Problem 111 - Chemistry The Central Science In Si Units

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 Neon in the mixture is approximately 38.8%.

Step 1: Calculate the mass of Argon

First, we need to determine the mass of Argon (Ar) when the vessel is filled with it. The mass of the vessel when filled with Ar is given as \(339.854\, \text{g}\), and when it is evacuated, it has a mass of \(337.428\, \text{g}\). The mass of Ar alone is calculated by subtracting the evacuated vessel's mass from the filled vessel's mass: \[ \text{mass of Ar} = 339.854 \text{ g} - 337.428 \text{ g} = 2.426 \text{ g}. \]

Step 2: Calculate the mass of the Ne/Ar mixture

Next, we need the mass of the gas mixture consisting of Neon (Ne) and Argon (Ar). The vessel filled with the mixture has a mass of \(339.076\, \text{g}\). Subtract the mass of the evacuated vessel to find the mass of the gas mixture: \[ \text{mass of mixture} = 339.076 \text{ g} - 337.428 \text{ g} = 1.648 \text{ g}. \]

Step 3: Determine the mass of Neon

We assume that the vessel's volume and the conditions of temperature and pressure are the same, so the number of moles of Ar remains the same in both conditions. The mass of the Argon portion of the mixture is known to be \(2.426\, \text{g}\), calculated from when the vessel was filled only with Ar. Check for the reduction in gas mass when both Ne and Ar are present: \[ \text{mass of Ne} = 2.426 \text{ g} - 1.648 \text{ g} = 0.778 \text{ g}. \]

Step 4: Convert masses to moles

Given the atomic masses of Ar (39.948 g/mol) and Ne (20.18 g/mol), we convert grams to moles using the formula \( n = \frac{\text{mass}}{\text{molar mass}} \). First, for Ne: \[ n_{\text{Ne}} = \frac{0.778 \text{ g}}{20.18 \text{ g/mol}} \approx 0.0385 \text{ moles}. \] For Ar, the number of moles in the mixture equals the moles when filled with only Ar (found using Ar's mass when alone): \[ n_{\text{Ar}} = \frac{2.426 \text{ g}}{39.948 \text{ g/mol}} \approx 0.0607 \text{ moles}. \]

Step 5: Calculate mole percent of Neon

The mole percent is calculated using the formula: \[ \text{Mole percent of Ne} = \frac{n_{\text{Ne}}}{n_{\text{Ne}} + n_{\text{Ar}}} \times 100\%\]. Substituting the values we get: \[ \text{Mole percent of Ne} = \frac{0.0385}{0.0385 + 0.0607} \times 100\% \approx 38.8\%\].

Key Concepts

Chemical Mixtures

Chemical mixtures are made up of two or more substances combined together, where each substance retains its own identity and properties. In this exercise, we're dealing with a mixture of Neon (Ne) and Argon (Ar), both of which are inert gases. When a chemical mixture is created, its properties such as mass, volume, and pressure depend on the individual substances within the mixture. This can be key in various scientific fields, such as chemistry and physics, where understanding the proportions and behavior of mixtures is crucial.
In a chemical mixture like the one in our exercise, it's important to remember that the overall mass is just the total of its parts. This allows us to perform calculations to find out how much of each substance is present in the mixture, which is exactly what we needed to determine the mole percent of Ne in the gas mixture.

Molar Mass

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a substance, usually expressed in grams per mole (g/mol). To figure out the amount of a substance in a chemical mixture, we often need to convert mass into moles using the molar mass.
For instance, in our solution, the molar mass of Argon is given as 39.948 g/mol and that of Neon is 20.18 g/mol. By dividing the mass of a substance by its molar mass, we get its amount in moles. This is crucial because the properties and behavior of gases often depend more directly on the number of moles rather than the mass itself.
This conversion to moles allows us to further calculate mole percents, which involve comparing the moles of one component of the mixture to the total moles.

Gas Laws

Gas laws describe how gases behave in terms of pressure, volume, and temperature. A key feature of gases is that their volume and number of moles can be directly connected through these variables. In the exercise, we assume the conditions of temperature and pressure remain the same when handling the different gases and mixtures within the vessel.
One of the gas laws, Avogadro's law, states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. This principle allows us to understand that even though the gases have different molar masses, under the same temperature and pressure conditions, a difference in mass directly indicates a difference in the number of moles.
The gas laws are critical for performing accurate measurements and calculations with gas mixtures. They help us understand how gas composition will affect overall properties such as mass, which was essential for calculating the mole percent of Neon in the mixture.