Problem 154 - Chemistry The Science in Context

Question

A gas mixture used experimentally for asthma treatments contains 17.5 mol of helium for every 0.938 mol of oxygen. What is the mole fraction of oxygen in the mixture?

Step-by-Step Solution

Answer

Answer: The mole fraction of oxygen in the gas mixture is approximately 0.0509, or 5.09%.

Step 1: Calculate Total Moles

Considering both helium and oxygen molecules, we will calculate the total moles of the mixture. Add the moles of helium (17.5 mol) and the moles of oxygen (0.938 mol) to get the total moles. Total moles = moles of helium + moles of oxygen

Step 2: Formula for Mole Fraction

The mole fraction of a component in a mixture is the ratio of the moles of that component to the total moles of the mixture. We will use the following formula to calculate the mole fraction of oxygen: Mole_fraction_oxygen = Moles of oxygen / Total moles

Step 3: Calculate Mole Fraction of Oxygen

Now, we will plug in the values from Step 1 into the formula from Step 2 to determine the mole fraction of oxygen in the mixture. Mole_fraction_oxygen = 0.938 mol / (17.5 mol + 0.938 mol)

Step 4: Simplify the Expression

Calculate the value of the mole fraction of oxygen by simplifying the expression: Mole_fraction_oxygen = 0.938 mol / 18.438 mol Mole_fraction_oxygen ≈ 0.0509

Step 5: Write the Final Answer

The mole fraction of oxygen in the gas mixture is approximately 0.0509, or 5.09%.

Key Concepts

Understanding Gas Mixtures

In the world of chemistry, a gas mixture refers to a combination of two or more gases. These gases occupy the same volume, just as liquids or solids would in a mixture. One fundamental concept to understand is that each gas in a mixture behaves independently of the others. This means that the properties of gas mixtures include contributions from each of the individual gases. For asthma treatments, for instance, gases like helium and oxygen are combined due to their beneficial properties. Helium is used because of its low density and non-reactive nature, allowing for easier breathing, while oxygen is essential for combustion in our cells.
To fully grasp a gas mixture, it's vital to know about mole fractions, which are a way to express the quantity of one gas in relation to the entire mixture. This concept is crucial because it helps us determine the concentration of each component—like oxygen—in the mixture.

Approaching Chemistry Problem Solving

When tackling chemistry problems, especially those involving gas mixtures, a systematic approach is key. The first step is understanding what is being asked—like finding the mole fraction in our given exercise. Once you comprehend the question, break down the problem into smaller, manageable steps.

• Identify each component in the mixture—in this case, helium and oxygen.
• Calculate the total moles by adding the moles of each gas together.
• Use the mole fraction formula, which involves dividing the moles of the component of interest by the total moles.

By following these steps, you're set up to find the solution accurately. Remember, patience and careful calculations will lead to success. Ensuring that each part of the solution is logically sound will also improve your confidence in handling similar problems in the future.

Mastering Mole Calculations

Mole calculations are essential in determining the composition of mixtures in chemistry. A mole represents a number of atoms, ions, or molecules, which is approximately 6.022 x 10²³ particles. This number is known as Avogadro's number, and it allows chemists to work with substance amounts at the atomic scale.
To solve for the mole fraction of a gas like oxygen in a mixture, you first need to calculate the total moles present using the sum of all individual mole quantities, as shown in the exercise. Next, applying the mole fraction formula—where you divide the moles of the gas of interest (oxygen in this instance) by the total moles of the mixture—will give you the proportion of that gas.
It's also important to cross-check your calculations, ensuring that the fractions add up to, or are close to, 1 (in case of minor rounding differences). Understanding mole calculations enriches your comprehension of chemical composition and reactions, forming a bridge between theoretical chemistry and practical application.