(a) What are the mole fractions of N 2 in a mixture of 15.08 g of O 2 , 8.17 g of N 2 , and 2.64 g of H 2 ?

hey everyone in this example, we have a flask containing all of the given masses of these three gasses. Xenon chlorine and helium and we need to calculate the mole fraction of chlorine gas in this molecule or in this flask. Sorry. So we want to recall our formula for mole fraction which is taking the moles of our designated gas, which in this case is the chlorine gas molecule and dividing it by our total moles. As you can see in the prompt were given masses and grams and we want to go ahead and find the moles of each of these gasses. So beginning with our moles of xenon, We would find that taking the given massive zine on 16.3 g. We're going to refer to our periodic tables for xenon and find the molar mass of xenon equal to 131.29 g for one mole of xenon. So now we're able to cancel out our units of grams. Leaving us with moles of xenon, which is what we want. And this is going to give us a value equal to 0.1241 moles of arson on gas. Moving on to the next mask, they give us were given for to find the molds of cl two were given 7.52 g of cl two. And we're going to pay close attention here because when we look to our periodic table, we see for the molar mass of one atom of chlorine and that's equal to 35.45 g per mole. But because we have cl two, we're going to take that molar mass and multiply it by two. And that's gonna give us a molar mass of 70.9 g of cl two for one mole of cl two. And so this gives us an amount of molds equal to 0.1061 moles of our cl two gas molecule since it's a halogen. And so next we have our molds of helium that we need to find. And so we're given a mass of 4.15 g of helium from the prompt and utilizing the molar mass of our Noble gas helium in our denominator we're going to find according to the product table, we have a molar mass of 4.003g of helium for one mole of helium. And so now we're able to yet again cancel out our units of g. Just like we've done above leaving us with moles of helium as our final unit and we should have had moles of helium here. Or sorry, M.olds of chlorine for our prior setup. And so what we're going to get here is a value equal to 1.0367 moles of our helium gas. And so according to this problem, we want to find mole fraction which we can recall is represented by this x here. Next to our given designated gas. So we're gonna go ahead and find our mole fraction of cl two and this is going to equal in our numerator. Are molds of our gas which are designated gas that this question is asking about is our Cl two molecule. So we did find the molds of our Cl two molecule here, which we're gonna plug in the numerator. So we're plugging that in as 20.1061 moles of cl two. And then in our denominator, we want to plug in our total molds of all of our gas is so we're going to add all of these molds of our gas is up and place that in our denominator. And so adding these three values up here, we would get our total moles For a denominator equal to a value of 1.2669 moles. So we can plug that into our denominator, 1.2669 moles Of all of our gasses. And this is going to be equal to our mole fraction of chlorine gas, equal to a value of 0.0837. And so to complete this example, this would be our final answer for our mole fraction of our chlorine gas molecule. So I hope that everything I reviewed was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video

Ch.10 - Gases

Brown - Chemistry: The Central Science 14th Edition

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Ch.10 - Gases

Problem 72a2

Chapter 10, Problem 72a2

(a) What are the mole fractions of N₂ in a mixture of 15.08 g of O₂, 8.17 g of N₂, and 2.64 g of H₂?

Verified step by step guidance

Calculate the molar mass of each gas: O_2, N_2, and H_2.

Convert the mass of each gas to moles using the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).

Sum the moles of all gases to find the total moles in the mixture.

Calculate the mole fraction of N_2 using the formula: \( \text{mole fraction of N}_2 = \frac{\text{moles of N}_2}{\text{total moles}} \).

Express the mole fraction as a decimal.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a specific component to the total number of moles of all components in the mixture. This dimensionless quantity helps in understanding the composition of gas mixtures and is crucial for calculations involving partial pressures and gas laws.

Calculating Moles from Mass

To find the mole fraction, one must first convert the mass of each gas into moles using the formula: moles = mass (g) / molar mass (g/mol). The molar mass is a characteristic property of each substance, allowing for the determination of how many moles are present in a given mass. This step is essential for accurately calculating the mole fractions of the gases in the mixture.

Total Moles in a Mixture

The total number of moles in a mixture is the sum of the moles of all individual components. Once the moles of each gas are calculated, they are added together to find the total moles. This total is necessary for determining the mole fraction of each component, as it serves as the denominator in the mole fraction formula, ensuring that the fractions represent the correct proportions of each gas in the mixture.