Question

How many grams of \(\mathrm{LiOH}\) are there in \(750 \mathrm{~mL}\) of an aqueous LiOH solution having an \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration of \(2.30 \times 10^{-13} \mathrm{M} ?\)

Short answer

The mass of LiOH in the solution is calculated as follows: Step 1: Determine the concentration of OH⁻ ions: \([\mathrm{OH}^{-}] = \frac{1.0 \times 10^{-14}}{2.30 \times 10^{-13} \ {\rm M}} = 4.35 \times 10^{-2}\ {\rm M}\) Step 2: Calculate the number of moles of LiOH: \(moles = (4.35 \times 10^{-2} \ {\rm M}) \times \left(\frac{750 \ {\rm mL}}{1000 \ {\rm mL}}\right) = 3.26 \times 10^{-2} \ {\rm mol}\) Step 3: Convert the moles of LiOH to grams: \(\text{Mass} = (3.26 \times 10^{-2} \ {\rm mol}) \times (6.94 + 15.99 + 1.01) \ {\rm g/mol} = 0.795 \ {\rm g}\) So, there are \(0.795 \ {\rm g}\) of LiOH present in the 750 mL aqueous solution.

Step-by-step solution

Determine the concentration of LiOH

We are given the H₃O⁺ concentration (\(2.30 \times 10^{-13} \mathrm{M}\)), which is inversely related to the OH⁻ concentration via the ion product of water, Kw. Formula: \(K_w = [\mathrm{H}_{3}\mathrm{O}^{+}][\mathrm{OH}^{-}]\) Where Kw is the ion product of water, which is \(1.0 \times 10^{-14}\) at 25°C. Since LiOH is a strong base, the concentration of LiOH is equal to the concentration of hydroxide ions, OH⁻. First, solve for the concentration of OH⁻ ions: \[[\mathrm{OH}^{-}] = \frac{K_w}{[\mathrm{H}_{3}\mathrm{O}^{+}]}\]

Calculate the number of moles of LiOH

Now that we have the concentration of LiOH, we can calculate the number of moles of LiOH in the solution. Use the formula: \(moles = \text{concentration} \times \text{volume}\) Where volume must be in liters. Remember that 1 L = 1000 mL. So, first, convert the volume to liters: \[\text{Volume in L} = \frac{750 \text{ mL}}{1000} \text{ L/m L}\] Then, calculate the number of moles of LiOH present in the solution.

Convert the moles of LiOH to grams

To find the mass of LiOH in grams, we need to convert moles to grams using the molar mass of LiOH. The molar mass of LiOH is: \(6.94 \text{ g/mol (Li)} + 15.99 \text{ g/mol (O)} + 1.01 \text{ g/mol (H)}\) Now, use the formula: \[\text{Mass} = \text{moles} \times \text{molar mass}\] Calculate the mass of LiOH in the given solution and express the result in grams.

Key concepts

Ion Product of Water

Understanding the ion product of water, commonly represented as Kw, is crucial for examining acid-base chemistry. This concept describes the relationship between the hydrogen ions (\text{H⁺}) or hydronium ions (\text{H₃O⁺}) and hydroxide ions (\text{OH⁻}) in water. At a specific temperature (25°C), the product of their concentrations is constant and equal to approximately \(1.0 \times 10^{-14}\).This equilibrium constant provides valuable information for solving problems related to the acidity or basicity of solutions. In the case of a strong base like lithium hydroxide, LiOH, it dissociates completely in water, providing an equivalent amount of hydroxide ions. To determine the concentration of hydroxide ions in solution, you use the formula \([OH^-] = \frac{K_w}{[H_3O^+]}\). Using the known concentration of hydronium ions from the problem, you can then calculate the concentration of hydroxide ions, which is also the concentration of LiOH in a strong base scenario.

Molar Concentration

Molar concentration, also known as molarity, is a measure of the amount of a solute that is dissolved in a given volume of solution. The unit for molarity is moles per liter (M), and it is a fundamental concept when dealing with chemical solutions. You calculate the molarity by dividing the number of moles of solute by the solution's volume in liters.For instance, if you have a solution where the number of moles of LiOH and the volume in liters are known, the molarity of the solution will just be the quotient of these values. When converting from milliliters to liters, as required when creating solutions, remember that \(1 \text{ L} = 1000 \text{ mL}\). Thus, to work with the proper units, you must convert the volume from mL to L before calculating molarity.

Molar Mass

Molar mass is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. The unit used is grams per mole (g/mol). It corresponds to the mass of one mole of a substance.To find the molar mass of a compound, such as LiOH, you add the molar masses of each individual element in the compound. Each element's molar mass is found on the periodic table and typically rounded to two decimal points for calculations. For LiOH, you would add the molar mass of lithium (Li), oxygen (O), and hydrogen (H) to get the compound's total molar mass. This value is then used to convert moles to grams, which is especially helpful when dealing with chemical reactions and solution preparation.

Stoichiometry

Stoichiometry is the part of chemistry that deals with the quantitative relationships and calculations between the reactants and products in a chemical reaction. The calculations are based on the balanced chemical equation and involve using the mole concept to predict the masses of reactants and products involved.In problems concerning solution concentration, stoichiometry allows us to relate amount of solute in moles to its mass in grams and vice versa. After determining the number of moles of LiOH using the volume and molarity of the solution, stoichiometry guides the final step of the process: converting moles to grams. This conversion uses the compound's molar mass as a conversion factor. Understanding and applying stoichiometry is essential for precise and accurate calculations in chemistry.