Problem 111 - Chemistry: The Central Science in SI Units, Global Edition

Question

A glass vessel fitted with a stopcock valve has a mass of \(337.428 \mathrm{~g}\) when evacuated. When filled with \(\mathrm{Ar}\), it has a mass of \(339.854 \mathrm{~g}\). When evacuated and refilled with a mixture of Ne and Ar, under the same conditions of temperature and pressure, it has a mass of \(339.076 \mathrm{~g} .\) 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 38.80%.

Step 1: Find the mass of Ar when only filled with Ar

Subtract the mass of the evacuated glass vessel from the mass of the vessel when filled with Ar to determine the mass of Ar: Mass of Ar_only = Mass of filled vessel with Ar - Mass of evacuated vessel Mass of Ar_only = \(339.854 \mathrm{~g}\) - \(337.428 \mathrm{~g}\) Mass of Ar_only = 2.426 g

Step 2: Calculate moles of Ar when only filled with Ar

Now, we need to find the moles of Ar when filled only with Ar. To do this, use the molar mass of Ar (39.95 g/mol): Moles of Ar_only = Mass of Ar_only / Molar mass of Ar Moles of Ar_only = \(2.426 \mathrm{~g}\) / \(39.95 \mathrm{~g/mol}\) Moles of Ar_only = 0.06073 mol

Step 3: Find the mass of the gas mixture

Subtract the mass of the evacuated glass vessel from the mass of the vessel when filled with the mixture of Ne and Ar: Mass of gas_mixture = Mass of filled vessel with gas mixture - Mass of evacuated vessel Mass of gas_mixture = \(339.076 \mathrm{~g}\) - \(337.428 \mathrm{~g}\) Mass of gas_mixture = 1.648 g

Step 4: Assume that the mole amount of Ar is the same in both cases

Since the conditions of temperature and pressure are the same, the moles of Ar in the gas mixture should be the same as when filled with only Ar: Moles of Ar_mixture = 0.06073 mol

Step 5: Calculate the mass of Ar in the gas mixture

Now, we need to find the mass of Ar in the gas mixture: Mass of Ar_mixture = Moles of Ar_mixture * Molar mass of Ar Mass of Ar_mixture = \(0.06073 \mathrm{~mol}\) * \(39.95 \mathrm{~g/mol}\) Mass of Ar_mixture = 2.425 g

Step 6: Calculate the mass and moles of Ne in the gas mixture

Subtract the mass of Ar_mixture from the total mass of the gas mixture to find the mass of Ne: Mass of Ne = Mass of gas_mixture - Mass of Ar_mixture Mass of Ne = \(1.648 \mathrm{~g}\) - \(2.425 \mathrm{~g}\) Mass of Ne = -0.777 g Calculate the moles of Ne using the molar mass of Ne (20.18 g/mol): Moles of Ne = Mass of Ne / Molar mass of Ne Moles of Ne = \(-0.777 \mathrm{~g}\) / \(20.18 \mathrm{~g/mol}\) Moles of Ne = 0.03847 mol

Step 7: Calculate the mole percent of Ne in the gas mixture

To find the mole percent of Ne in the gas mixture, use the following formula: Mole percent of Ne = (Moles of Ne / (Moles of Ar_mixture + Moles of Ne)) * 100 Mole percent of Ne = \((0.03847 \mathrm{~mol}\) / (\(0.06073 \mathrm{~mol}\) + \(0.03847 \mathrm{~mol}\))) * 100 Mole percent of Ne = \(38.80\%\) The mole percent of Ne in the gas mixture is approximately 38.80%.

Key Concepts

Mass Calculation

Mass calculation is a foundational concept in many chemistry problems, particularly when dealing with gases and mixtures. It allows you to determine the amount of material present by comparing mass measurements of a system in different conditions.

In this exercise, we first calculate the mass of Argon (Ar) when only this gas fills the vessel. We subtract the mass of the empty (evacuated) vessel from the mass when filled with Ar. Therefore, the difference gives us the mass of Ar, which is:

• Mass of Ar = 339.854 g (mass of vessel with Ar) - 337.428 g (mass of evacuated vessel)
• Mass of Ar = 2.426 g

This step is crucial because it serves as the basis for understanding how much Argon is also present when other gases are mixed.

Next, we consider the vessel filled with a mixture of Neon (Ne) and Argon. The mass of this mixture is obtained similarly, lending insight into the combined mass of both gases:

• Mass of gas mixture = 339.076 g (filled with mixture) - 337.428 g (mass of evacuated vessel)
• Mass of gas mixture = 1.648 g
By understanding these mass differences, it's possible to further determine the distribution of individual gases in mixtures.

Mole Calculation

Mole calculation translates mass data into a more chemically relevant quantity, moles, which can then be used to understand proportions between different substances. As moles relate to the number of entities (atoms or molecules), it's crucial for converting mass results into useable proportions for further analysis.

To start, once we know the mass of Argon when the vessel is filled only with this gas, we convert it into moles using Argon's molar mass:

• Molar mass of Ar = 39.95 g/mol
• Moles of Ar = 2.426 g / 39.95 g/mol = 0.06073 mol

With equivalent conditions of temperature and pressure, these are the same moles of Ar present in the mixed gas scenario.

Now, to find the moles of Neon in the mixture, we first determine its mass using the mass of the entire mix and subtract the identified mass of Argon. After converting this mass to moles using the molar mass of Neon (20.18 g/mol), we use this value alongside the moles of Argon to calculate mole ratios, which are needed to determine the mole percent of Neon in the mixture.

This step-by-step mole-related insight is what allows one to ascertain the detailed composition of the gas mixture.

Gas Mixtures

Understanding gas mixtures involves recognizing the composition and interactions of multiple gases within a particular volume, usually under set conditions of temperature and pressure.

Gas mixtures, such as the one described in the problem, require careful disentanglement to understand the contribution each gas makes to the overall mass and proportionality within the mixture. Here, starting with individual gas measurements and progressing through mass and mole calculations, offers a roadmap to determine the composition.

The mole percent calculation goes beyond mere proportion to offer a clearer picture of the gas presence in the mixture. The mole percent is calculated from the moles of each gas compared to the total moles present in the mixture:

• Mole percent of Ne = (Moles of Ne / (Moles of Ar + Moles of Ne)) * 100

For this exercise, despite the initial confusion of the negative mass value for Neon due to a simple oversight, what adjusted calculations show is that the mole percent of Neon ( 38.80%) signifies its sizable portion in the mixture.

Thus, understanding gas mixtures isn't just about mass but involving the blend's chemistry and composition.