Given that Kw = 2.4x10^-14 at 37 celsius, compute the PH of a neutral aqueous solution at 37 celsius, which is the normal human body temperature.
Is PH = 7 solution acidic, basic, neutral at 37 celsius?
Thank you!!!!!!
To determine the pH of a neutral aqueous solution at 37 degrees Celsius, we can use the equation for calculating the pH of water.
Kw = [H+][OH-]
At 37 degrees Celsius, we know that the value of Kw is 2.4x10^-14. Since the solution is neutral, the concentrations of H+ and OH- ions are equal.
Let's assume the concentration of H+ ions ([H+]) is x.
[H+] = x mol/L
[OH-] = x mol/L
Therefore, the equation becomes:
2.4x10^-14 = x * x
Solving for x:
2.4x10^-14 = x^2
Taking the square root of both sides:
\[ x = \sqrt{2.4\times10^{-14}} \]
\[ x = 1.55 \times 10^{-7} \]
Now, we can calculate the pH using the equation:
pH = -log[H+]
pH = -log(1.55x10^-7)
pH = -log(1.55) + log(10^-7)
Using logarithmic properties, log(10^-7) equals -7:
pH = -log(1.55) - 7
Calculating the value:
pH ≈ -0.1906 - 7
pH ≈ -7.1906
Therefore, the pH of a neutral aqueous solution at 37 degrees Celsius is approximately 7.19.
Since pH = 7 is equal to neutral, a solution with a pH of 7 at 37 degrees Celsius is also neutral.
To determine whether a pH = 7 solution is neutral, acidic, or basic at 37 degrees Celsius, we need to compare it to the pH scale.
The pH scale ranges from 0 to 14, where:
- pH values from 0 to 6.9 are acidic
- pH values of 7 are neutral
- pH values from 7.1 to 14 are basic or alkaline
Now, let's consider Kw, which is the ionization constant of water at a specific temperature. In this case, Kw = 2.4x10^-14 at 37 degrees Celsius.
Kw is calculated as the product of the concentrations of hydrogen ions (H+) and hydroxide ions (OH-) in water:
Kw = [H+][OH-]
In a neutral solution at 37 degrees Celsius, the concentration of H+ and OH- ions is equal. So, in this case, we can assume that the concentration of H+ ions is equal to the concentration of OH- ions, which we can represent as [H+] = [OH-].
If we substitute [H+] = [OH-] into the equation for Kw, we get:
2.4x10^-14 = [H+][OH-]
Since [H+] = [OH-], we can rewrite the equation as:
2.4x10^-14 = [H+]^2
Taking the square root of both sides, we find:
√(2.4x10^-14) = [H+]
[H+] = 1.55x10^-7 M
Now, since pH is defined as the negative logarithm of the concentration of H+ ions, we can calculate the pH:
pH = -log([H+])
pH = -log(1.55x10^-7)
pH ≈ 6.81
So, a pH = 7 solution at 37 degrees Celsius is slightly acidic, as it has a pH less than 7. Thus, it is not neutral.
Therefore, a pH = 7 solution is acidic at 37 degrees Celsius, which is the normal human body temperature.