If [H+] is 1000,000 times larger than [OH-] at 25 °C, what is the pH?
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[H+]*[OH-] = 10^-14
[H+] = 10^6*[OH-]
10^6*[OH-]^2 = 10^-14
[OH-] = 10^-10
[H+] = 10^-4
pH = 4.0
To determine the pH, we need to calculate the concentration of H+ ions using the given information.
The relationship between the concentrations of H+ and OH- ions in water can be described by the equation Kw = [H+][OH-], where Kw is the ion product constant of water.
At 25 °C, Kw has a value of 1.0 x 10^-14. Since [OH-] is smaller than [H+], let's assume [OH-] as x and [H+] as 1,000,000x.
Then, we can substitute these values into the equation above:
Kw = [H+][OH-]
1.0 x 10^-14 = (1,000,000x)(x)
1.0 x 10^-14 = x^2 * 1,000,000
1.0 x 10^-14 = x^2 * 1.0 x 10^6
Now, let's solve for x:
x^2 = (1.0 x 10^-14) / (1.0 x 10^6)
x^2 = 1.0 x 10^-20
To simplify this further, we can take the square root:
x ≈ 1.0 x 10^-10
Since [OH-] is smaller than [H+], we can ignore the smaller value. Thus, we use [OH-] = 1.0 x 10^-10.
Now, we can substitute this value into the equation for pH:
pH = -log[H+]
Since [H+] is 1,000,000 times larger than [OH-], it follows that [H+] = 1,000,000 * 1.0 x 10^-10.
Substituting this value into the equation for pH:
pH = -log(1,000,000 * 1.0 x 10^-10)
pH = -log(1.0 x 10^-4)
Using logarithmic identity log(a * b) = log(a) + log(b):
pH = - (log(1.0) + log(10^-4))
Since log(1.0) = 0 and log(10^-4) = -4:
pH = - (0 + (-4))
pH = - (-4)
pH = 4
Therefore, the pH of the solution is 4.