Water molecules can dissociate into hydronium ions
(H3O+ ,often just called H+ for shorthand) and hydroxide ions (OH-). The concentration of each of these ions in pure water is 10^-7. In other words, in pure water one out of every 10 million molecules is dissociated into a hydroxide ion and a hydronium ion.
A. What is the pH of a solution with a [H+]=10^ -8?
B. What is the pH of a solution with a [OH-] of 10^ -2
C. The pH of a solution is 6.5 What are the [H+] and [OH-] of the solution ?
a. pH = -log(H^+)
b. pOH = -log(OH^-); then pH + pOH = pKw = 14. YOu know pOH and pKw, solve for pH.
c. See a and b above. Solve for pOH, then H^+ and OH^-
Post your work if you get stuck.
A. The pH of a solution with a [H+] of 10^-8 can be determined using the formula:
pH = -log[H+]
Using this formula, plug in the value of [H+]:
pH = -log(10^-8)
= -(-8)
= 8
Therefore, the pH of the solution is 8.
B. The pOH of a solution with a [OH-] of 10^-2 can be determined using the formula:
pOH = -log[OH-]
Using this formula, plug in the value of [OH-]:
pOH = -log(10^-2)
= -(-2)
= 2
To find the pH, subtract the pOH from 14:
pH = 14 - pOH
= 14 - 2
= 12
Therefore, the pH of the solution is 12.
C. The pH of a solution is 6.5. To find the [H+], we need to convert the pH value to [H+]:
[H+] = 10^(-pH)
Plugging in the value for pH:
[H+] = 10^(-6.5)
Using a calculator, we find that [H+] is approximately 3.16 x 10^(-7).
To find the [OH-] concentration, we can use the equation:
[H+][OH-] = 10^(-14)
Rearranging the equation, we can solve for [OH-]:
[OH-] = 10^(-14) / [H+]
Substituting the value for [H+]:
[OH-] = 10^(-14) / (3.16 x 10^(-7))
Using a calculator, we find that [OH-] is approximately 3.16 x 10^(-8).
Therefore, the [H+] concentration is approximately 3.16 x 10^(-7) and the [OH-] concentration is approximately 3.16 x 10^(-8) in the solution.
To answer these questions, we need to understand the relationship between pH and the concentration of hydronium ions ([H+]) in a solution. The pH scale is a logarithmic scale that measures the acidity or alkalinity of a solution. Mathematically, it is defined as the negative logarithm (base 10) of the hydronium ion concentration:
pH = -log[H+]
A. To find the pH of a solution with a hydronium ion concentration [H+] = 10^-8, we take the negative logarithm of this concentration:
pH = -log(10^-8) = 8
Therefore, the pH of the solution with [H+] = 10^-8 is 8.
B. Similarly, to find the pH of a solution with a hydroxide ion concentration [OH-] = 10^-2, we can use the relationship between [H+] and [OH-]. In pure water, the concentration of [H+] and [OH-] are both 10^-7. This means that [H+][OH-] = 10^-14.
Now, we can determine the concentration of hydronium ions [H+] in the solution with [OH-] = 10^-2 using this relationship:
[H+][OH-] = 10^-14
[H+](10^-2) = 10^-14
[H+] = 10^-14 / (10^-2)
[H+] = 10^-12
Taking the negative logarithm of [H+], we find:
pH = -log(10^-12) = 12
Hence, the pH of the solution with [OH-] = 10^-2 is 12.
C. If the pH of a solution is 6.5, we can determine the hydronium ion concentration [H+] using the reverse of the logarithmic equation:
pH = -log[H+]
10^-pH = [H+]
Substituting pH = 6.5 into the equation:
[H+] = 10^-6.5
To find the hydroxide ion concentration [OH-], we can use the relationship [H+][OH-] = 10^-14 and the fact that water is neutral (pH = 7). Thus, [H+] = [OH-] = 10^-7, which gives:
[H+][OH-] = (10^-6.5)(10^-7) = 10^-13
Therefore, the [H+] and [OH-] concentrations of the solution with a pH of 6.5 are both 10^-6.5 and 10^-7, respectively.