How many grams of lithium chloride must decompose to produce 56.8 milliliters of lithium metal, if the density of lithium is 0.534 g/mL? Show all steps of your calculation as well as the final answer. LiCl → Li + Cl2

To determine how many grams of lithium chloride (LiCl) need to decompose to produce 56.8 milliliters (mL) of lithium metal, we must follow these steps:

Step 1: Calculate the mass of lithium metal First, we need to find the mass of the lithium that can be obtained from 56.8 mL of lithium metal using the given density.

Mass = Density × Volume Mass of Li = 0.534 g/mL × 56.8 mL = 30.3312 g (rounded to four significant figures)

Step 2: Determine the molar mass of lithium and lithium chloride Next, we need to find the molar mass of lithium (Li) and lithium chloride (LiCl) to relate the mass of lithium metal to the mass of lithium chloride.

Molar mass of Li = approximately 6.94 g/mol (using the periodic table). Molar mass of LiCl = approximately 6.94 g/mol (Li) + 35.45 g/mol (Cl) = 42.39 g/mol (rounded to four significant figures)

Step 3: Relate the mass of lithium to the mass of lithium chloride using stoichiometry Since the decomposition of LiCl produces Li and Cl2 in a 1:1 molar ratio as shown in the balanced chemical equation:

LiCl → Li + Cl2

We need to use the stoichiometry to relate the mass of lithium produced to the mass of LiCl needed. The ratio is 1 mole of Li to 1 mole of LiCl. Use this ratio to calculate the number of moles of LiCl required to produce the calculated moles of Li.

Moles of Li produced = Mass of Li / Molar mass of Li Moles of Li produced = 30.3312 g / 6.94 g/mol ≈ 4.3718 mol (rounded to four significant figures)

Since the ratio is 1:1, the moles of LiCl needed will also be 4.3718 moles.

Step 4: Calculate the mass of lithium chloride needed Finally, calculate the mass of lithium chloride (LiCl) required by using the molar mass of LiCl.

Mass of LiCl needed = Moles of LiCl × Molar mass of LiCl Mass of LiCl needed = 4.3718 mol × 42.39 g/mol ≈ 185.39 g (rounded to four significant figures)

Final Answer: Approximately 185.39 grams of lithium chloride must decompose to produce 56.8 mL of lithium metal.