Find the hydroxide-ion concentration in an aqueous solution when the hydronium-ion concentration is 1×10^−10M. Recall that 10^a×10^b=10^(a+b). Express your answer to one significant figure and include the appropriate units.
To find the hydroxide-ion concentration in an aqueous solution, we can use the concept of the ion product of water, known as Kw. The ion product of water is the product of the concentrations of hydronium ions (H3O+) and hydroxide ions (OH-) in water, and is always equal to 1.0 × 10^(-14) at 25 degrees Celsius.
Mathematically, Kw = [H3O+][OH-] = 1.0 × 10^(-14)
Given the hydronium-ion concentration [H3O+] = 1 × 10^(-10) M, we can substitute this value into the equation to solve for [OH-].
1.0 × 10^(-14) = (1 × 10^(-10))( [OH-] )
Now, rearranging the equation to solve for [OH-]:
[OH-] = (1.0 × 10^(-14)) / (1 × 10^(-10))
Simplifying the expression:
[OH-] = 1.0 × 10^(-14 - (-10))
[OH-] = 1.0 × 10^(-14 + 10)
[OH-] = 1.0 × 10^(-4)
Therefore, the hydroxide-ion concentration in the aqueous solution is 1.0 × 10^(-4) M (with one significant figure) and the units are moles per liter (M).