The Density of a Gas

We can rearrange the ideal gas law to calculate the density of a gas from its molar mass. Recall that the number of moles (n) is the mass (m) divided by the molar mass (jR), n = m/M. Substituting for n in the ideal gas law gives 

The second of these relationships explains why, for example, safety experts recommend staying near the floor when escaping from a fire to avoid the hot, and therefore less dense, noxious gases. We use Equation 5.9 to find the density of a gas at any temperature and pressure near standard conditions. 

Problem A chemical engineer uses waste CO2 from a manufacturing process, instead of chlorofluorocarbons, as a blowing agent in the production of polystyrene containers. Find the density (in g/L) of CO2 and the number of molecules per liter (a) at STP (0°C and 1 atm) and (b) at room conditions (20.°C and 1.00 atm). 

Plan We must find the density (d) and number of molecules of CO2, given the two sets of P and T data. We find M, convert T to kelvins, and calculate d with Equation 5.9. Then we convert the mass per liter to molecules per liter with Avogadro s number. 

Solution (a) Density and molecules per liter of CO2 at STP. Summary of gas properties  

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The pressure and the density of a gas are related by an equation of state. If the maximum pressure permitted within the centrifuge bowl is not too high, the equation of state for an ideal gas will suffice. The relationship between the pressure and density of an ideal gas is given by the weU-known equation ... 

Density The measure of the amount of mass in a unit volume. The density of a gas is a function of its pressure and temperature, It can be determined by using the ideal gas laws. 

The density of a gas decreases when the temperature of the gas is increased. The heated air in the balloon is lighter than the air around the balloon. This density 5 difference causes the balloon to rise (after it is untethered). 

From this equation we see that the density of a gas is dependent on—... 

As the density of a gas increases, free rotation of the molecules is gradually transformed into rotational diffusion of the molecular orientation. After unfreezing , rotational motion in molecular crystals also transforms into rotational diffusion. Although a phenomenological description of rotational diffusion with the Debye theory [1] is universal, the gas-like and solid-like mechanisms are different in essence. In a dense gas the change of molecular orientation results from a sequence of short free rotations interrupted by collisions [2], In contrast, reorientation in solids results from jumps between various directions defined by a crystal structure, and in these orientational sites libration occurs during intervals between jumps. We consider these mechanisms to be competing models of molecular rotation in liquids. The only way to discriminate between them is to compare the theory with experiment, which is mainly spectroscopic. 

We see that, for a given pressure and temperature, the greater the molar mass of the gas, the greater its density. Equation 10 also shows that, at constant temperature, the density of a gas increases with pressure. When a gas is compressed, its density increases because the same number of molecules are confined in a smaller volume. Similarly, heating a gas that is free to expand at constant pressure increases the volume occupied by the gas and therefore reduces its density. The effect of temperature on density is the principle behind hot-air balloons the hot air inside the envelope of the balloon has a lower density than that of the surrounding cool air. Equation 10 is also the basis for using density measurements to determine the molar mass of a gas or vapor. 

The molar concentrations and densities of gases increase as they are compressed but decrease as they are heated. The density of a gas depends on its molar mass. 

Since few chemicals (e.g. hydrogen, methane, ammonia) have a molecular weight less than that of air, under ambient conditions most gases or vapours are heavier than air. For example, for common toxic gases refer to Table 3.1 for flammable vapours refer to Table 5.1. At constant pressure the density of a gas or vapour is, as shown, inversely proportional to the absolute temperature. As a result ... 

Whereas liquids and solids have well-defined densities, the density of a gas varies strongly with the conditions. To see this, we combine the ideal gas equation and the mole-mass relation and rearrange to obtain an equation for... 

Since the density of a gas is strongly dependent on the temperature and pressure, knowing only the volumetric flow rate is not adequate. For this reason the flow is given above as so many standard cubic feet per minute (scfm). This is the volume of fluid that would be transferred at a temperature of 60°F (15.6°C) and a pressure of 14.7 psia(1.033 kg/cm2). For design purposes, this rate is usually increased by 5%.27... 

The density of a gas depends quite strongly on its temperature, so hot air has a smaller density than does cold air colder air is more dense than hot air. From everyday experience, we know that something is dense if it tries to drop, which is why a stone drops to the bottom of a pond and a coin sinks to the bottom of a pan of water. This relative motion occurs because both the stone and the coin have higher densities than does water, so they drop. Similarly, we are more dense than air and will drop if we fall off a roof. 

However, the sohd density is approximately 1000 times the density of a gas at atmospheric pressure, and molecules in gases and liquids have much higher drSusivities than in solids. Therefore, the reacting boundary (I or R) moves very slowly compared to the motion of gas molecules to and from the boundary, and we can assume that concentration profiles near this boundary remain in steady state while we calculate the steady-state concentration profiles in the reaction... 

What happens to the density of a gas as it is compressed into a smaller volume ... 

Internal fluctuations are caused by the discrete nature of matter. The density of a gas fluctuates because the gas consists of molecules fluctuations in a chemical reaction arise because the reaction consists of individual reactive collisions current fluctuations exist because the current is made up of electrons radioactive decay fluctuates owing to the individuality of the nuclei. Incidentally, this explains why the formulas for fluctuations in physical systems always contain atomic constants, such as Avogadro s number, the mass of a molecule, or the charge of an electron. 

