Units for the Gas Constant

Rate = kPx for a first-order reaction of a gas X. What are the units for the rate constants when partial pressures are expressed in torr and time is expressed in seconds for (a) zero-order reactions (b) first-order reactions (c) second-order reactions ... 

The units for kG will depend on the units used for the gas constant ... 

Fig. 2.10. Smoothed value for the 3He specific heat (in units of the gas constant R) measured at molar volume V corresponding to nominal sample pressure of 0.0 bar. Data from [28].

Using the above units, we obtain the following figures for the gas constant R ... 

The ideal gas equation combines the variables of temperature, pressure and volume that we have been dealing with in the previous sections, but also allows us to calculate the mass in either grammes or moles and also an approximate molar mass for the particular gas. The previous gas laws involved an unknown constant that we eliminated from the calculation by taking temperatures, etc, at two different levels. In the ideal gas equation, we are introduced to the universal gas constant, R, which enables us to do the measurements under one set of conditions only. The difficulty arising from this is that the units of the gas constant are dependent on the units in which the other variables are measured, so it is important to think about the units you are working in. A selection of values for R using different units is listed in Table 4.5.3. 

In the case we are considering, there is no mechanical power extracted, and so we may set P = 0. In line with our choice of kmol units for the gas mixture, we will make the assumption that it acts as a gas with Z = 1 or a near-ideal gas (Z = constant). We may then substitute... 

It is not always apparent to a student just what value should be used for the gas constant, R, but one can always calculate the appropriate value using the units used for H and remembering that 1 mol of gas occupies 22.4 L at standard temperature and pressure. For example, given that // = 2910 Pa m mol at 25°C,... 

Because logarithms have no units, the numerator in this equation is dimensionless. The denominator has the units of 1/T, namely, K . Thus, the overall units for the slope are K. The slope equals —EjR. We use the value for the gas constant R in units of J/mol-K (Table 10.2). We thus obtain... 

Fig. 16. Temperature dependence of 4f-derived specific heat, C, and entropy in units of the gas constant, SJR, for (a) CeRu j Gcj and (b) CeCu GCj (Felten et al. 1987). Solid curves in upper parts show Schottky anomalies corresponding to the CF splitting of Ce given in the text.

Fig. 17. 4f-derived specific heat for crystal-field-split doublet-doublet system in units of the gas constant, CJR, as a function of TIT (on a logarithmic scale) for different ratios For... 

A good recommendation is to always use SI units when evaluating this expression. If different units are eventually needed, such a conversion can be done after the gas concentration has been calculated using SI values. Using this approach, you will always use the exact same set of units when evaluating Equation 2.43 and you will always use the exact same value for the gas constant R. Thus, there will be fewer opportunities for error or confusion. See Example 2.6 for an illustration of this approach. 

State the given and needed quantities. When three of the four quantities (P, V, n, and T) are known, we use the ideal gas law equation to solve for the unknown quantity. It is helpful to organize the data in a table. The temperature is converted from degrees Celsius to kelvins so that the units of V, n, and T match the unit of the gas constant R. 

For equations of state which are not in dimensionless form, care must be taken to adopt the units appropriate to the equation of state coefficients. This applies particularly to the numerical value used for the gas constant R. 

As indicated in Eq. (27.13), the specific heat capacity depends unambiguously on 0D and hence on the size, temperature, and the bond nature involved. Figure 27.6a shows the reduced Cy (in units of the gas constant R) versus temperature (TIBdo) for Si nanowires (m = 4.88) and A1 nanowires (m = 1) of different diameters (A = 5, 10, and 20). The shape of the Cy curve is similar to that of the bulk but the size induces a depression over the whole temperature range. For the same A at a given Tl9 o, the reduction in heat capacity increases with the m value. 

In the literature the ideal gas law is sometimes given with other units of pressure and volume than those standardized in the SI system. Determine the numerical value for the gas constant R with the unit f torr/mol K, and calculate with this value of R the pressure p (torr) in 30 g of an ideal gas given the following conditions V = 15.0f 0 = 22.0°C M = 42.00g/mol. The unit of pressure 1 torr = 1 mmHg = 1/760atm. 

Temperature dependence of the specific heat C i in units of the gas constant / for the sequences S1-S4. Also shown are typicai iow-energy conformations of the peptides. Note the changed iocation of proiine (P) in sequence S3, if compared to the other sequences, and the different type of its secondary structure. After [343],... 

Values for the gas constant, R, in different units are given in Table 1.1. The ideal gas model was empirically developed largely through the work of the chemists Boyle, Gay-Lussac, and Charles. It is valid for gases in the limits of low pressure and high temperature. In practice, the behavior of most gases at atmospheric pressure is well approximated... 

So far, so good. The situation is really no different, say, than the ideal gas law, in which the gas constant is numerically different and has different units depending on the units chosen for p and V, The unit change in Example 10.1 is analogous to changing the gas constant from liter-atmospheres to calories it is apparent that one system is physically more meaningful than another in specific problems. Several considerations interfere with this straightforward parallel, however, and cause confusion ... 

M refer to the density and molecular weight of /, and R is the gas constant. For simplicity, we assume each component to be monodisperse mote complex expressions result when polydispersity is considered (6). This model also assumes the heat of mixing pet unit volume follows a van Laar-type relation where B is... 

Tj is the surface excess (Davies and Rideal, Jnteifacial Phenomena, 2d ed.. Academic, New York, 1963). For most purposes, it is sufficient to view Vj as the concentration of adsorbed component i at the surface in units of, say (g mol)/cm . R is the gas constant, T is the absolute temperature, Y is the surface tension, and a is the activity of component i. The minus sign shows that material which concentrates at the surface generally lowers the surface tension, and vice versa. This can sometimes be a guide in determining preliminarily what materials can be separated. 

In this book, we will express our thermodynamic quantities in SI units as much as possible. Thus, length will be expressed in meters (m), mass in kilograms (kg), time in seconds (s), temperature in Kelvins (K), electric current in amperes (A), amount in moles (mol), and luminous intensity in candella (cd). Related units are cubic meters (m3) for volume, Pascals (Pa) for pressure. Joules (J) for energy, and Newtons (N) for force. The gas constant R in SI units has the value of 8.314510 J K l - mol-1, and this is the value we will use almost exclusively in our calculations. 

The slope of the Arrhenius plot has units (temperature) 1 but activation energies are usually expressed as an energy (kJ mol 1), since the measured slope is divided by the gas constant. There is a difficulty, however, in assigning a meaning to the term mole in solid state reactions. In certain reversible reactions, the enthalpy (AH) = E, since E for the reverse reaction is small or approaching zero. Therefore, if an independently measured AH value is available (from DSC or DTA data), and is referred to a mole of reactant, an estimation of the mole of activated complex can be made. 

The constant R is called the gas constant and has the same value for all gases because R is independent of the identity of the gas, we say that it is a universal constant. The value of the gas constant can be found by measuring P, V, n, and T and substituting their values into R = PV/nT. When we use SI units (pressure in pascals, volume in meters cubed, temperature in kelvins, and amount in moles),... 

In this equation, T is the temperature in kelvins, is Avogadro s number (units of molecules/mol), and R is the gas constant. For energy calculations, we express R in SI units, which gives kinetic energy in joules per molecule. The value of R in SI units is i = 8.314 J mol K ... 

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