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When dealing with gases, partial pressures represent the pressure contribution of an individual gas in a mixture. This is an important concept in the study of gas behavior, especially when using the Ideal Gas Law. In a mixture, each gas exerts its own pressure, known as its partial pressure. This pressure depends on the number of moles of the gas, the temperature, and the volume of its container.

The total pressure of a gas mixture is simply the sum of these partial pressures. For the problem you are working on, the partial pressures of helium and oxygen sum up to provide the total pressure of the mix:

• The partial pressure of helium is given as 42.5 torr.
• The partial pressure of oxygen is given as 158 torr.

Knowing how to add these pressures is key to understanding the system's behavior under these conditions.

Calculating the number of moles is a fundamental part of applying the Ideal Gas Law. Moles are a way to express amounts of a substance in chemistry. They help us connect macroscopic and microscopic events through the use of Avogadro's number.

To convert from mass to moles, we need to use the formula: \[ n = \frac{\text{mass of the gas}}{\text{molar mass}} \] Let’s see how this works:

• For helium, with a molar mass of 4.00 g/mol, if we have 1.42 grams, we find the moles by dividing the mass by the molar mass: \[ n_{He} = \frac{1.42}{4.00} = 0.355 \text{ mol} \]
• Understanding this conversion is crucial as it allows us to apply the ratio of partial pressures to find moles of the other gas, in this case, oxygen, within the mixture.

By using the partial pressure data, you can find a relation between different gases in the mixture without knowing individual temperatures and volumes.

Molar mass is an essential element when working with the Ideal Gas Law. It allows you to convert between grams and moles, which is a critical skill when solving chemistry problems.

Each element has a specific molar mass which tells you how much one mole of that substance weighs in grams. For oxygen in its diatomic form, which is common in problems like yours, the molar mass is 32.00 g/mol.

• You calculate the molar mass of a compound by adding up the molar masses of its individual elements.
• For example, oxygen gas \((O_2)\) is made of two oxygen atoms, each with a molar mass of 16.00 g/mol, leading to a molar mass of 32.00 g/mol for \(O_2\).
• Once you find the moles of a substance using the partial pressure and moles calculation, like for oxygen, multiply by its molar mass: \[ \text{mass of } O_2 = 1.319 \text{ mol} \times 32.00 \frac{\text{g}}{\text{mol}} = 42.21 \text{ g} \]

This conversion from moles to mass helps you quantify how much of a substance you actually have in a container, tying together the concepts of partial pressures, moles, and molar mass.