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Chapter 5: Problem 29

How is the mass percent of elements in a compound different for a 1.0-g sample versus a 100.-g sample versus a 1-mole sample of the compound?

Short Answer

Expert verified
The mass percent of elements in a compound remains the same regardless of the sample size (1.0 g, 100 g, or 1-mole). This is because the ratio of individual elements' masses to the total mass of the compound remains constant. Mass percent can be calculated as: \[\frac{\text{mass of element}}{\text{total mass of compound}} \times 100\% .\]

Step by step solution

01

Determine the molar mass of the compound

First, we need to determine the molar mass of the compound. Molar mass is the sum of the atomic masses of all the elements present in the compound. For element A and B, the atomic masses are given by 'm_A' (mass of A in g/mol) and 'm_B' (mass of B in g/mol). So, the molar mass of the compound A_x B_y = x * m_A + y * m_B.
02

Mass percent of elements in a 1.0-g sample

For a 1.0-g sample of the compound, the mass of element A present in the sample is given by (x * m_A) / (x * m_A + y * m_B) * 1.0 g. Similarly, the mass of element B present in the sample is given by (y * m_B) / (x * m_A + y * m_B) * 1.0 g. Now, calculate the mass percent of elements A and B by dividing their respective masses in the sample by the total mass (1.0 g) and multiplying by 100.
03

Mass percent of elements in a 100.-g sample

Similarly, for a 100.-g sample, the mass of element A present in the sample is given by (x * m_A) / (x * m_A + y * m_B) * 100 g and the mass of element B present in the sample is given by (y * m_B) / (x * m_A + y * m_B) * 100 g. Calculate the mass percent of elements A and B by dividing their masses in the sample by the total mass (100 g) and multiplying by 100.
04

Mass percent of elements in a 1-mole sample

To find the mass percent in a 1-mole sample, first find the mass of a 1-mole sample of the compound. The mass of one mole of the compound equals its molar mass, which is x * m_A + y * m_B. Now, calculate the mass percent of elements A and B by dividing their masses in the 1-mole sample by the total mass (x * m_A + y * m_B) and multiplying by 100.
05

Compare the results

Compare the mass percentages of elements A and B in the 1.0-g, 100.-g, and 1-mole samples. In all cases, the mass percentage for each element should remain the same, as the ratio of individual elements' masses to the total mass of the compound remains constant.

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Most popular questions from this chapter

A 0.755-g sample of hydrated copper(II) sulfate $$\mathrm{CuSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O}$$ was heated carefully until it had changed completely to anhydrous copper(II) sulfate (CuSO_) with a mass of 0.483 g. Determine the value of \(x .\) [This number is called the number of waters of hydration of copper(II) sulfate. It specifies the number of water molecules per formula unit of \(\mathrm{CuSO}_{4}\) in the hydrated crystal.]

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