Question

Two flasks of equal volume and at the same temperature contain different gases. One flask contains \(1.00 \mathrm{~g}\) of \(\mathrm{Ne}\), and the other flask contains \(1.00 \mathrm{~g}\) of He. Which of the following statements are correct? Explain your answers. a. Both flasks contain the same number of atoms. b. The pressures in the flasks are the same. c. The flask that contains helium has a higher pressure than the flask that contains neon. d. The densities of the gases are the same.

Short answer

c and d are correct. c) He has higher pressure. d) Densities are the same.

Step-by-step solution

Identify the Given Data

Two flasks of equal volume and at the same temperature contain 1.00 g of Ne and 1.00 g of He.

Calculate the Molar Masses

Determine the molar masses of Ne (Neon) and He (Helium). The molar mass of Ne is 20.18 g/mol and the molar mass of He is 4.00 g/mol.

Determine the Number of Moles

Use the formula \( n = \frac{m}{M} \), where \( n \) is the number of moles, \( m \) is the mass, and \( M \) is the molar mass. For Ne: \( n_{Ne} = \frac{1.00 \, \text{g}}{20.18 \, \text{g/mol}} \approx 0.0496 \, \text{mol} \) For He: \( n_{He} = \frac{1.00 \, \text{g}}{4.00 \, \text{g/mol}} = 0.25 \, \text{mol} \)

Determine the Number of Atoms

Use Avogadro's number (\( 6.022 \times 10^{23} \) atoms/mol) to find the number of atoms in each flask. For Ne: \( 0.0496 \, \text{mol} \times 6.022 \times 10^{23} \approx 2.99 \times 10^{22} \, \text{atoms} \) For He: \( 0.25 \, \text{mol} \times 6.022 \times 10^{23} \approx 1.51 \times 10^{23} \, \text{atoms} \)

Analyze the Pressures

Since the volume and temperature are the same, according to the Ideal Gas Law (\( PV = nRT \)), the pressure is directly proportional to the number of moles. Since He has more moles than Ne, the pressure in the He flask is higher.

Analyze the Densities

The density of a gas is given by \( \rho = \frac{m}{V} \), where \( m \) is mass and \( V \) is volume. Both gases have the same mass and volume, so their densities are the same.

Conclude the Statements

a. The number of atoms is not the same (disproven in Step 4).b. The pressures are not the same (disproven in Step 5).c. The pressure in the helium flask is higher (proven in Step 5).d. The densities are the same (proven in Step 6).

Key concepts

Molar Mass Calculation

Molar mass is a crucial concept in chemistry that links the mass of a substance to the amount of substance in moles. To calculate the molar mass of an element or compound, you need the formula and the periodic table. The molar mass is the sum of the atomic masses of each element in a molecule.
For instance, in the given exercise, the molar mass of Neon (Ne) is 20.18 g/mol and for Helium (He) it is 4.00 g/mol.
This calculation is essential for converting grams of a substance into moles, which is a fundamental step in solving many chemistry problems.

Number of Moles

The number of moles, denoted as n, can be calculated using the formula: where m is the mass of the substance and M is the molar mass. For example, for Neon (Ne), if you have 1.00 g, the number of moles is: Approximate calculations give us 0.0496 moles for Neon. For Helium (He), if you have 1.00 g, the number of moles is: This results in 0.25 moles. Calculating the number of moles is crucial because it allows you to work directly with Avogadro's number and other gas laws.

Avogadro's Number

Avogadro's number is a constant, defined as the number of constituent particles (usually atoms or molecules) in one mole of a given substance. The value of Avogadro's number is 6.022 x 10^23. It provides a bridge between atomic and macroscopic scales.
In the exercise, Avogadro's number helps us calculate the actual number of atoms in the flasks. For Neon (Ne), which has approximately 0.0496 moles, the total number of atoms is: Similarly, for Helium (He) with 0.25 moles, the number of atoms is: Hence, Helium has more atoms than Neon, even though the masses are the same. This is crucial in understanding why the pressures differ in the two flasks, according to the Ideal Gas Law.

Pressure Analysis

Pressure in a gas is directly related to the amount of gas (number of moles) present, according to the Ideal Gas Law: PV=nRT. Here, P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.
Given that the two flasks have the same volume and temperature, the pressure will be proportional to the number of moles. Since the Helium flask has 0.25 moles compared to the Neon flask's 0.0496 moles, Helium will exert a higher pressure.
Understanding this relationship is key in analyzing the behavior of gases under different conditions.

Density Calculation

Density (ρ) is defined as the mass per unit volume of a substance, given by the formula: In the context of gases, even though Helium and Neon have different molar masses and number of atoms, their densities remain the same in this exercise. This is because both gases have the same mass (1.00 g) and occupy the same volume in their respective flasks. Therefore, the density of the gases can be described as equal despite the differences in the number of particles.
Understanding density in gases helps in determining how gases will behave under certain conditions, especially in terms of buoyancy and diffusion.