Given the consentration of either hrgrogen ion or hydroxide ion, use the product constant of water to calculate the consentration of the other ion at 298 K.
A: [H+]=1.0x10^-4M
B: [OH-]= 1.3x10^-11M
(H^+)(OH^-) = Kw = 1E-14
To calculate the concentration of the other ion (either [H+] or [OH-]) using the product constant of water, we can use the equation Kw = [H+][OH-], where Kw represents the ion product constant of water.
At 298 K, the value of Kw is known to be 1.0 x 10^-14.
Let's consider two scenarios:
Scenario A: Given [H+] = 1.0 x 10^-4 M
To find [OH-], we will rearrange the equation Kw = [H+][OH-] and solve for [OH-]:
1.0 x 10^-14 = (1.0 x 10^-4)([OH-])
Divide both sides of the equation by [H+]:
[OH-] = (1.0 x 10^-14) / (1.0 x 10^-4)
= 1.0 x 10^-14 / 1.0 x 10^-4
= 1.0 x 10^-10 M
Therefore, in Scenario A, [OH-] = 1.0 x 10^-10 M.
Scenario B: Given [OH-] = 1.3 x 10^-11 M
To find [H+], we will rearrange the equation Kw = [H+][OH-] and solve for [H+]:
1.0 x 10^-14 = [H+](1.3 x 10^-11)
Divide both sides of the equation by [OH-]:
[H+] = (1.0 x 10^-14) / (1.3 x 10^-11)
= 1.0 x 10^-14 / 1.3 x 10^-11
= 0.769 x 10^-3 M
= 7.69 x 10^-4 M (in scientific notation)
Therefore, in Scenario B, [H+] = 7.69 x 10^-4 M.
In summary, when given the concentration of either [H+] or [OH-], we can use the ion product constant of water (Kw = 1.0 x 10^-14) to calculate the concentration of the other ion.