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Chapter 5: Problem 182

The compound \(\mathrm{As}_{2} \mathrm{I}_{4}\) is synthesized by reaction of arsenic metal with arsenic triiodide. If a solid cubic block of arsenic \(\left(d=5.72 \mathrm{g} / \mathrm{cm}^{3}\right)\) that is \(3.00 \mathrm{cm}\) on edge is allowed to react with \(1.01 \times 10^{24}\) molecules of arsenic triiodide, what mass of \(\mathrm{As}_{2} \mathrm{I}_{4}\) can be prepared? If the percent yield of \(\mathrm{As}_{2} \mathrm{I}_{4}\) was \(75.6 \%\) what mass of \(\mathrm{As}_{2} \mathrm{I}_{4}\) was actually isolated?

Short Answer

Expert verified
The theoretical mass of As₂I₄ that can be prepared is 670.20 g, and the actual mass of As₂I₄ isolated with a percent yield of 75.6% is 506.51 g.

Step by step solution

01

Calculate the mass of arsenic metal

To calculate the mass of arsenic metal, we need to use the density formula as follows: mass = density × volume. The volume of the arsenic cubic block can be calculated as side × side × side. Density = 5.72 g/cm³ Side = 3.00 cm Volume = 3.00 cm × 3.00 cm × 3.00 cm = 27 cm³ Now, we can calculate the mass of arsenic: Mass of arsenic = density × volume = 5.72 g/cm³ × 27 cm³ = 154.44 g
02

Calculate the moles of arsenic and arsenic triiodide

To determine the moles of arsenic and arsenic triiodide, we will use the following relationship: moles = mass / molar mass Molar mass of arsenic (As) = 74.92 g/mol Moles of arsenic = mass of arsenic / molar mass of arsenic = 154.44 g / 74.92 g/mol = 2.061 mol We are given the number of molecules of arsenic triiodide, so we need to convert it to moles. We will use Avogadro's number, which is 6.022 × 10²³ molecules/mol: Moles of arsenic triiodide = (1.01 × 10²⁴ molecules) / (6.022 × 10²³ molecules/mol) = 1.678 mol
03

Determine the limiting reactant

To find out the limiting reactant, we need to compare the molar ratio of arsenic to arsenic triiodide with the stoichiometric ratio. The balanced chemical equation for the reaction is: 2 As + 2 AsI₃ → As₂I₄ Stoichiometric ratio of As to AsI₃ = 1 : 1 Molar ratio of As to AsI₃ = 2.061 mol : 1.678 mol = 1 : 0.815 Since the molar ratio of As to AsI₃ is greater than the stoichiometric ratio, arsenic triiodide is the limiting reactant.
04

Calculate the theoretical mass of As₂I₄ that can be prepared

As AsI₃ is the limiting reactant, we can use the stoichiometry of the reaction to find the theoretical amount of As₂I₄ that can be produced: 1.678 mol AsI₃ × (1 mol As₂I₄ / 2 mol AsI₃) = 0.839 mol As₂I₄ Now we can convert the moles of As₂I₄ to mass. The molar mass of As₂I₄ = 2 × 74.92 g/mol (As) + 4 × 126.90 g/mol (I) = 799.44 g/mol Mass of As₂I₄ = 0.839 mol × 799.44 g/mol = 670.20 g (theoretical yield)
05

Calculate the actual mass of As₂I₄ isolated

The percent yield of As₂I₄ is given as 75.6%. We can use this information to find the actual mass of As₂I₄ that was isolated: Actual mass of As₂I₄ = (75.6 / 100) × theoretical mass of As₂I₄ = 0.756 × 670.20 g = 506.51 g So, the actual mass of As₂I₄ isolated is 506.51 g.

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