imes 10^−7; M label16.3.6>

Therefore the number of dissociated water molecules is very tiny indeed, approximately 2 ppb.

Substituting the values for () and also () at 25 °C right into this expression

Hence, to 3 considerable figures, (K_w = 1.01 imes 10^−14) at room temperature, and label16.3.7b>.

Like any type of various other equilibrium constant, (K_w) varies through temperature, ranging from (1.15 imes 10^−15) at 0 °C to (4.99 imes 10^−13) at 100 °C.

In pure water, the concentrations of the hydronium ion and the hydroxide ion are equal, and the solution is therefore neutral. If ( > ), but, the solution is acidic, whereas if (

The Relationship among pH, pOH, and also (pK_w)

The pH range is a concise way of describing the (H_3O^+) concentration and hence the acidity or basicity of a solution. Recall that pH and also the (H^+) ((H_3O^+)) concentration are connected as follows:

label16.3.8>

<=10^−pH label16.3.9>

Since the scale is logarithmic, a pH distinction of 1 between two remedies coincides to a distinction of a factor of 10 in their hydronium ion concentrations. Recontact also that the pH of a neutral solution is 7.00 (( = 1.0 imes 10^−7; M)), whereas acidic options have actually pH 1.0 imes 10^−7)) and basic services have pH > 7.00 (corresponding to ( Zero is the the majority of acidic and also fourteen is the many standard on the pH scale. Zero is the a lot of basic and fourteenager is the many acidic on the pOH range. What Is A Plus Or Minus Score Used For In English Literature?

B

Equation ef16.3.6b reflects that (K_w = ). Since ( = ) in a neutral solution, we have the right to let (x = = ):

<eginalign* K_w &= \<4pt> &=(x)(x)=x^2 \<4pt> x&=sqrtK_w \<4pt> &=sqrt4.99 imes 10^−13 \<4pt> &=7.06 imes 10^−7; M endalign*>

Because (x) is equal to both () and also (),

<eginalign* pH &= pOH = −log(7.06 imes 10^−7) \<4pt> &= 6.15 ,,, ext(to two decimal places) endalign* >

We might attain the same answer even more conveniently (without utilizing logarithms) by using the (pK_w). In this situation, we recognize that (pK_w = 12.302), and also from Equation ef16.3.12, we understand that (pK_w = pH + pOH). Because (pH = pOH) in a neutral solution, we deserve to usage Equation ef16.3.12 straight, setting (pH = pOH = y). Solving to 2 decimal areas we acquire the following:

<eginalign* pK_w &= pH + pOH \<4pt> &= y + y \<4pt> &= 2y \<4pt> y &=dfracpK_w2 \<4pt> &=dfrac12.3022 \<4pt> &=6.15 =pH=pOH endalign*>





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