91Ó°ÊÓ

Understanding molecular weight is crucial in chemistry, especially when dealing with gas mixtures. The molecular weight of a mixture is a weighted average based on the mole fraction and the individual molecular weights of its components. Each gas contributes to the total molecular weight proportionally to its presence in the mixture. In our specific helium (He) and xenon (Xe) mixture, helium has a mole fraction of 0.75 while xenon has 0.25. The molecular weight of each gas is 4 g/mol for helium and 131.29 g/mol for xenon. By calculating \[\text{Molecular Weight} = (0.75 \times 4) + (0.25 \times 131.29),\]we find the molecular weight of the mixture to be 32.8225 g/mol. This value helps us understand how heavy or light the gas molecules are on average.

The mass fraction is an important concept in chemistry that tells us how much of the total mass of the mixture is made up by each component. To find the mass fraction of helium, we first calculate the mass of each component using their mole fractions and molecular weights. Helium contributes 3 g/mol, while xenon contributes 32.8225 g/mol. The mass fraction of helium is calculated using \[\text{Mass Fraction of He} = \frac{3}{3 + 32.8225},\]resulting in 0.084. This shows that helium makes up only a small portion of the mixture's mass. Mass fraction is useful when assessing the proportionate presence of different elements in a compound.

Molar concentration, also known as molarity, refers to the number of moles of a solute per liter of solution. For gases, it is determined using the ideal gas law, which is a fundamental concept in chemistry describing how gases behave under different conditions. At 300 K and 1 atm, the ideal gas law \(PV = nRT\) helps us find the volume occupied by one mole of gas. With R as 0.0821 L atm/mol K, we calculate \[V = \frac{RT}{P} = \frac{0.0821 \times 300}{1} = 24.63 \text{ L/mol}.\]Thus, the molar concentration of the mixture is \[C = \frac{1}{24.63} = 0.0406 \text{ mol/L}.\]Molar concentration is vital for calculating reactant quantities in chemical reactions and processes.

Mass density is defined as the mass per unit volume of a substance. It's an essential property that allows us to compare how much mass is contained in a given volume of a material, which is especially applicable in gases. For our helium-xenon mixture, the mass density is determined by multiplying the molar concentration by the molecular weight of the mixture: \[\text{Mass Density} = 0.0406 \times 32.8225 = 1.33 \text{ g/L}.\]This means each liter of the gas mixture weighs 1.33 grams. Mass density helps engineers design systems where specific weight and capacity considerations are crucial, such as in cooling systems for electronics. Understanding this concept ensures efficient material usage and optimal system performance.