A mixture of XCl3 and XCl5 weighing 10.00 g contains 81.04% Cl by mass. How many grams of XCl3 and how many grams of XCl5 are present in the mixture?

Name: Chemistry
Author: McMurry
ISBN: 9781292336145

Verified step by step guidance

Step 1: Define variables for the masses of XCl3 and XCl5 in the mixture. Let m1 be the mass of XCl3 and m2 be the mass of XCl5.

Step 2: Set up the equation for the total mass of the mixture: m1 + m2 = 10.00 g.

Step 3: Calculate the mass percentage of Cl in each compound. For XCl3, the mass percentage of Cl is (3 * M_Cl) / (M_X + 3 * M_Cl) * 100%, and for XCl5, it is (5 * M_Cl) / (M_X + 5 * M_Cl) * 100%, where M_Cl is the molar mass of Cl and M_X is the molar mass of X.

Step 4: Set up the equation for the total mass of Cl in the mixture using the given percentage: 0.8104 * 10.00 g = (mass percentage of Cl in XCl3 * m1) + (mass percentage of Cl in XCl5 * m2).

Step 5: Solve the system of equations from Step 2 and Step 4 to find the values of m1 and m2, which represent the masses of XCl3 and XCl5, respectively.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mass Percent Composition

Mass percent composition is a way to express the concentration of an element in a compound or mixture. It is calculated by dividing the mass of the element by the total mass of the compound or mixture and multiplying by 100. In this question, understanding how to calculate the mass percent of chlorine in the mixture is essential for determining the amounts of XCl3 and XCl5.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For this problem, calculating the molar masses of XCl3 and XCl5 is crucial, as it allows for the conversion between mass and moles, facilitating the determination of the amounts of each compound in the mixture based on their respective contributions to the total mass.

System of Equations

A system of equations is a set of equations with multiple variables that can be solved simultaneously. In this scenario, two variables represent the masses of XCl3 and XCl5. By setting up equations based on the total mass of the mixture and the mass percent of chlorine, one can solve for the individual masses of the components in the mixture.

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