A 100-m^3 storage tank with fuel gases is at 20^∘ C, 100 kPa containing a mixture of acetylene (

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

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

A $100-\mathrm{m}^{3}$ storage tank with fuel gases is at $20^{\circ} \mathrm{C}, 100 \mathrm{kPa}$ containing a mixture of acetylene $\left(\mathrm{C}_{2} \mathrm{H}_{2}\right),$ propane $\left(\mathrm{C}_{3} \mathrm{H}_{8}\right),$ and butane $\left(\mathrm{C}_{4} \mathrm{H}_{10}\right) . \mathrm{A}$
test shows that the partial pressure of the $\mathrm{C}_{2} \mathrm{H}_{2}$ is $15 \mathrm{kPa}$ and that of the $\mathrm{C}_{3} \mathrm{H}_{8}$ 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 (PV = nRT) is a fundamental principle in thermodynamics that relates the pressure, volume, temperature, and number of moles of a gas. It serves as the basis for computing the amount of gas, given any three of these state variables, and is essential for analyzing gas behavior in confined systems.

Dalton's Law of Partial Pressures

Dalton's Law states that for a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of individual gases. This law allows us to relate a component's partial pressure to its mole fraction, which is critical when analyzing mixtures of gases.

Mole Fraction

The mole fraction of a gas in a mixture is defined as the ratio of the number of moles of that specific gas to the total number of moles in the mixture. It is directly proportional to the partial pressure of the gas, providing a simple method for determining the composition of the mixture.

Molar Mass and Mass Calculation

Molar mass is the mass of one mole of a substance and is used to convert the number of moles obtained from gas laws into a mass. By calculating the moles of each component gas and then multiplying by the corresponding molar mass, one can determine the mass of each gas in the mixture.

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