The ionization constant for water (Kw) is 9.311 ×10^-14 at 60^∘ C . Calculate [H3 O^+],[OH^-], p

The ionization constant for water (Kw) is 9.311 ×10^-14 at...

Key Concepts

Temperature Dependence of Equilibrium

The equilibrium constant for the autoionization of water, Kw, is not fixed but varies with temperature. As the temperature increases or decreases, the value of Kw changes, which in turn alters the concentrations of hydronium and hydroxide ions in water. This temperature dependence must be taken into account when calculating pH and pOH at temperatures different from the standard 25°C.

Ionization Constant (Kw)

The ionization constant of water, Kw, is a measure of the self-ionization (autoionization) of water into hydronium (H3O+) and hydroxide (OH–) ions. It is defined as the product of their molar concentrations ([H3O+][OH–]). This constant is temperature dependent, meaning its value changes as the temperature of water changes, which in turn affects the acid-base properties of water.

Autoionization of Water

Autoionization of water refers to the process by which water molecules react with each other to form hydronium and hydroxide ions. In pure water, this process establishes an equilibrium where the concentrations of these ions are equal. The equilibrium is represented by the equation H2O ? H+ + OH– (often written as H3O+ for the protonated water), and its extent is described by the constant Kw.

Relationship Between [H3O+] and [OH–] in Pure Water

In pure water, the autoionization reaction produces equal amounts of hydronium and hydroxide ions, which means that [H3O+] is equal to [OH–]. This equality simplifies many calculations in acid-base chemistry, allowing the use of the square root of Kw to determine the concentration of each ion at equilibrium.

pH and pOH

pH and pOH are logarithmic measures of the concentrations of hydronium and hydroxide ions, respectively. pH is defined as -log[H3O+], and pOH is defined as -log[OH–]. These scales are used to quantify the acidity and basicity of a solution, and they are related through the equation pH + pOH = pKw, where pKw is the negative logarithm of the ionization constant, reflecting the balance between the two ions.

Transcript

00:01 Problem 17 from chapter 14 is asking us to calculate the hydronium and hydroxide ion concentrations, the ph, and p -o -h for pure water at 60 degrees celsius.

00:14 So because we're talking about pure water, that must mean that the solution is neutral, meaning that the hydronium and hydroxide ion concentrations are going to be the same.

00:26 So we are given the ionization constant, which is 9 .310.

00:31 1 times 10 to minus 14.

00:33 And to solve for the hydronium and hydroxide ion concentrations, what we need to do is just go ahead and plug in our ionization constant and take the square root of that.

00:46 And that is because our hydronium ions and our hydroxide ions are in the same concentration.

00:54 So it is the same as writing hydronium squared or the same as writing hydroxide squared because they are of the same concentration and they're being multiplied against each other saying the same thing.

01:27 So all we need to do is go ahead and plug in our ionization constant 9 .311 times 10 to the minus 14 and you you can choose whichever ion you like with this part, because they will be the same value.

02:02 So that's squared.

02:03 So all we need to do to find out the, actually we'll do this, just so we know that it's the answer for both of these.

02:26 I'm not going to fix that a little bit.

02:29 Okay, that's squared as well.

02:31 And all i need to do is take the square root of this value of our ionization constant.

02:39 And that gives us 3 .05 times 10 to the minus 7 moles per liter for each hydrogenium and hydroxide.

03:02 Great...