How do I solve these?

[OH-]=3.2 X 10^-8 M (calculating the H3O+ ion concentration from the OH- ion concentration)
[H3O+]=7.3 X 10^-10 M (calculating the OH- ion concentration from the H3O+ ion concentration)

1 Answer
Truong-Son N.
Jun 5, 2018

You recall the value of K_w and do one algebraic step...

...remembering to use parentheses, or E notation to ensure proper scientific notation in your calculator.

...and at 25^@ "C", the so-called autodissociation constant of water is

K_w = ["H"_3"O"^(+)]["OH"^(-)] = 10^(-14)

for the reaction

2"H"_2"O"(l) rightleftharpoons "H"_3"O"^(+)(aq) + "OH"^(-)(aq).

Thus,

(a) if ["OH"^(-)] = 3.2 xx 10^(-8) "M",

color(blue)(["H"_3"O"^(+)]) = K_w/(["OH"^(-)]) = color(blue)(3.1_3 xx 10^(-7) "M")

where the subscript indicates the digit past the last significant digit.

(b) if ["H"_3"O"^(+)] = 7.3 xx 10^(-10) "M",

color(blue)(["OH"^(-)]) = K_w/(["H"_3"O"^(+)]) = color(blue)(1.3_7 xx 10^(-5) "M")

where the subscript indicates the digit past the last significant digit.

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