Question

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 \((d=5.72\) \(\mathrm{g} / \mathrm{cm}^{3}\) ) 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

The mass of As$_2$I$_4$ that can be prepared is 629.02 g, and the mass of As$_2$I$_4$ actually isolated considering the percent yield is 475.40 g.

Step-by-step solution

Calculate the volume and mass of the arsenic block.

First, find the volume of the cubic block of arsenic metal: Volume = side³ = (3.00 cm)³ = 27.0 cm³ Next, find the mass of the arsenic block using its density: Density = mass/volume mass = Density × volume mass of As = 5.72 g/cm³ × 27.0 cm³ = 154.44 g

Calculate the moles of arsenic metal.

The molar mass of arsenic (As) is 74.9216 g/mol. Moles of As = mass/molar mass = 154.44 g / 74.9216 g/mol = 2.0613 mol

Calculate the moles of AsI3.

Given 1.01 × 10²⁴ molecules of AsI3. Convert the molecules of AsI3 to moles using Avogadro's number (6.022 × 10²³ molecules/mol): Moles of AsI3 = 1.01 × 10²⁴ molecules / 6.022 × 10²³ molecules/mol = 1.6783 mol

Determine the limiting reactant.

The stoichiometry of the reaction is 2As + 2AsI3 → As2I4. For every 2 moles of As, we need 2 moles of AsI3. We can determine the limiting reactant by comparing the mole ratios. Mole ratio of As to AsI3 = Moles of As / moles of AsI3 = 2.0613 mol / 1.6783 mol = 1.228 Since we need 2 moles of As for each 2 moles of AsI3, and the mole ratio is more significant than 1, the limiting reactant is AsI3.

Calculate the moles of As2I4 produced.

Using the stoichiometry of the reaction (2AsI3 → As2I4) and the moles of the limiting reactant (AsI3): Moles of As2I4 = Moles of AsI3 * (1 mol As2I4 / 2 mol AsI3) = 1.6783 mol * (1/2) = 0.83915 mol

Calculate the mass of As2I4 and the mass of As2I4 actually isolated.

Calculate the molar mass of As2I4: Molar mass of As2I4 = 2x molar mass of As + 4x molar mass of I = 2x74.9216 g/mol + 4x126.9045 g/mol = 749.682 g/mol Calculate the mass of As2I4 produced: Mass of As2I4 = moles of As2I4 × molar mass of As2I4 = 0.83915 mol × 749.682 g/mol = 629.02 g Next, calculate the mass of As2I4 actually isolated considering the percent yield: Percent yield = (Actual yield / Theoretical yield) × 100 Actual yield = Percent yield × Theoretical yield / 100 = (75.6% × 629.02 g) / 100 = 475.40 g The mass of As2I4 that can be prepared is 629.02 g, and the mass of As2I4 actually isolated considering the percent yield is 475.40 g.

Key concepts

Limiting Reactant

Understanding the concept of the limiting reactant is crucial in predicting the amount of product that can be formed in a chemical reaction. It is the reactant that will be entirely consumed first, thus limiting the extent of the reaction and determining the theoretical yield of the product. To identify the limiting reactant, one must compare the mole ratios of the reactants used to those required by the balanced chemical equation. For example, if a reaction requires two moles of Substance A for every one mole of Substance B, and you have more moles of A than needed when compared to B, then Substance B is the limiting reactant.

In the textbook exercise, the balanced chemical equation is given, from which the stoichiometric ratios can be inferred. By calculating and comparing the number of moles of each reactant, arsenic (As) and arsenic triiodide (AsI3), the limiting reactant was determined to be AsI3 since it had fewer moles than required by As. This critical step ensures that students appreciate the importance of stoichiometry in predicting the outcome of chemical reactions.

Mole Concept

The mole concept is a fundamental principle in chemistry that helps in the quantification of chemical substances. One mole is defined as the amount of substance containing as many entities (atoms, molecules, ions, or other particles) as there are atoms in exactly 12 grams of carbon-12. This number is Avogadro's number, approximately equal to \(6.022 \times 10^{23}\) entities. The mole allows chemists to count particles by weighing them. In the exercise, the students are required to convert the mass of arsenic to moles using the molar mass of arsenic and then calculate the moles of arsenic triiodide from the given number of molecules using Avogadro's number. These computations exhibit the practical usage of the mole concept.

Percent Yield

Percent yield is a measure of the efficiency of a chemical reaction. It is the ratio of the actual yield (the amount of product actually obtained from the reaction) to the theoretical yield (the amount of product expected based on stoichiometric calculations) multiplied by 100%. It's an indicator of how much product was produced compared to what could have been produced if the reaction were perfect. The percent yield can be affected by many factors, such as incomplete reactions, side reactions, and loss of product during recovery.

Understanding percent yield is essential for practical chemistry applications, including industrial and laboratory settings, where yield needs to be maximized for cost efficiency and environmental considerations. The exercise includes a calculation of the theoretic and actual yield of \(\mathrm{As}_{2} \mathrm{I}_{4}\), demonstrating the difference between the two and how to calculate the percent yield.

Molar Mass

Molar mass is the weight of one mole of a given substance expressed in grams per mole (g/mol). It is numerically equivalent to the substance's atomic or molecular weight, taken from the periodic table, based on the isotopic composition of the elements involved. The molar mass is vital for converting between grams and moles, allowing chemists to use mass, a measurable quantity, in stoichiometric calculations.

In the example problem, the student is required to calculate the molar mass of \(\mathrm{As}_{2} \mathrm{I}_{4}\) by adding together the molar masses of arsenic and iodine. Knowledge of molar mass helps in predicting the quantity of products formed from a known mass of reactants and is integral to the solution of the problem provided in the textbook.