You take three compounds, each consisting of two elements \((\mathrm{X}, \mathrm{Y}\), and \(/ \mathrm{or} \mathrm{Z})\), and decompose them to their respective elements. To determine the relative masses of \(\mathrm{X}, \mathrm{Y}\), and \(\mathrm{Z}\), you collect and weigh the elements, obtaining the following data: $$ \begin{array}{|ll|} \hline \text { Elements in Compound } & \text { Masses of Elements } \\ \hline \text { 1. } \mathrm{X} \text { and } \mathrm{Y} & \mathrm{X}=0.4 \mathrm{~g}, \mathrm{Y}=4.2 \mathrm{~g} \\ \text { 2. Y and } \mathrm{Z} & \mathrm{Y}=1.4 \mathrm{~g}, \mathrm{Z}=1.0 \mathrm{~g} \\ \text { 3. } \mathrm{X} \text { and } \mathrm{Y} & \mathrm{X}=2.0 \mathrm{~g}, \mathrm{Y}=7.0 \mathrm{~g} \\ \hline \end{array} $$ a. What are the assumptions needed to solve this problem? b. What are the relative masses of \(\mathrm{X}, \mathrm{Y}\), and \(\mathrm{Z} ?\) c. What are the chemical formulas of the three compounds? d. If you decompose \(21 \mathrm{~g}\) of compound \(\mathrm{XY}\), how much of each element is present?

Step by step solution

01

a. Assumptions

1. The compounds are pure, which means there are no impurities, and all the mass comes from the elements themselves. 2. The elements combine to form compounds in definite proportions. 3. The mass of each element in the compound is directly proportional to the number of moles of that element.

02

b. Determining the relative masses of X, Y, and Z

First, we can find the ratio of the masses of each element in the different compounds by using the given masses: Compound 1 (X and Y): 0.4 g X ≈ 4.2 g Y → 0.4/4.2 ≈ 1/10.5 Compound 2 (Y and Z): 1.4 g Y ≈ 1.0 g Z → 1.4/1.0 ≈ 14/10 Compound 3 (X and Y): 2.0 g X ≈ 7.0 g Y → 2.0/7.0 ≈ 2/7 Now, let's find the relative masses of X and Y: Using Compound 1 and Compound 3 data: 0.4 g X : 4.2 g Y = 2.0 g X : 7.0 g Y Comparing the ratios, we find that their simplified forms are equal: 1/10.5 = 2/7 Thus, the relative masses of X and Y are: X : Y = 2 : 7 Now, let's determine the relative mass of Z with respect to Y: Using Compound 2 data: Y : Z = 14 : 10 Now, let's determine the relative masses for all three elements: X : Y : Z = 2 : 7 : 7/14(10) = 2 : 7 : 5 Thus, the relative masses of X, Y, and Z are 2, 7, and 5 respectively.

03

c. Determining the chemical formulas of the compounds

Since we have found the relative masses of X, Y, and Z, we can now find the chemical formulas of the compounds: Compound 1 (X and Y): X₀Y₁ since X : Y = 2 : 7 (with X having the smallest mass) Compound 2 (Y and Z): Y₁Z₁ since Y : Z = 14 : 10 (with equal masses) Compound 3 (X and Y): X₂Y₁ since X : Y = 2/7 : 7/7 Thus, the chemical formulas of the compounds are: Compound 1: XY Compound 2: YZ Compound 3: X₂Y

04

d. Decomposing 21 g of compound XY

To find the amount of each element present when decomposing 21 g of compound XY, we can use the proportions of the chemical formula and the masses of the elements in the compound. For compound XY, the ratio of X to Y is 2 : 7. Let's find the mass of X and Y in 21 g of the compound. Mass of X = Total mass × (ratio of X / total ratio) = 21 × (2 / (2 + 7)) ≈ 6 g Mass of Y = Total mass × (ratio of Y / total ratio) = 21 × (7 / (2 + 7)) ≈ 15 g Thus upon decomposing 21 g of compound XY, there will be 6 g of X and 15 g of Y.

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