Like all equilibrium constants, Kw varies somewhat with temperature. Given that Kw is 7.51×10−13 at some temperature, compute

the pH of a neutral aqueous solution at that temperature.

To compute the pH of a neutral aqueous solution at a given temperature, we need to find the concentration of hydrogen ions (H+) or hydroxide ions (OH-) in the solution.

At equilibrium, in a neutral solution, the concentration of hydrogen ions (H+) is equal to the concentration of hydroxide ions (OH-). This can be represented as [H+] = [OH-].

The value of the equilibrium constant for water (Kw) is equal to the product of the concentrations of hydrogen ions and hydroxide ions in water. At 25 degrees Celsius, Kw is equal to 1.0 × 10^-14.

However, in this case, we are given that Kw is 7.51 × 10^-13 at some temperature. Since Kw remains proportional to the concentration of hydrogen ions and hydroxide ions, we can set up the following equation:

Kw = [H+][OH-]
7.51 × 10^-13 = [H+][OH-]

Since the solution is neutral, [H+] = [OH-]. We can substitute [H+] for [OH-]:

7.51 × 10^-13 = [H+]^2

Taking the square root of both sides:

[H+] = sqrt(7.51 × 10^-13)

[H+] = 8.66 × 10^-7

Now, to find the pH of the solution, we use the formula:

pH = -log[H+]

pH = -log(8.66 × 10^-7)

pH ≈ 6.06

Therefore, at the given temperature, the pH of the neutral aqueous solution would be approximately 6.06.

To compute the pH of a neutral aqueous solution at a given temperature, we need to understand the concept of the ion product of water (Kw) and its relationship with pH.

The ion product of water (Kw) is the equilibrium constant for the self-ionization of water. It is defined as the product of the concentration of hydrogen ions (H+) and hydroxide ions (OH-) in water.
The general equation for the self-ionization of water is as follows:
2H2O ⇌ H3O+ + OH-

At 25°C, the value of Kw is 1.0 x 10^-14. However, you have stated that at the given temperature, Kw is 7.51 x 10^-13. This indicates that the solution is not neutral but slightly acidic.

To compute the pH of a neutral aqueous solution, we need to know the concentration of hydrogen ions (H+). In neutral solutions, the concentration of H+ is equal to the concentration of OH-, and their product (H+ concentration multiplied by OH- concentration) is equal to Kw.

Therefore, to find the pH, we can use the equation:
pH = -log[H+]

Since the solution is neutral, [H+] = [OH-], and at equilibrium, their product is equal to Kw:
[H+][OH-] = Kw

Given that Kw = 7.51 x 10^-13, we can find the concentration of H+ (and OH-) from this equation.

First, take the square root of Kw to get [H+] or [OH-]:
[H+] = [OH-] = √Kw

[H+] = √(7.51 x 10^-13)
[H+] ≈ 8.66 x 10^-7 (approximately)

Now, we can calculate the pH using the equation:
pH = -log[H+]
pH = -log(8.66 x 10^-7)
pH ≈ 6.06

Therefore, at the given temperature, the pH of the neutral aqueous solution is approximately 6.06.

........H2O ==> H^+ + OH^-

I......liquid....0.....0
C......liquid....x......x
E.....liquid.....x......x

So Kw = (H^+)(OH^-)
Substitute and solve for H^+ and pH.