Question

a natural gas has a following composition by volume methane=82%, ethylene=12% N2=6% Calculate the density of gas at 288 k and 101.325kPa and composition in weight%​

Answer 1

Answer:

The ideal gas law relates four macroscopic properties of ideal gases (pressure, volume, number of moles, and temperature). If we know the values of three of these properties, we can use the ideal gas law to solve for the fourth. In this video, we'll use the ideal gas law to solve for the number of moles (and ultimately molecules) in a sample of gas.

Explanation:

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a natural gas has a following composition by volume methane=82%, ethylene=12% N2=6% Calculate the density of gas at 288 k and 101.325kPa and composition in weight%

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Priyanshu 20:14

Recall that the density of a gas is its mass to volume ratio,

ρ=mV

. Therefore, if we can determine the mass of some volume of a gas, we will get its density. The density of an unknown gas can used to determine its molar mass and thereby assist in its identification. The ideal gas law, PV = nRT, provides us with a means of deriving such a mathematical formula to relate the density of a gas to its volume in the proof shown in Example 1.

Example 1

Derivation of a Density Formula from the Ideal Gas Law

Use PV = nRT to derive a formula for the density of gas in g/L

Solution

PV = nRT

Rearrange to get (mol/L):

nv=PRT

Multiply each side of the equation by the molar mass, M

. When moles are multiplied by M in g/mol, g are obtained:(M)(nV)=(PRT)(M) g/L=ρ=PMRT

Check Your Learning

A gas was found to have a density of 0.0847 g/L at 17.0 °C and a pressure of 760 torr. What is its molar mass? What is the gas?

Answer:

ρ=PMRT

0.0847

g/L=760torr×1atm

760torr×M0.0821

Latm/mol K×290KM

= 2.02 g/mol; therefore, the gas must be hydrogen (H2, 2.02 g/mol)

We must specify both the temperature and the pressure of a gas when calculating its density because the number of moles of a gas (and thus the mass of the gas) in a liter changes with temperature or pressure. Gas densities are often reported at STP.