How Do You Calculate the Mass of Each Gas Component in a Heated Mixture?

[Jacob87411]

1. A mixture at T=300 K and P=100 kPa is made up of .1 oxygen, .2 carbon dioxide, and .7 Nitrogen. It is then heated to 300 kPa and 500 K. Find the mass of each component


I originally thought using PV=NRT, ideal gas but there doesn't seem to be enough givens. Can you also find the molar mass of the mixture by doing:

.7(28)+.2(44)+.1(32), so then you can find the mass of the component when you find the number of moles N but I am having problems doing that

 

[Gokul43201]

Yes, the question is incomplete. In addition, it's ambiguous, as it does not state whether .1, .2 and .7 are mass or molar (ie, volume) ratios (assuming they are ratios).

 

[Blueshift5]

.

I would approach this problem by first converting the given percentages into mole fractions. This can be done by dividing the given mass fraction by the molar mass of each component. In this case, the molar masses are 28 g/mol for oxygen, 44 g/mol for carbon dioxide, and 32 g/mol for nitrogen.

Next, I would use the ideal gas law, PV = nRT, to calculate the number of moles of the mixture at the initial conditions (T=300 K and P=100 kPa). The volume can be assumed to be constant, so the number of moles will also be constant.

Then, I would use the same equation to calculate the number of moles at the final conditions (T=500 K and P=300 kPa). Again, the volume can be assumed to be constant.

Using the mole fractions calculated earlier, the number of moles of each component can be determined. Finally, the mass of each component can be found by multiplying the number of moles by the molar mass.

Alternatively, as you suggested, the molar mass of the mixture can also be calculated by adding the molar masses of each component multiplied by their respective mole fractions. This can then be used to find the mass of each component when the number of moles is known.

In conclusion, to solve this problem, we need to use the ideal gas law and mole fractions to calculate the number of moles of the mixture at both initial and final conditions. Then, we can use the molar mass of the mixture or the molar masses of each component to find the mass of each component.