A gas may be defined as a homogeneous fluid of low density and low viscosity, which has neither independent shape nor Volume but expands to fill completely the vessel in which it is contained. The properties of gases differ considerably from the properties of liquids, mainly because the molecules in gases are much farther apart than molecules in liquids. For instance, a change in pressure has a much greater effect on the density of a gas than of a liquid. 

Since density is defined as the mass of gas per unit volume, an equation of state can be used to calculate the densities of a gas at various... 

VAPOR DENSITY. The density of a gas referred to the density of hydrogen or air as unity, If the density- of hydrogen is taken as 2, the vapor density is approximately the molecular weight if it is taken as one, the vapor density equals about half die molecular weight,... 

The molar concentration of a gas and a related quantity, the density of a gas, are both of great interest to meteorologists as well as to engineers. As we saw in Section G, the molar concentration is the number of moles of molecules divided by the volume of the sample (n/V). It follows from the ideal gas law that, for a gas behaving ideally,... 

As the density of a gas is increased and/or its temperature is lowered towards or below the critical temperature, Tc, new phenomena associated with the trapping and localization of positrons are sometimes encountered, indicating that many-body processes affect positron annihilation. We briefly describe these phenomena here, but a much more detailed treatment can be found in the review of Iakubov and Khrapak (1982). 

Unlike solids and liquids, the density of a gas depends very strongly on the temperature and pressure. Also, unlike solids and liquids, we can easily calculate the density of a gas if we know the temperature and pressure. For example, what is the density of air under normal conditions (25°C and 750 torr) Recall that air is approximately 79% nitrogen and 21% oxygen (by volume). If we want to calculate the density of a sample, we need to know its mass and volume. Since density is an intrinsic physical property, we can take any sample size we want, so let s take a sample volume of 1.0 L. 

Thus the only way to make a complex is to transfer some of the internal energy to another system. In practice, this means three or more molecules have to all be close enough to interact at the same time. The mean distance between molecules is approximately (V/N)1 /3 (the quantity V/N is the amount of space available for each molecule, and the cube root gives us an average dimension of this space). At STP 6.02 x 1023 gas molecules occupy 22.4 L (.0224 m3) so (V/N)1/3 is 3.7 nm—on the order of 10 molecular diameters. This is expected because the density of a gas at STP is typically a factor of 103 less than the density of a liquid or solid. So three-body collisions are rare. In addition, if the well depth V (rmin) is not much greater than the average kinetic en-... 

Suppose the density of a gas is kept constant, but the temperature is doubled. Predict what would happen to (a) the mean free path A. (b) the mean time between collisions r (c) the diffusion constant D. If you can, use your intuition about the physical process, rather than substitution into equations derived in this chapter. 

As previously discussed, the density of the fluid whose flow is to be measured can have a large effect on flow sensing instrumentation. The effect of density is most important when the flow sensing instrumentation is measuring gas flows, such as steam. Since the density of a gas is directly affected by temperature and pressure, any changes in either of these parameters will have a direct effect on the measured flow. Therefore, any changes in fluid temperature or pressure must be compensated for to achieve an accurate measurement of flow. 

The density of a gas can be measured in the same way as the density of a solid or liquid—by dividing its mass by its volume. Because the particles in a gas are very spread out, gas densities are very small numbers and are usually described in units of grams per liter as opposed to grams/mL or grams/cm3 (as would be the case for solids or liquids). The AP test occasionally has gas density questions on it, so you should be familiar with the method for solving them. The equation for calculating gas density can be derived from the ideal gas equation. 

One of the laboratory procedures that you are expected to know involves the determination of molar mass from gas density. In the sample calculation that follows, you will solve for the density of a gas, but understand that a simple rearrangement of the equation allows you to solve for the molar mass. 

The density of a gas is similar to the density of a solid or a liquid. Density is found by dividing mass by volume. The density of a gas is usually reported in units of g/L. 

You will be debating a question related to gas pollution in the Unit Issue. How does the density of a gas determine whether the gas pollutes Earths surface or the atmosphere ... 

The relationship between the different state variables of a system subjected to no external forces other than a constant hydrostatic pressure can generally be described by an equation of state (EOS). In physical chemistry, several semiempirical equations (gas laws) have been formulated that describe how the density of a gas changes with pressure and temperature. Such equations contain experimentally derived constants characteristic of the particular gas. In a similar manner, the density of a sohd also changes with temperature or pressure, although to a considerably lesser extent than a gas does. Equations of state describing the pressure, volume, and temperature behavior of a homogeneous solid utilize thermophysical parameters analogous to the constants used in the various gas laws, such as the bulk modulus, B (the inverse of compressibUity), and the volume coefficient of thermal expansion, /3. 

Matter occurs in three states, or phases sohd, liquid, and gaseous. A solid has a definite shape and a definite volume. A liquid has a definite volume but assumes the shape of its container. A gas does not have a definite volume or shape it expands to fill the entire volume of the container it occupies. The density of a gas is generally very much lower than the density of the same substance in the solid or liquid state. A gas (like a liquid) exerts a pressure in all directions at any point within the gas. 

We can calculate the density of a gas using the ideal gas law plus molar mass data. 

The density of a gas can be converted to moles per liter, and that value used in the ideal gas law equation. 

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