Final answer:
To find the number of millimoles of OH⁻ in a 1.0 x 10⁻¹⁰ M OH⁻ solution, multiply the molarity by 1000 to convert to millimoles, resulting in 0.01 millimoles per liter. If volume is given, multiply it with the molarity and then by 1000 to get millimoles. Use the ion product constant for water (Kw) to find OH⁻ if H3O+ concentration is known.
Step-by-step explanation:
Calculating Millimoles of OH⁻ in an Aqueous Solution
To calculate the number of millimoles of hydroxide ions (OH⁻) in the unknown aqueous solution, we need to understand the relationship between molarity and millimoles. Molarity is the number of moles of solute per liter of solution, and one millimole is one-thousandth of a mole. If the molarity of OH⁻ is given as 1.0 x 10⁻¹⁰ M, converting this to millimoles involves simply multiplying by the volume in liters and then by 1000 (since there are 1000 millimoles in a mole).
However, if you were provided with a volume, for example 5.00 mL of 1.00 M NaOH, to find the number of millimoles of OH⁻, you would multiply the volume in liters (0.005 L) by the molarity (1 M), and then by 1000, resulting in 5 millimoles of OH⁻. The ion product constant for water (Kw) might be used to relate the concentrations of OH⁻ and H3O+ in the solution. If the concentration of H3O+ is known, you can use the relationship Kw = [H3O+][OH⁻] to find the concentration of OH⁻. For example, if [H3O+] is 1.0 × 10⁻¹M, then [OH⁻] can be computed knowing that Kw is 1.0 × 10⁻¹⁴ at 25°C.
Let’s assume we have the concentration of OH⁻ as 1.0 x 10⁻¹⁰ M and we wish to know the millimoles in 1 liter of this solution. Simple multiplication yields 1.0 x 10⁻¹⁰ moles/L × 1000 millimoles/mole = 1.0 x 10⁻⁷ millimoles, or equivalently, 0.01 millimoles of OH⁻ per liter. This is how we deal with calculating the concentration of hydroxide ions in different situational problems.