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### Course: AP®︎/College Chemistry > Unit 8

Lesson 1: Introduction to acids and bases# Autoionization of water

In the autoionization of water, a proton is transferred from one water molecule to another to produce a hydronium ion (H₃O⁺) and a hydroxide ion (OH⁻). The equilibrium expression for this reaction is

*Kw*= [H₃O⁺][OH⁻], where*Kw*is the autoionization constant for water. At 25°C, the value of*Kw*is 1.0 x 10⁻¹⁴. In pure water, the concentrations of H₃O⁺ and OH⁻ are equal, and the water is considered to be neutral. Created by Jay.## Want to join the conversation?

- How did you get 1.0*10^-14 for the equilibrium constant equation for [H3O+][OH-]?(4 votes)
- It's just Kw at 25°C. It's a constant which is found in any chemistry textbook's data tables.(9 votes)

- im confused how did you get x=2.5 x 10^-9M(6 votes)
- You know [H3O+] = 4.0 x 10^-6 M and that the solution is at equilibrium at 25°C. Therefore, you also know Kw = 1.0 x 10^-14

So,

Kw = [H3O+][OH-]

[OH-] = Kw/ [H3O+]

[OH-] = (1.0 x 10^-14)/(4.0 x 10^-6)

[OH-] = 2.5 x 10^-9 M

Because [H3O+] > [OH-], the solution is acidic.*(At least it‘s what I understood)*(1 vote)

- why was the concentration of water (left reactants) left out of the equilibrium expression for the autoionization of water?(1 vote)
- Chemicals species which are pure liquids or solids are excluded from equilibrium expressions. Jay mentions this at1:19.

For solids this is physically understood that the concentration of a solid is its density. And since density depends on the identity of a chemical, it does not change. So for simplicity sake they are given a value of 1 in the equilibrium expression and effectively ignored.

For pure liquids the reasoning is similar. The concentration does not change since the solution is primarily composed of that liquid (the solvent). So liquids also have values of 1 and are also ignored.

Hope that helps.(6 votes)

- Why do we need to know this? If I'm going into biology, I don't need to know what a strong acid versus a weak one is, right?(3 votes)
- the equation x squared equals Kw where x is the concentration of H3O and OH can only be used for a neutral solution right? Because otherwise the H3O and OH would have different concentrations?(2 votes)
- Yep, that's correct.(2 votes)

- 1.3:54. How can the solution be acidic / basic if the hydronium and hydroxide are only made with the 1:1 ratio? In the autoionization equation , if 2 moles of water molecule react , there can only be 1mole of hydronium and hydroxide , which means the solution can never be acidic or basic.

2. at3:22how can the one proton be equivalent to one hydronium? It makes no sense. Because , hydronium is consisted of 3 H atom and 1 oxygen atom , but proton is just the one proton , one ion of hydrogen.(1 vote)- Jay is just describing how we define an acid, basic, and neutral solutions. Whether the solutions have more hydronium or hydroxide. Not that these solutions are created by autoionization of water.

If you take the net ionic equation of an acid-base reaction, acids can be simplified to just H^(+). It’s not what is happening of course, but it’s a simplification to make equations more condensed.

Hope that helps.(2 votes)

- 1*10^-14 divided by 4*10^-6 is 2. * 10^-21st. how was thgis answer obtained at5:28(2 votes)
- Looks like you multiplied instead of divided.(0 votes)

- how does the electron thing work ? like why does the hydrogen leave its electron behind ?/(1 vote)
- Oxygen is more electronegative compared to hydrogen so it has an easier time of holding onto electrons. So it's not so much the hydrogen leaving its electrons, it's that the oxygen is taking the electrons.

Hope that helps.(1 vote)

- What will be the concentration of other temperature apart from 25 degree and 50 degree(1 vote)
- The trend is that when temperature increases the ionisation constant of pure water increases. You can search up the actual values(1 vote)

- why would the reaction shift to the right if an increased temperature leads to an increased Kw? Increasing Kw would increase concentrations of OH- and H3O+... so wouldn't that cause the reaction to shift left in favor of H2O + H2O?(1 vote)

