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Consider a mixture of three different gases: 1.20 \(\mathrm{g}\) of argon (molecular mass \(=39.948\) g/mol), 2.60 \(\mathrm{g}\) of neon (molecular mass \(=\) \(20.180 \mathrm{g} / \mathrm{mol},\) and 3.20 \(\mathrm{g}\) of helium (molecular mass \(=4.0026 \mathrm{g} / \mathrm{mol} )\) For this mixture, determine the percentage of the total number of atoms that corresponds to each of the components.

Short Answer

Expert verified
Argon: 3.14%, Neon: 13.44%, Helium: 83.42%

Step by step solution

01

Calculate Moles of Each Gas

First, calculate the moles of each gas using the formula \( \text{moles} = \frac{\text{mass}}{\text{molecular mass}} \).For Argon: \[\text{moles of Ar} = \frac{1.20 \text{ g}}{39.948 \text{ g/mol}} = 0.030055 \text{ mol}\]For Neon:\[\text{moles of Ne} = \frac{2.60 \text{ g}}{20.180 \text{ g/mol}} = 0.128782 \text{ mol}\]For Helium:\[\text{moles of He} = \frac{3.20 \text{ g}}{4.0026 \text{ g/mol}} = 0.79952 \text{ mol}\]
02

Calculate Total Moles

Add the moles of each gas together to find the total moles present in the mixture. \[\text{Total moles} = 0.030055 \text{ mol} + 0.128782 \text{ mol} + 0.79952 \text{ mol} = 0.958357 \text{ mol}\]
03

Calculate Percentage for Each Gas

Calculate the percentage of the total number of atoms for each gas by dividing the moles of that gas by the total moles, and multiplying by 100.For Argon:\[\text{Percentage of Ar} = \left(\frac{0.030055}{0.958357}\right) \times 100 \approx 3.14\%\]For Neon:\[\text{Percentage of Ne} = \left(\frac{0.128782}{0.958357}\right) \times 100 \approx 13.44\%\]For Helium:\[\text{Percentage of He} = \left(\frac{0.79952}{0.958357}\right) \times 100 \approx 83.42\%\]
04

Summarize the Results

The calculated percentages account for the portion of each gas in the total number of atoms within the mixture:- Argon: \(3.14\%\)- Neon: \(13.44\%\)- Helium: \(83.42\%\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molecular Mass
Understanding molecular mass is crucial in gas mixture calculations. Molecular mass refers to the mass of a molecule determined by adding the atomic masses of all atoms present, as found on the periodic table. This mass is often measured in grams per mole (g/mol), which helps in converting between the mass and the moles of a substance.

For calculating gas mixtures, knowing the molecular mass of each gas is essential to determine the amount of substance in moles. Each gas has a specific molecular mass that you need to know to carry out calculations. For instance, argon has a molecular mass of 39.948 g/mol, neon has 20.180 g/mol, and helium has 4.0026 g/mol. These values are used to convert the given mass of each gas in grams to moles, which is a fundamental step in analyzing gas mixtures.

Whenever you're dealing with chemical reactions or mixtures, molecular mass helps in predicting how different gases would interact based on their quantities.
Moles Calculation
Moles calculation is a crucial step in analyzing gas mixtures, as it allows you to convert the mass of a given substance into moles. Moles are a measure of the number of particles, such as atoms or molecules, in a given sample.

The formula used to calculate the moles of any substance is: \[ \text{moles} = \frac{\text{mass (g)}}{\text{molecular mass (g/mol)}} \] This formula is applied for each gas in the mixture:
  • For Argon: Using 1.20 g of argon and its molecular mass of 39.948 g/mol. Thus, the moles of argon is \(0.030055\) mol.
  • For Neon: With 2.60 g of neon and a molecular mass of 20.180 g/mol, the moles amount to approximately \(0.128782\) mol.
  • For Helium: Given 3.20 g and a molecular mass of 4.0026 g/mol, you find \(0.79952\) mol of helium.
Adding these moles together gives the total number of moles in the mixture, which is a critical step before calculating percentages.
Percentage Composition
Percentage composition in gas mixtures involves calculating the proportion of each gas in terms of moles, relative to the total amount of moles in the mixture. To determine this, you divide the moles of each component by the total moles of all gases combined, and then multiply by 100 to get a percentage.

This calculation is significant because it shows the contribution of each gas to the total mixture, which is important in understanding the composition of the mixture and its potential behavior or reactivity.
  • Argon’s percentage is calculated by \(\left( \frac{0.030055}{0.958357} \right) \times 100\), resulting in approximately 3.14\%.
  • Neon’s percentage is determined through \(\left( \frac{0.128782}{0.958357} \right) \times 100\) which gives about 13.44\%.
  • Finally, helium, with the highest moles, represents \(\left( \frac{0.79952}{0.958357} \right) \times 100\) equating to 83.42\% of the mixture.
This step ensures that you have a clear quantitative understanding of each component's presence in the mixture, often leading towards further analysis such as determining the gas mixture's behavior under different conditions.

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