Given that Kw for water is 2.4× 10–14 at 37 °C, compute the pH of a neutral aqueous solution at 37 °C, which is the normal human body temperature.
kw=conccH+ * concOH- where they are equal.
kw=x^2
x=sqrt kw=sqrt(2.4E-14)=1.55 E-7
pH=-log (1.55E-7)=6.81
To compute the pH of a neutral aqueous solution, we need to use the equation:
pH = -log[H+]
In a neutral solution, the concentration of hydrogen ions (H+) is equal to the concentration of hydroxide ions (OH-). Since Kw is the product of [H+] and [OH-], we can calculate the concentration of hydrogen ions using the value of Kw at 37 °C.
Here's how you can compute the pH of a neutral aqueous solution at 37 °C:
Step 1: Write down the equation for Kw:
Kw = [H+][OH-]
Given that Kw at 37 °C is 2.4 × 10^(-14), we can assume that the concentration of hydrogen ions ([H+]) is equal to the concentration of hydroxide ions ([OH-]) in a neutral solution.
Step 2: Solve for [H+] using the value of Kw:
2.4 × 10^(-14) = [H+][H+]
[H+]^2 = 2.4 × 10^(-14)
Taking the square root of both sides:
[H+] = √(2.4 × 10^(-14))
Step 3: Calculate the pH using the equation:
pH = -log[H+]
Substitute the value of [H+] obtained from Step 2 into the pH equation:
pH = -log(√(2.4 × 10^(-14)))
Using a scientific calculator (or Python code), compute the value inside the logarithm and take its negative logarithm to find the pH.
Note: The pH value obtained represents the concentration of hydrogen ions in the neutral solution at 37 °C. At 37 °C, the pH of a neutral solution should be around 7.