Gas molar volumes

Based on Avogadro s law, one mole of a gas occupies the same volume as one mole of another gas at the same temperature and pressure. The molar volume of a gas is the space that is occupied by one mole of the gas. Molar volume is measured in units of L/mol. You can find the molar volume of a gas by dividing its volume by the number of moles that are present (- ). Look at the Sample Problem below to find out how to calculate molar volume. Then complete the following Thought Lab to find the molar volumes of carbon dioxide gas, oxygen gas, and methane gas at STP. 

So, the Ideal Gas Law can be used to verify our value for the volume occupied by one mole of any gas (molar volume) at STP. Remember that one dm3 is equivalent to one liter, so these units are interchangeable. 

While the same eos-derived ([) equation is used for both ( ),l and ( ) the input variables to the equation are different for (() l, the liquid mol fractions X and liquid molar volume are the input for (j) the gas mol fractions and gas molar volume Vy are the input. Find the liquid volume Vl by solving the eos at specified [X p,] and pick the small root find the vapor volume Vy by solving the eos at specified, [y p,] and pick the large root. The vapor-liquid equilibrium calculations using K values are much the same as in the use of y-cj) K values. 

Here, as in (4.1.16), the pure ideal-gas molar volumes are related to the mixture molar volume by t , = Nv/N. Equation (4.2.13) applies to both first-law and second-law properties, and we have... 

The fact that at any temperature other than the Boyle temperature B is nonzero is significant since it means that in the limit as p approaches zero at constant T and the gas approaches ideal-gas behavior, the dijference between the actual molar volume Fm and the ideal-gas molar volume RTJp does not approach zero. Instead, V,s. — RT/p s5)proaches the nonzero value B (see Eq. 2.2.8). However, the ratio of the actual and ideal molar volumes, V /( RT/p), approaches unity in this limit. 

It follows from Avogadro s law that the volume occupied by one mole of molecules must be the same for all gases (Figure 1.46). It is known as the gas molar volume and has an approximate value of 22.7 dm at 0°C (273 K) and 1 atmosphere (100 kPa). These conditions are known as standard temperature and pressure (STP). 

Well, because MATLAB in essence deals with matrices (pancake) and vectors (corn flicks) as its favorite meal, then values of temperature and pressure can be entered here as row vectors. Figure 11.14 shows t5 ical results for the calculated ideal gas molar volume expressed in L/mol. A set of three values of T and P was entered twice and the corresponding molar volumes were calculated for each of the two sets. Notice how the molar volume, V, increases with T fFig. 11.14. top) and decreases with P tFig. 11.14. bottom). 

Figure 11.14 The calculated ideal gas molar volume is shown in the third Edit-Text box as a function of input temperature and pressure. Three isobaric (P = 1 atm) temperature values were entered to see the effect of increasing temperature on volume top) on the other hand, three isothermal (T = 25°C) pressure values were entered to see the effect of increasing pressure on volume (bottom).

Suppose that we would like to calculate the following volume-related properties of a pure substance (not necessarily an ideal gas)—the gas molar volume, liquid molar volume, isothermal compressibility factor (kappa, k), thermal expansion coefficient (alpha, a), and compressibility factor (Z)—while inputting both the pressure in atmosphere and temperature in Kelvin. The calculation is based on the van der Waals equation of state. Let us design a GUI that handles such a duty. Details on how to add controls to a blank GUI and how to customize them are shown in previous sections. However, more features are explored here that have not been covered before. Given that a database exists in the form of an Excel sheet, which lists the name of a substance, its chemical formula, its critical pressure, and its critical temperature, we would like the user to search for the substance of interest via a keyword that is based either on name or chemical formula. The search results shall be presented and the user will then decide on the substance of interest via selecting the corresponding... 

Figure 11.21 The heart of GUI where the essential steps are carried out upon clicking the Calculate Properties push button. The gas molar volume, liquid molar volume, isothermal compressibility factor (kappa, k) for both phases, thermal expansion coefficient (alpha, a) for both phases, and the compressibility factor (Z) are all estimated for a given selected substance while inputting both the pressure in atmosphere units and temperature in Kelvin. The calculations are based on van der Waals equation of state.

Subtracting the ideal gas molar volume and inserting in Equation 5.18 yields... 

In 1873, van der Waals [2] first used these ideas to account for the deviation of real gases from the ideal gas law P V= RT in which P, Tand T are the pressure, molar volume and temperature of the gas and R is the gas constant. Fie argried that the incompressible molecules occupied a volume b leaving only the volume V- b free for the molecules to move in. Fie further argried that the attractive forces between the molecules reduced the pressure they exerted on the container by a/V thus the pressure appropriate for the gas law isP + a/V rather than P. These ideas led him to the van der Waals equation of state ... 

When, for a one-component system, one of the two phases in equilibrium is a sufficiently dilute gas, i.e. is at a pressure well below 1 atm, one can obtain a very usefiil approximate equation from equation (A2.1.52). The molar volume of the gas is at least two orders of magnitude larger than that of the liquid or solid, and is very nearly an ideal gas. Then one can write... 

Although later models for other kinds of systems are syimnetrical and thus easier to deal with, the first analytic treatment of critical phenomena is that of van der Waals (1873) for coexisting liquid and gas [. The familiar van der Waals equation gives the pressure p as a fiinction of temperature T and molar volume F,... 

Unlike the pressure where p = 0 has physical meaning, the zero of free energy is arbitrary, so, instead of the ideal gas volume, we can use as a reference the molar volume of the real fluid at its critical point. A reduced Helmlioltz free energy in tenns of the reduced variables and F can be obtained by replacing a and b by their values m tenns of the critical constants... 

This equation describes the additional amount of gas adsorbed into the pores due to capillary action. In this case, V is the molar volume of the gas, y its surface tension, R the gas constant, T absolute temperature and r the Kelvin radius. The distribution in the sizes of micropores may be detenninated using the Horvath-Kawazoe method [19]. If the sample has both micropores and mesopores, then the J-plot calculation may be used [20]. The J-plot is obtained by plotting the volume adsorbed against the statistical thickness of adsorbate. This thickness is derived from the surface area of a non-porous sample, and the volume of the liquified gas. 

Since the molar volume of the liquid, V, is very small compared with that of the vapour, and if the vapour fi behaves as a perfect gas, then Equation (3.16) becomes... 

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