A small cube of lithium 1density = 0.535 g/cm32 measuring 1.0 mm on each edge is added to 0.500 L of water. The following reaction occurs: 2 Li1s2 + 2 H2O1l2 ¡ 2 LiOH1aq2 + H21g2 What is the freezing point of the resulting solution, assuming that the reaction goes to completion?

Verified step by step guidance

1. Calculate the volume of the lithium cube using the formula for the volume of a cube: $V = \text{side}^3$. Convert the side length from millimeters to centimeters before calculating.
2. Determine the mass of the lithium cube using its density: $\text{mass} = \text{density} \times \text{volume}$. Use the given density of lithium.
3. Convert the mass of lithium to moles using its molar mass: $\text{moles of Li} = \frac{\text{mass of Li}}{\text{molar mass of Li}}$. The molar mass of lithium is approximately 6.94 g/mol.
4. Use the stoichiometry of the balanced chemical equation to find the moles of LiOH produced. According to the equation, 2 moles of Li produce 2 moles of LiOH.
5. Calculate the freezing point depression using the formula $\Delta T_f = i \cdot K_f \cdot m$, where $i$ is the van't Hoff factor for LiOH, $K_f$ is the freezing point depression constant for water, and $m$ is the molality of the solution.

Key Concepts

Density and Volume Calculations

Density is defined as mass per unit volume, and it is crucial for determining the mass of lithium in the given cube. The volume of the cube can be calculated using the formula for the volume of a cube (V = side^3). Knowing the density allows us to find the mass of lithium, which is essential for stoichiometric calculations in the reaction with water.

Stoichiometry of Chemical Reactions

Stoichiometry involves the calculation of reactants and products in a chemical reaction based on balanced equations. In this case, the balanced equation shows that 2 moles of lithium react with 2 moles of water to produce 2 moles of lithium hydroxide and 1 mole of hydrogen gas. Understanding stoichiometry is vital for determining the amounts of products formed and the concentration of ions in the solution.

Freezing Point Depression

Freezing point depression is a colligative property that describes how the freezing point of a solvent decreases when a solute is added. The extent of freezing point depression depends on the number of solute particles in solution. In this scenario, calculating the molality of the lithium hydroxide produced will allow us to determine the change in freezing point of the water, which is essential for finding the final freezing point of the solution.