Using Figure 5.15 (a) estimate the density of methane gas at...

Using Figure 5.15
(a) estimate the density of methane gas at 100 atm.
(b) compare the value obtained in (a) with that calculated from the ideal gas law.
(c) determine the pressure at which the calculated density and the actual density of methane will be the same.

Key Concepts

Compressibility Factor

The compressibility factor, denoted as Z, is a dimensionless quantity that quantifies how much a real gas deviates from ideal behavior. It is defined as the ratio of the actual molar volume of a gas to the molar volume predicted by the Ideal Gas Law at the same temperature and pressure. A value of Z close to 1 indicates that the gas behaves almost ideally, while values significantly different from 1 indicate strong non-ideal behavior.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics, expressed as PV = nRT, which relates pressure, volume, temperature, and the number of moles of a gas. It assumes that the gas particles do not interact and that their volumes are negligible, simplifying the behavior of gases under many conditions, especially at low pressures and high temperatures.

Real Gas Behavior

Real gases deviate from the Ideal Gas Law under conditions of high pressure or low temperature, where intermolecular forces and the finite size of gas molecules become significant. Understanding real gas behavior involves recognizing these deviations and applying corrective factors or alternative equations of state to obtain more accurate predictions of properties such as density.

Gas Density Calculation

Calculating the density of a gas, particularly under non-ideal conditions, involves determining the mass per unit volume and accounting for deviations from ideal behavior. For an ideal gas, density can be estimated using the relation ? = PM/RT, where M is the molar mass. However, for real gases, corrections based on experimental data, compressibility factors, or alternative equations of state are incorporated to yield accurate density estimates.

Transcript

00:01 In this video, we're looking at figure 5 .15 in chapter 5 of the textbook.

00:07 So we are asked to estimate the density of methane gas at 100 atmosphere.

00:15 What the figure shows is a plot of the ratio of the molar volumes against the pressure for methane at 25 degrees celsius.

00:30 Molar volume is equal to the volume divided by the moles, and molar volume is v when n is equal to 1.

00:46 Now, vm is the experimentally observed molar volume, and we compare that to the molar volume calculated from ideal gas law.

01:00 So this is how we would get it.

01:14 The pressure is changing while r and t are staying the same.

01:20 And t is equal to 25 degrees celsius and we have to convert that to calvin when working with the ideal gas law.

01:29 So we're going to add 273 .15 and what we are going to get is 298 .15 kelvin.

01:44 Now we're out to find the density and as you know density is equal to mass divided by volume.

01:50 So first of all, we should find the standard molar volume from the ideal gas.

01:55 Law.

01:56 So we have to plug in the values here and then the pressure is 100.

02:19 So plug that into your calculator.

02:34 We end up getting 0 .245 liters.

02:42 So this is the volume that is predicted from the ideal gas law...

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