## Video transcript

- [Instructor] The
autoionization of water refers to the reaction of water
molecules to form two ions, the hydronium ion, which is H3O+, and the hydroxide ion, which is OH-. Water can function as an acid or a base, and in this reaction, one water molecule functions
as a Bronsted-Lowry acid and donates a proton and another water molecule functions as a Bronsted-Lowry base and accepts a proton. In the reaction, the base takes an H+ ion from the acid and these two electrons are
left behind on this oxygen. Adding an H+ to H2O gives
the hydronium ion H3O+, and taking away an H+ from H2O
gives the hydroxide ion OH-. We can write an equilibrium
constant expression for this reaction. So we would write the equilibrium
constant K is equal to, we would start with our products. We'd have the concentration
of hydronium ions. And since we have a coefficient
of one in front of hydronium in the balanced equation, it'd be the concentration
of hydronium ions raised to the first power times the concentration of hydroxide ions. And once again, there's
a coefficient of one, the balanced equation. So it's the concentration
of hydroxide ions raised to the first power. For the reactants, liquid water is left out of the equilibrium constant expression. Normally we would write KC, where the C stands for concentration for the equilibrium constant, since we're dealing with concentrations. However, this is a special
equilibrium constant expression for the autoionization of water, so instead of writing KC, we're gonna write KW, where W stands for water. KW is equal to 1.0 times
10 to the negative 14 at 25 degrees Celsius, And with such a low value for KW, so this value is much less than one, that tells us at equilibrium, we have an extremely small
concentration of hydronium and hydroxide ions. So mostly we have H2O
molecules at equilibrium. Let's go ahead and solve
for the concentration of hydronium ions and
hydroxide ions at equilibrium. In the balanced equation, there's a coefficient of one in front of both hydronium and hydroxide. Therefore, at equilibrium, these two concentrations are equal. Since we don't know what
those concentrations are, we're gonna represent
it by writing in here X. So this would be X times X is equal to 1.0 times 10 to the negative 14. So we would have X squared is equal to 1.0 times 10 to the negative 14. And taking the square root of both sides, we would find that X is equal to 1.0 times 10 to the negative seven. Therefore, if we had
a sample of pure water at 25 degrees Celsius, the concentration of hydronium ions and the concentration of hydroxide ions would be equal to 1.0 times 10 to the negative seventh molar. Instead of using two water molecules to show the autoionization of water, it's also possible to show it
using only one water molecule. So H2O could break up to form H+ and OH-. So H+, which is the hydrogen ion, is sometimes used
interchangeably with H3O+, which is the hydronium ion. We've just seen that pure
water has a concentration of hydronium ions equal
to the concentration of hydroxide ions. Therefore, pure water
is a neutral substance, and for any aqueous solution
where the concentration of hydronium ion is equal to the concentration of hydroxide ion, we would classify that
as a neutral solution. If an aqueous solution has a concentration of hydronium ions that's
greater than the concentration of hydroxide ions, we would classify the solution
as an acidic solution. And if an aqueous solution
has a concentration of hydronium ions that's
less than the concentration of hydroxide ions, or you could say the
concentration of hydroxide ions is greater than that of hydronium, the solution would be
considered a basic solution. In the equation that we've
already talked about, the concentration of hydronium ions times the concentration of hydroxide ions is equal to KW, which is equal to 1.0
times 10 to the negative 14 at 25 degrees Celsius. This equation is true if you're dealing with an acidic solution, a neutral solution, or a basic solution. And I'll call this equation
the KW equation from now on. Let's say we have an aqueous solution and the concentration of
hydronium ions in the solution is equal to 4.0 times 10
to the negative six molar at 25 degrees Celsius, and our goal is to
calculate the concentration of hydroxide ions in the
solution at 25 degrees Celsius. To solve for the concentration
of hydroxide ion, we can use our KW equation. So we need to plug in
for the concentration of hydronium ion. So that gives us 4.0 times
10 to the negative six times the concentration of hydroxide ion, which we'll just go ahead and make X here, and all that's equal to KW, which is equal to 1.0 times
10 to the negative 14. Solving for X, we find the X is equal to 2.5
times 10 to the negative nine. And since X is equal to the
concentration of hydroxide ion, the concentration of
hydroxide ion is equal to 2.5 times 10 to the negative ninth molar. For this aqueous solution, the concentration of
hydronium ion is greater than the concentration of hydroxide ion. Therefore, this is an acidic solution. So let me go ahead and write that in here. This is an acidic solution. An equilibrium constant is only constant at a specific temperature. For example, at 25 degrees Celsius, KW is equal to 1.0 times
10 to the negative 14. But if you change the temperature, you change the value for KW. At 50 degrees Celsius, KW is equal to 5.5 times
10 to the negative 14. So an increase in temperature
from 25 degrees Celsius to 50 degrees Celsius causes an increase in the value for KW. So increase in temperature
causes an increase in KW. And we can use Le Chatelier's
principle to predict if the autoionization of water
is an endothermic reaction or an exothermic reaction. An increase in KW means
an increased concentration of hydronium ion and
hydroxide ion at equilibrium. Therefore, the net reaction
must have gone to the right to increase the amount of our products. And if we treat heat as a reactant and we increase the temperature, it's as if we've increased the amount of one of our reactants. Therefore, according to
Le Chatelier's principle, the net reaction is
gonna shift to the right to make more of the product. Since that's what we observed by increasing the value for KW, we know that the autoionization of water is an endothermic reaction. If we had put heat on the product side and treated this like
an exothermic reaction, we would've gotten a shift
in the wrong direction. We would've got a shift back to the left. So we know it's not exothermic. Finally, let's calculate the
concentration of hydronium ions and hydroxide ions in
a sample of pure water at 50 degrees Celsius. We can still use the KW equation. So KW is equal to the
concentration of hydronium ions times the concentration of hydroxide ions. However, since the temperature
is now 50 degrees Celsius, we can't use 1.0 times
10 to the negative 14 because that's the KW
at 25 degrees Celsius. We need to use the KW
at 50 degrees Celsius, which is 5.5 times 10 to the negative 14. For the autoionization of water, the mole ratio of hydronium ion to hydroxide ion is one-to-one. Therefore the concentration
of hydronium ion is equal to the concentration
of hydroxide ion. So when we plug in for hydronium, if we say that concentration is X, then the concentration of
hydroxide would also be X. So we have X times X is equal to KW, which is equal to 5.5 times
10 to the negative 14. So X squared is equal to 5.5
times 10 to the negative 14. And to solve for X, we simply take the square
root of both sides. So X is equal to 2.3 times
10 to the negative seven. So the concentration of hydronium ions is equal to the concentration
of hydroxide ions, which is 2.3 times 10 to
the negative seventh molar. Notice that this is a higher concentration than we got at 25 degrees Celsius, which makes sense because the
value for KW has increased. However, since the
concentration of hydronium is still equal to the
concentration of hydroxide ions, pure water is still neutral.