A 100 m^3 storage tank with fuel gases is at 20^∘ C and 100 kPa containing a mixture of acetylen

A 100 m^3 storage tank with fuel gases is at 20^∘ C and 100...

A $100 \mathrm{m}^{3}$ storage tank with fuel gases is at $20^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$ containing a mixture of acetylene $\mathrm{C}_{2} \mathrm{H}_{2},$ propane $\mathrm{C}_{3} \mathrm{H}_{8},$ and butane $\mathrm{C}_{4} \mathrm{H}_{10} .$ A test shows the partial pressure of the $\mathrm{C}_{2} \mathrm{H}_{2}$ is $15 \mathrm{kPa}$ and that of $\mathrm{C}_{3} \mathrm{H}_{8}$ is $65 \mathrm{kPa}$. How much mass is there of each component?

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Key Concepts

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, connects the pressure, volume, temperature, and number of moles of a gas. It is fundamental in determining the amount of individual gas components in a mixture when operating under known state conditions, such as fixed temperature and volume.

Dalton's Law of Partial Pressures

Dalton's law states that in a mixture of non-reacting gases, the total pressure is the sum of the partial pressures of the individual gases. This principle allows one to assign a pressure contribution to each gas, which can then be used to determine its mole fraction and amount.

Molar Mass and Mass Calculations

Molar mass is the mass of one mole of a substance and is essential for converting from moles, as determined by the ideal gas law, to the actual mass of each component. This conversion is crucial in quantifying the material present in a gaseous mixture.

Gas Mixtures and Mole Fractions

Understanding mole fractions in gas mixtures, which relate the number of moles of a given component to the total number of moles, is important when applying Dalton's and the ideal gas laws together. It helps in interpreting the contribution of each gas in terms of its partial pressure and overall composition.

Transcript

00:01 Hi, everybody.

00:01 So for this one, it is asking how much, how much mass is there of each component? so for this, where we have the partial pressure of, so i'll put partial pressure, and i'll just put p for pressure, okay, pressure of the p .c for each 10, okay.

00:32 And here we have p minus p c2h2 minus p c3h8.

00:43 And here we have 100 minus 15 minus 65.

00:50 And we get 20k past goals, okay? so now we have your y, c2h2, and that's going to equal to pressure of c2.

01:02 H2 divided by pressure and here we have 15 divided by 100.

01:09 Okay.

01:12 And here we get 0 .15 and we can do the y of c3h8.

01:20 And here we have the pressure of c3h8 divided by the pressure and here we have 65 divided by 100.

01:31 Equals 0 .65, okay? and we're just going to do the same thing to see for each 10.

01:41 Okay, and that's going to be 20 divided by 100 equals 0 .2.

01:48 Okay.

01:50 And now we can find the number of moles.

01:54 We have pv divided by r2, divided by rt.