Question

Two different compounds are composed of Elements \(\mathrm{X}\) and \(\mathrm{Y}\) . The formulas of the compounds are \(\mathrm{X}_{2} \mathrm{Y}_{3}\) and \(\mathrm{XY}\) . A 0.25 mol sample of \(\mathrm{XY}\) has a mass of \(17.96 \mathrm{g},\) and a 0.25 mol sample of \(\mathrm{X}_{2} \mathrm{Y}_{3}\) has a mass of 39.92 \(\mathrm{g}\) . a. What are the atomic masses of elements \(\mathrm{X}\) and \(\mathrm{Y}\) ? b. What are the formulas for the compounds?

Short answer

a) The atomic masses of elements X and Y are 1.49 g/mol and 3 g/mol, respectively. b) The formulas of the compounds are already given as X2Y3 and XY.

Step-by-step solution

Determine the mass of X and Y in each compound.

First, we need to calculate the total mass of each element in both compounds, given that we have 0.25 moles of each compound. For compound XY, with a mass of 17.96 g: Mass of X and Y in XY: 0.25 moles * (Mass of XY) For compound X2Y3, with a mass of 39.92 g: Mass of X and Y in X2Y3: 0.25 moles * (Mass of X2Y3)

Write the equations of mass for compounds XY and X2Y3

Now we can use the mass information from step 1 to write equations that represent the relationship between the mass of X and Y within each compound. Equation 1 (Compound XY): Mass of X + Mass of Y = Mass of XY Equation 2 (Compound X2Y3): 2 * Mass of X + 3 * Mass of Y = Mass of X2Y3

Solve for the mass of X and Y

Now, we will use the provided information about the masses of the compounds to solve for the mass of X and Y in the first equation. From computational results, we obtain the masses of X and Y in both compounds: Mass of XY: 0.25 moles * 17.96 g = 4.49 g Mass of X2Y3: 0.25 moles * 39.92 g = 9.98 g

Substitute the known values into the equations

Now we can substitute these values into the equations from Step 2: Equation 1: Mass of X + Mass of Y = 4.49 g Equation 2: 2 * Mass of X + 3 * Mass of Y = 9.98 g

Solve for the mass of X and Y using the system of equations

Now we will solve this system of linear equations to find the values of Mass of X and Mass of Y: First, we can solve Equation 1 for Mass of X: Mass of X = 4.49 g - Mass of Y Substitute this into Equation 2: 2 * (4.49 g - Mass of Y) + 3 * Mass of Y = 9.98 g Solving this equation we get: Mass of Y = 3 g Mass of X = 1.49 g So the atomic masses are: Element X: 1.49 g/mol Element Y: 3 g/mol a) The atomic masses of elements X and Y are 1.49 g/mol and 3 g/mol, respectively. b) The formulas of the compounds are already given as X2Y3 and XY.

Key concepts

Compounds

Compounds are fascinating chemical structures made when two or more different elements bond together chemically. These can range from simple molecules like water, consisting of two hydrogen atoms and one oxygen atom, to more complex ones involving many atoms of different elements.
In the exercise, we are dealing with two compounds. Each comprises different arrangements of the same two elements, X and Y. Each compound's chemical formula provides insight into the ratio and types of atoms present. For instance, the compound XY implies one atom of X is bonded to one atom of Y.
It's essential to understand that the properties of a compound are distinct from the elements that comprise it. Both chemical and physical properties can change dramatically once the compound is formed. In our case, X and Y each have unique weights, but when bonded differently (as in XY and X2Y3), they make entirely different compounds with separate properties, such as their respective molar masses.

Molecular Formulas

A molecular formula is like a detailed recipe for a compound. It tells us exactly how many atoms of each element are within a single molecule of a compound. For example, the molecular formula XY suggests one X atom bonded to one Y atom. Meanwhile, X2Y3 indicates two X atoms and three Y atoms form each molecule.
Knowing the molecular formula is incredibly useful as it allows chemists to determine the molar mass (the mass of one mole of a compound). In our scenario, knowing each compound's molecular formula allows us to calculate the total mass for 0.25 moles of each compound. This was crucial in determining the atomic masses of X and Y.
Understanding molecular formulas gives us deeper insights into how elements interact and bond with each other to form new and exciting compounds, revealing the beautiful complexity within chemical reactions.

Stoichiometry

Stoichiometry is an area of chemistry focused on the relationships between the quantities of reactants and products in a chemical reaction. It's like the math of chemistry, allowing us to calculate how much of a compound is formed from specified amounts of reactants.
In the exercise, stoichiometry helps us calculate the atomic masses of X and Y using the given quantities of compounds. By knowing the moles of the compounds and their respective masses, we could set up equations to solve for each element's mass. This task showcased one of stoichiometry's most powerful uses: figuring out unknown quantities when certain data is provided.
Precision in stoichiometry ensures correct results, and it plays a vital role in practical applications such as industrial chemical manufacturing, where precise quantities are crucial to avoid wastage and ensure safety.