Values of the Universal Gas Constant

PROOF THAT FOR A FLUID AT REST THE PRESSURE IS THE SAME IN ALL DIRECTIONS  

The laws of fluid mechanics work perfectly well in any gravity situation, including the zero gravity of an earth satellite. The following proof is shown for zero gravity, because that makes it simple. The result is then extended for a finite gravity field. The proof rests on the definition of a fluid A fluid, when subject to any shear stress, moves.  

Consider a prism of fluid, as shown in Fig. B.l. For the fluid to be at rest, there can be no shear forces on any surfaces of the prism. Furthermore, because it is at rest, there are no unbalanced forces i.e., the sum of the forces in any direction is zero. For the sum of the forces in the z direction to be zero, the pressure force on ABCD must equal the z component of the pressure force on BCFD, or 

Equation B.2 is true for any angle 8. It shows that the pressure in any direction is the same as the pressure vertically upward and he nce that the pressure is the same in all directions. j 

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Values of the universal gas constant, R (from Engineering Data Book, GPSA, 1987, with permission)... 

Table 17.1 shows the standard enthalpy change as a function of pH for both aqueous chlorine and chloramines, and Table 17.2 shows the various possible values of the universal gas constant. 

RT. The control card RT is used to set the value of the variable RT used only when printing the value of PIE, the Lagrange multipliers computed by the program. PIE RT, the true value for the Gibbs free energy, is also printed. RT is set to its nominal value of 616.27403 by the control card CLEAR. It is the value of the universal gas constant times absolute temperature in gram-calories per mole at... 

The osmotic pressure of the solution can be calculated using Equation 10.108, where molarity of salt is approximately 0.6 and at room temperature (298 K) the value of the universal gas constant s R = 0.08205 I atm/K mol. Substituting, thus, into Equation 10.108 ... 

Find the value for the universal gas constant R for the following combinations of units ... 

The constant 10.722 is from the generally used value for the universal gas constant of 1544 when the pressure is in Ib/ft absolute. 

In this very useful form, Rg is known as the universal gas constant, has a value of 1545 and is the same for all gases. The specific gas constant (i i) for any gas can be obtained by dividing 1545 by the molecular weight. Rg is only equal to 1545 when gas pressure (p) is in PSIA volume (y) is expressed as cubic feet per pound mole and temperature (T) is in Rankine or absolute, i.e. °F + 460. 

Thus, if the saturated vapor pressure is known at the azeotropic composition, the activity coefficient can be calculated. If the composition of the azeotrope is known, then the compositions and activity of the coefficients at the azeotrope can be substituted into the Wilson equation to determine the interaction parameters. For the 2-propanol-water system, the azeotropic composition of 2-propanol can be assumed to be at a mole fraction of 0.69 and temperature of 353.4 K at 1 atm. By combining Equation 4.93 with the Wilson equation for a binary system, set up two simultaneous equations and solve Au and A21. Vapor pressure data can be taken from Table 4.11 and the universal gas constant can be taken to be 8.3145 kJ-kmol 1-K 1. Then, using the values of molar volume in Table 4.12, calculate the interaction parameters for the Wilson equation and compare with the values in Table 4.12. 

If there is exactly 1 mol of gas, the pressure is expressed in pascals (Pa), the temperature is in kelvin and the volume is in cubic metres (both SI units), then the value of the constant is 8.314 JK-1 mol-1. We call it the gas constant and give it the symbol R. (Some old books may call R the universal gas constant , molar gas constant or just the gas constant . You will find a discussion about R on p. 54) More generally, Equation (1.12) is rewritten as... 

A change in the temperature at which a reaction is taking place affects the rate constant k. As the temperature increases, the value of the rate constant increases and the reaction is faster. The Swedish scientist Arrhenius derived a relationship in 1889 that related the rate constant and temperature. The Arrhenius equation has the form k= Ae EalPT where k is the rate constant, A is a term called the frequency factor that accounts for molecular orientation, e is the natural logarithm base, R is the universal gas constant 8.314 J mol K-, / is the Kelvin temperature, and Ea is the activation energy, the minimum amount of energy that is needed to initiate or start a chemical reaction. 

Where Q is the reaction quotient (discussed in Chapter 14), n is the number of electrons transferred in the redox reaction, R is the universal gas constant 8.31 J/(mol K), T is the temperature in kelvins, and Fis the Faraday constant 9.65x10 coulombs/mol, where coulomb is a unit of electric charge. With this information, you can assign quantitative values to the EMFs of batteries. The equation also reveals that the EMF of a battery depends on temperature, which is why batteries are less likely to function well in the cold. 

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