Problem 111 - Chemistry The Central Science

Question

A glass vessel fitted with a stopcock valve has a mass of 337.428 g when evacuated. When filled with Ar, it has a mass of 339.854 g. When evacuated and refilled with a mixture of Ne and Ar, under the same conditions of temperature and pressure, it has a mass of 339.076 g. What is the mole percent of Ne in the gas mixture?

Step-by-Step Solution

Answer

The mole percent of Ne in the gas mixture is approximately 63.5%.

Step 1: Determine the mass of each gas

First, we need to determine the mass of the Ar gas and the Ne and Ar gas mixture separately. We will do this by subtracting the mass of the empty glass vessel from the mass of the vessel with each filling condition. Mass of Ar Gas = Mass of Glass Vessel with Ar - Mass of Empty Glass Vessel Mass of Ne and Ar Mixture = Mass of Glass Vessel with Mixture - Mass of Empty Glass Vessel

Step 2: Calculate the moles of each gas using the molar mass

Next, we will calculate the moles of each gas using the molar mass of each element. The molar mass of Ar is 39.948 g/mol, and the molar mass of Ne is 20.180 g/mol. To find the amount (moles) of each gas, we can use the formula: Moles = Mass/Molar Mass

Step 3: Determine the mole percent of Ne in the gas mixture

We now need to find the mole percent of Ne in the gas mixture. Let x be the mole fraction of Ne in the mixture. Then the mole fraction of Ar would be (1-x). The total mass of the mixture can be written as: Mass of Ne and Ar Mixture = (x * moles of Ne) + [(1-x) * moles of Ar] We can solve for x and then find the mole percent of Ne in the mixture by multiplying x by 100. Mole percent of Ne = x * 100

Step 4: Calculate the moles of each gas using the mass of each gas

Calculate the mass and moles of Ar gas and Ne, Ar gas mixture using the values we have: Mass of Ar Gas = 339.854 g - 337.428 g = 2.426 g Mass of Ne and Ar Mixture = 339.076 g - 337.428 g = 1.648 g Moles of Ar Gas = 2.426 g / 39.948 g/mol = 0.0607 mol

Step 5: Create an equation to find the mole percent of Ne in the mixture and solve for x

We can write an equation with x as the mole fraction of Ne in the mixture: 1.648 g = x * (0.0607 mol of Ne * 20.180 g/mol) + (1-x) * (0.0607 mol * 39.948 g/mol) Now, we will solve this equation to find the mole fraction x of Ne in the mixture. 1.648 g = x * (1.225 g) + (1-x) * (2.426 g) Solving for x: x ≈ 0.635 Thus, the mole percent of Ne in the mixture is: Mole percent of Ne = 0.635 * 100 ≈ 63.5%

Key Concepts

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of the quantities of reactants and products involved in a chemical reaction. It is a powerful tool that allows chemists to predict the outcomes of reactions, design experiments, and make conversions between different chemical entities such as moles, atoms, or molecules.

One of the key concepts in stoichiometry is the mole, which is a standard unit of measurement that represents a large quantity of very small entities such as atoms, molecules, or other particles. One mole is equivalent to Avogadro's number, which is approximately 6.022 \( \times \) 10^23 entities.

In the context of our problem, stoichiometry is used to calculate the mole percent of neon (Ne) in a mixture with argon (Ar). To do so, we must first determine the molar masses of the gases involved and use them to calculate the number of moles from the mass of gas in the vessel. With the number of moles of each gas, we can then find the composition of the gas mixture – a prime example of stoichiometry in action.

Molar Mass

The molar mass of a substance is the mass of one mole of that substance. It is a critical concept in chemistry, particularly in stoichiometry, because it allows for the conversion between moles and grams. The molar mass is usually reported in grams per mole (g/mol), and it is numerically equivalent to the average mass of one molecule of the substance, expressed in unified atomic mass units (u or amu).

For instance, the molar mass of argon (Ar) is 39.948 g/mol, while that of neon (Ne) is 20.180 g/mol. These values are pivotal in the exercise at hand because they help to calculate the number of moles of each gas in the mixture by using the formula \( \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \). Through this formula, the mass of the gas mixture obtained from the vessel can be used to determine the moles of each constituent gas.

Gas Mixture Composition

Understanding the composition of a gas mixture is fundamental in various fields, including chemistry, environmental science, and industrial processes. It involves determining the percentage by volume or by mole of each gas within a mixture. In practical scenarios, this would allow scientists and engineers to control reactions, optimize processes, and monitor environmental conditions.

The mole percent is a way of expressing the concentration of a component in a mixture. It is calculated by taking the number of moles of one component and dividing it by the total number of moles of all components in the mixture, then multiplying by 100 to get a percentage.

In the given exercise, once the masses of the individual gases are known, the students can use molar masses to find the moles of Ne and Ar. Then, by creating the equation mentioned in the solution, which involves mass and mole calculations, they can solve for the mole fraction of Ne in the mixture. Multiplying the mole fraction by 100 yields the mole percent of Ne, giving insight into the composition of the gas mixture.