Question

A gaseous mixture contains \(40 \% \mathrm{H}_{2}\) and \(60 \% \mathrm{He}\), by volume. What is the total number of moles of gases present in \(10 \mathrm{~g}\) of such mixture? (a) 5 (b) \(2.5\) (c) \(3.33\) (d) \(3.125\)

Short answer

(A) 3.0 (B) 3.3 (C) 3.6 (D) 4.0 (E) 4.2 Answer: The total number of moles of gases present in 10g of such mixture is 3.5 moles. However, this value does not match any of the options provided. Therefore, there might be an error in the given options or the problem formulation itself.

Step-by-step solution

Determine the mass of each component in the mixture.

To do this, we will use the given volume percentages of the mixture and the total mass of the mixture (10g). We have 40% hydrogen and 60% helium, so the mass of each component can be calculated as follows: Mass of hydrogen = (40% of 10g) = 0.4 * 10g = 4g Mass of helium = (60% of 10g) = 0.6 * 10g = 6g

Calculate the number of moles of each component.

We can use the molecular weights of hydrogen and helium to calculate the moles of each gas in the mixture. The molecular weight of hydrogen (H2) is 2 g/mol, and the molecular weight of helium (He) is 4 g/mol. Moles of hydrogen = (mass of hydrogen) / (molecular weight of hydrogen) = 4g / 2 g/mol = 2 moles Moles of helium = (mass of helium) / (molecular weight of helium) = 6g / 4 g/mol = 1.5 moles

Calculate the total moles of gases in the mixture.

Now that we have the moles of both hydrogen and helium, we can find the total moles of the mixture by summing them up: Total moles of gases = Moles of hydrogen + Moles of helium = 2 moles + 1.5 moles = 3.5 moles So, the total number of moles of gases present in 10g of such mixture is 3.5 moles. However, this value does not match any of the options provided. Based on the analysis, there may be an error in the given options or the problem formulation itself.

Key concepts

Molecular Weight

Molecular weight, also known as molecular mass, is a critical concept when working with chemical substances. It can be defined as the sum of the atomic weights of all the atoms in a molecule, expressed in atomic mass units (u) or grams per mole (g/mol). Knowing the molecular weight of a substance allows us to relate the mass of a substance to the number of molecules or moles present.

For example, a molecule of water (H₂O) is composed of two hydrogen atoms and one oxygen atom. Considering that hydrogen has an atomic weight of approximately 1 u and oxygen has an atomic weight of about 16 u, the molecular weight of water would be calculated as 2(1) + 16 = 18 g/mol. This means that one mole of water, which contains Avogadro's number (approximately 6.022 x 10²³) of molecules, weighs 18 grams.

Volume Percentage Composition

Volume percentage composition is another valuable concept in chemistry, particularly when dealing with mixtures of gases. It reflects the proportion of the total volume occupied by each component gas in a mixture. The volume percentage is calculated by dividing the volume of one component by the total volume of the mixture and then multiplying by 100%. This information is especially useful when the gases in the mixture do not react with one another and occupy volume independently.

In the context of our example, we have a gaseous mixture with volume percentages listed as 40% hydrogen and 60% helium. This percentage merely tells us how much space each gas is occupying relative to the whole mixture and not directly how many particles or moles of gas there are. To calculate moles from volume percentage, we must also know the total mass or volume of the mixture along with the molecular weights of the gases.

Calculating Moles

Calculating moles is a fundamental skill in chemistry, as it allows us to measure the amount of a substance in a more meaningful way than just mass or volume. A mole is a unit that represents a set number of particles, specifically Avogadro's number of particles.

To calculate the number of moles of a substance, we divide the mass of the substance by its molecular weight. The formula for this calculation is:
\[ \text{moles} = \frac{\text{mass (g)}}{\text{molecular weight (g/mol)}} \]
Applying this to a mixture requires knowing the mass of each individual component, as we have in our exercise with hydrogen and helium. Once the moles of each component are calculated, the total moles of the mixture can simply be found by adding the moles of all components together. However, it's crucial to ensure that the mass proportions of each gas correspond correctly to their volume percentages, which has been illustrated in the example exercise.