Question

An element \(\mathrm{X}\) forms an iodide \(\left(\mathrm{XI}_{3}\right)\) and a chloride \(\left(\mathrm{XCl}_{3}\right)\). The iodide is quantitatively converted to the chloride when it is heated in a stream of chlorine: $$ 2 \mathrm{XI}_{3}+3 \mathrm{Cl}_{2} \longrightarrow 2 \mathrm{XCl}_{3}+3 \mathrm{I}_{2} $$ If \(0.5000 \mathrm{~g}\) of \(\mathrm{XI}_{3}\) is treated with chlorine, \(0.2360 \mathrm{~g}\) of \(\mathrm{XCl}_{3}\) is obtained. (a) Calculate the atomic weight of the element X. (b) Identify the element X.

Short answer

(a) The atomic weight of element X is approximately 30.975. (b) The element X is Gallium (Ga).

Step-by-step solution

Calculate the moles of XI3 and XCl3

First, let's calculate the moles of XI3 and XCl3 using their masses and molar masses. Moles of XI3 = (Mass of XI3) / (Molar mass of XI3) Moles of XCl3 = (Mass of XCl3) / (Molar mass of XCl3) We have masses of XI3 (0.5000 g) and XCl3 (0.2360 g), but we don't know the molar masses of these compounds because we don't yet know the atomic weight of X. Let's use the molar mass of Iodine(I) and Chlorine(Cl) for now. The molar mass of Iodine is 126.9045 g/mol and that of Chlorine is 35.453 g/mol. Molar mass of XI3 = (x + 3 * 126.9045) g/mol Molar mass of XCl3 = (x + 3 * 35.453) g/mol Using the mass values given, Moles of XI3 = 0.5000 / (x + 3 * 126.9045) Moles of XCl3 = 0.2360 / (x + 3 * 35.453)

Use stoichiometry of the reaction to relate moles of XI3 and XCl3

From the balanced equation, we see that 2 moles of XI3 react to form 2 moles of XCl3. So, their mole ratio is: Moles of XI3 : Moles of XCl3 = 1 : 1 Thus, Moles of XI3 = Moles of XCl3 Now, we can write: 0.5000 / (x + 3 * 126.9045) = 0.2360 / (x + 3 * 35.453)

Solve for the atomic weight of X

Let's solve for x in the above equation: 0.5000 * (x + 3 * 35.453) = 0.2360 * (x + 3 * 126.9045) Expanding and rearranging the terms: 0.5000x + 0.5000 * 3 * 35.453 = 0.2360x + 0.2360 * 3 * 126.9045 0.2640x = 0.2360 * 3 * 126.9045 - 0.5000 * 3 * 35.453 x ≈ 30.975 So, the atomic weight of element X is approximately 30.975.

Identify the element X

With the atomic weight of approximately 30.975, we can identify element X by checking the periodic table of elements. The element with an atomic weight close to 30.975 is Gallium (Ga), which has an atomic weight of 31. In this context, we can conclude that element X is Gallium (Ga). Answer: (a) The atomic weight of element X is approximately 30.975. (b) The element X is Gallium (Ga).

Key concepts

Atomic Weight Calculation

Atomic weight, often synonymous with atomic mass, refers to the weight of an element's atoms relative to each other. In practical chemistry exercises, it is fundamental to calculate the atomic weight for recognizing unknown elements in reactions.

In the problem given, we start by deducing the atomic weight of the unknown element, X. This involves solving a mathematical equation derived using stoichiometry principles laid down by the reaction of iodine and chlorine with X (forming compounds XI3 and XCl3, respectively). By knowing the mass of each compound formed during the reaction and leveraging the known atomic masses of iodine (126.9045 g/mol) and chlorine (35.453 g/mol), we can establish a relationship between the moles of compounds.

To proceed, break down the weights and stoichiometrically balance 2XI3 being converted to 2XCl3, allowing us to align mass ratios of XI3 to XCl3 and solve for the atomic mass of X. As shown in the problem, this calculation yields an atomic mass of approximately 30.975 g/mol, aiding the identification of the element.

Chemical Reactions

Chemical reactions are processes where reactants transform into products through the breaking and forming of chemical bonds. These transformations are depicted through balanced chemical equations to represent the stoichiometry of chemical reactions. Stoichiometry includes the calculations of reactants and products in chemical reactions.

In the presented exercise, a reaction is used to convert iodide (XI3) to chloride (XCl3) using chlorine gas, represented by the equation:

\[2 \mathrm{XI}_{3} + 3 \mathrm{Cl}_{2} \rightarrow 2 \mathrm{XCl}_{3} + 3 \mathrm{I}_{2}\]
This balanced equation informs us that two moles of XI3 react with three moles of Cl2 to produce two moles of XCl3. Understanding such balanced equations is crucial, as they illustrate the proportional relationships between reactants and products—essential knowledge when conducting stoichiometric calculations or predicting the yield of a chemical reaction.

Periodic Table

The Periodic Table is an organized chart of elements arranged by increasing atomic number. It offers a framework for predicting the characteristics and behaviors of elements based on their positions.

In our scenario, once the atomic weight of element X has been calculated to be approximately 30.975, the periodic table is our go-to resource for identifying the element. By matching this calculated atomic weight to those listed in the periodic table, we can determine that our element is Gallium, which sits between other elements in the table, highlighting its metallic nature.

In addition to atomic weight, the periodic table provides information about elemental family traits, electron configurations, and reactivity, which can help anticipate how elements will interact in different chemical contexts, such as elemental bonding or chemical reactivity.