At 50^∘ C, the ion-product constant for H2 O has the value Kw=5.48 ×10^-14 ·(𝐚) What is the pH o

At 50^∘ C, the ion-product constant for H2 O has the value...

At $50^{\circ} \mathrm{C}$, the ion-product constant for $\mathrm{H}_{2} \mathrm{O}$ has the value $K_{w}=5.48 \times 10^{-14} \cdot(\mathbf{a})$ What is the $\mathrm{pH}$ of pure water at $50^{\circ} \mathrm{C} ?$ (b) Based on the change in $K_{w}$ with temperature, predict whether $\Delta H$ is positive, negative, or zero for the autoionization reaction of water: $$ 2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{OH}^{-}(a q) $$

At $50^{\circ} \mathrm{C}$, the ion-product constant for $\mathrm{H}_{2} \mathrm{O}$ has the value $K_{w}=5.48 \times 10^{-14} \cdot(\mathbf{a})$ What is the $\mathrm{pH}$ of pure water at $50^{\circ} \mathrm{C} ?$ (b) Based on the change in $K_{w}$ with temperature, predict whether $\Delta H$ is positive, negative, or zero for the autoionization reaction of water:
$$
2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{OH}^{-}(a q)
$$

Key Concepts

Ion Product Constant (Kw)

The ion product constant for water, denoted as Kw, is the equilibrium constant for the self-ionization (autoionization) of water into hydronium (H3O+) and hydroxide (OH–) ions. It quantitatively describes the extent to which water naturally dissociates and is temperature dependent, meaning its value changes as the temperature changes.

pH Scale

The pH scale is a logarithmic measure of the concentration of hydrogen ions (or hydronium ions) in a solution. It is defined as the negative logarithm (base 10) of the hydronium ion concentration. In pure water that is neutral, where the concentrations of H3O+ and OH– are equal, the pH can be determined directly from the ion product constant of water.

Temperature Dependence of Equilibrium Constants

The equilibrium constant for a reaction can change with temperature, a relationship that is often described by the van't Hoff equation. This equation relates the change in the equilibrium constant with temperature to the standard enthalpy change (?H°) of the reaction. For endothermic reactions, an increase in temperature shifts the equilibrium position to favor products, thereby increasing the equilibrium constant.

Autoionization of Water and Reaction Enthalpy

The autoionization of water is the process by which water molecules react with each other to form hydronium and hydroxide ions. The temperature dependency of its equilibrium constant, Kw, provides insight into the reaction enthalpy (?H). An increase in Kw with temperature indicates that the autoionization reaction is endothermic, meaning it absorbs heat, while a decrease would indicate an exothermic reaction.

Transcript

00:01 Chapter 16, problem 120, the question's asking, at 50 degrees celsius, the iron product constant for h2o has the value of a kw of 5 .4 8 times 10 to negative 14.

00:17 The question is asking what is the ph of pure water at 50 degrees celsius, and then based on the chart change in kw with temperature, predict whether the delta h is positive, negative, or zero.

00:30 For the autoization reaction of water.

00:35 So first for part a, we are trying to find the concentration for our h -i, and we know that kw is equal to your k -a times your kb, which is also equal to your h.

00:50 Ion concentration times your oh minus.

00:54 And also, whenever we're dealing with water, they're equal to the same thing.

00:58 So they're just going to be your kw is equal to x squared.

01:04 So they're giving us a kw.

01:05 It's not just our general kw we use because we're at a different temperature and it changes for water.

01:12 So we're at 5 .48 times 10 to negative 14th and it's equal to x squared.

01:19 So to find x, we just have to take the square root of both sides and x is just equal to 2 .34 times 10 to negative 7.

01:30 And now we just need to find our p.

01:31 So our ph is equal to our negative log of our h ion concentration.

01:38 And like we said earlier, x is our h ion concentration.

01:42 The negative log of our 2 .3 4 times the 10 to negative 7...