Question

If a gaseous mixture is made of \(2.41 \mathrm{~g}\) of \(\mathrm{He}\) and \(2.79 \mathrm{~g}\) of \(\mathrm{Ne}\) in an evacuated 1.04-L container at 25 ' \(C\), what will be the partial pressure of each gas and the total pressure in the container?

Short answer

The partial pressure of He is \(\frac{(2.41 \mathrm{~g})}{(4.003 \mathrm{~g/mol})} \times \frac{0.08206 \mathrm{~L~atm/(K~mol)} \times 298.15 \mathrm{~K}}{1.04 \mathrm{~L}}\), and the partial pressure of Ne is \(\frac{(2.79 \mathrm{~g})}{(20.180 \mathrm{~g/mol})} \times \frac{0.08206 \mathrm{~L~atm/(K~mol)} \times 298.15 \mathrm{~K}}{1.04 \mathrm{~L}}\). The total pressure is the sum of these partial pressures.

Step-by-step solution

Calculate the moles of He and Ne

To find the moles of He and Ne, we will use their molar masses and the given masses: Moles of He = \(\frac{2.41 \, \text{g}}{4.003 \, \text{g/mol}}\) Moles of Ne = \(\frac{2.79 \, \text{g}}{20.180 \, \text{g/mol}}\)

Use the ideal gas law equation for partial pressure

The ideal gas law equation can be written as: \(P = \frac{nRT}{V}\) Where: P = pressure n = number of moles R = ideal gas constant = 0.08206 L atm / K mol T = temperature in Kelvin V = volume To find the partial pressure of each gas, we will substitute the values of moles, temperature, and volume into the equation. First, convert the temperature to Kelvin: T = 25°C + 273.15 = 298.15 K Then, calculate the partial pressures: Partial pressure of He = \(\frac{\text{Moles of He} \times R \times T}{V}\) Partial pressure of Ne = \(\frac{\text{Moles of Ne} \times R \times T}{V}\)

Calculate the total pressure

To find the total pressure, we will add the partial pressure of He and Ne: Total pressure = Partial pressure of He + Partial pressure of Ne

Key concepts

Ideal Gas Law

The ideal gas law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and amount of an ideal gas. Represented by the equation \( PV = nRT \), it describes the behavior of a gas under various conditions.

In this formula, \( P \) stands for the pressure of the gas, \( V \) represents the volume it occupies, \( n \) is the number of moles of gas present, \( R \) is the universal gas constant, which has a value of 0.08206 L atm / K mol, and \( T \) is the temperature in Kelvin.

For students, understanding this relationship is crucial for solving problems involving gases. For a mixture of gases, such as helium and neon in this exercise, the law applies to each gas independently, allowing us to calculate the partial pressure exerted by each gas in a mixture.

Molar Mass

Molar mass is defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It's a way of converting between grams and moles, which is essential in many stoichiometric calculations.

Each element on the periodic table has a specific molar mass. For example, helium (He) has a molar mass of 4.003 g/mol, while neon (Ne) has a molar mass of 20.180 g/mol. These values are critical when converting the given mass of an element in grams to the amount in moles, as shown in the exercise.

For students, remembering that the molar mass serves as a conversion factor is vital for understanding the relationship between the mass of a sample and the moles, especially when working with gas mixtures.

Gas Mixture

A gas mixture contains more than one type of gas, each contributing to the total pressure of the system. Dalton's Law of Partial Pressures states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of individual gases.

Understanding gas mixtures is essential when you're dealing with scenarios like the provided exercise, where helium and neon are combined in a container. Each gas will have its own partial pressure, which can be determined using the ideal gas law. Remember, the partial pressure is the pressure that each gas would exert if it were alone in the container.

Moles Calculation

In the realm of chemistry, moles calculation is a fundamental skill, enabling the quantification of substances involved in reactions and physical processes. The mole is a unit that measures the amount of substance, or the number of particles (atoms, molecules, ions, etc.) it contains.

To calculate the moles of a substance, you divide the mass of the sample by its molar mass (moles = mass / molar mass). In the context of the exercise, this step is critical for determining how many moles of helium and neon are in the mixture, which then allows for the calculation of their partial pressures using the ideal gas law.