Question

Given that Kw for water is 2.4x10⁻¹⁴ M² at 37 degree C, compute the pH of a neutral aqueous solution at 37 degree C, which is the normal human body temperature.

Answer 1

The pH of a neutral aqueous solution at 37 °C, with a given Kw of 2.4×10⁻¹⁴, is calculated as 6.81. This is due to equal concentrations of hydronium ([H₃O+]) and hydroxide ([OH⁻]) ions in a neutral solution. While slightly acidic compared to neutral pH at 25 °C, it is neutral for physiological purposes.

Step-by-step explanation:

The pH of a neutral aqueous solution at a given temperature can be calculated using the autoionization constant of water (Kw) at that temperature. For water at 37 °C, with a given Kw of 2.4×10⁻¹⁴ M², the pH is calculated using the formula pH = -log[H₃O+]. Since the solution is neutral, [H₃O+] equals [OH⁻], and thus Kw can be expressed as [H₃O+]^2 or [OH⁻]^2.

First, find the concentration of hydronium ions ([H₃O+]) by taking the square root of Kw, assuming equal concentrations of [H₃O+] and [OH⁻] in a neutral solution:

[H₃O+] = √Kw = √(2.4×10⁻¹⁴) = 1.55×10⁻· M

Now, calculate the pH:

pH = -log[H₃O+] = -log(1.55×10⁻·) = 6.81

Therefore, the pH of a neutral aqueous solution at 37 °C is 6.81, which is slightly acidic when compared to the standard neutral pH of 7.00 at 25 °C. However, in the context of the body's temperature, this pH is considered neutral for physiological purposes.