Final answer:
To find the [H₃O⁺] in pure water at body temperature (37°C), we use the equation Kₜ = [H₃O⁺]² since Kₜ is provided as 2.4 x 10⁻¹⁴. The concentration of [H₃O⁺] is determined to be 1.55 x 10⁻⁷ M. The water is neutral at a pH of approximately 7.00.
Step-by-step explanation:
The question asks about the concentration of hydronium ions ([H₃O⁺]) in pure water at a specific temperature. At body temperature (37°C), the ionization constant of water (Kₜ) is given as 2.4 x 10⁻¹⁴. To find the concentration of [H₃O⁺] in pure water at this temperature, we use the fact that in pure water, the concentration of hydronium ions ([H₃O⁺]) is equal to the concentration of hydroxide ions ([OH⁻]) due to the autoionization of water. Since Kₜ = [H₃O⁺][OH⁻] and [H₃O⁺] = [OH⁻], we can set up the equation (Kₜ) = [H₃O⁺]². Taking the square root of both sides to solve for [H₃O⁺], we get:
[H₃O⁺] = √(Kₜ) = √(2.4 x 10⁻¹⁴) ≈ 1.55 x 10⁻⁷ M
To determine if the water is acidic, basic, or neutral, we look at the pH, which is the negative logarithm of the [H₃O⁺] concentration. The pH of pure water at this temperature would be:
pH = -log([H₃O⁺]) = -log(1.55 x 10⁻⁷) ≈ 7.00
A pH of 7.00 is considered neutral, so water at 37°C with a [H₃O⁺] of 1.55 x 10⁻⁷ M is neutral.