Ch.3 - Mass Relationships in Chemical Reactions

Problem 59

Chapter 3, Problem 59

A sample that weighs 107.75 g is a mixture of 30% helium atoms and 70% krypton atoms. How many particles are present in the sample?

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Determine the mass of helium in the sample by multiplying the total mass by the percentage of helium: \( \text{mass of He} = 107.75 \text{ g} \times 0.30 \).

Determine the mass of krypton in the sample by multiplying the total mass by the percentage of krypton: \( \text{mass of Kr} = 107.75 \text{ g} \times 0.70 \).

Calculate the number of moles of helium using its molar mass (4.00 g/mol): \( \text{moles of He} = \frac{\text{mass of He}}{4.00 \text{ g/mol}} \).

Calculate the number of moles of krypton using its molar mass (83.80 g/mol): \( \text{moles of Kr} = \frac{\text{mass of Kr}}{83.80 \text{ g/mol}} \).

Use Avogadro's number (\(6.022 \times 10^{23}\) particles/mol) to find the total number of particles: \( \text{total particles} = (\text{moles of He} + \text{moles of Kr}) \times 6.022 \times 10^{23} \).

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Key Concepts

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

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For helium, the molar mass is approximately 4.00 g/mol, while for krypton, it is about 83.80 g/mol. Understanding molar mass is essential for converting between grams and moles, which is necessary for calculating the number of particles in a sample.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10²³, is the number of particles (atoms, molecules, etc.) in one mole of a substance. This constant allows chemists to relate the mass of a substance to the number of particles it contains. In this problem, it will be used to determine the total number of helium and krypton atoms in the mixture after calculating the moles of each gas.

Percentage Composition

Percentage composition refers to the mass percentage of each component in a mixture. In this case, the sample consists of 30% helium and 70% krypton by mass. This information is crucial for determining the mass of each gas in the sample, which is then used to calculate the number of moles and ultimately the total number of particles present.

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