Values of the Gas-Law Constant

scale Press. units Vol. units Wt. units Energy units R 

---

From the known standard conditions, calculate the value of the gas law constant R in the following sets of units ... 

Chlorination processes in bubble column reactors<9> are unusual in showing a significant gas-phase resistance to mass transfer. It will be seen from the low value of the Henry law constant 3 in the list of data for the example below, that the solubility of chlorine in toluene is much greater than the solubility of either the carbon dioxide or oxygen considered in the previous examples. This means that when the gas-phase mass transfer resistance is taken in combination with the liquid-phase resistance according to equation 4.19 which is derived in Volume 2, Chapter 12, then the gas side contribution to the resistance is much greater if 3 is small. 

Applying this equation to our redox system, assuming T = 25 C, using the value of Fgiven earlier and that of the gas law constant (R = 8.314 J mol-1 K-1), and converting from natural log to log base 10, one gets a simplified form of the Nemst equation ... 

When a solid such as charcoal is exposed in a closed space to a gas or vapour at some definite pressure, the solid begins to adsorb the gas and (if the solid is suspended, for example, on a spring balance) by an increase in the weight of the solid and a decrease in the pressure of the gas. After a time the pressure becomes constant at the value p, say, and correspondingly the weight ceases to increase any further. The amount of gas thus adsorbed can be calculated from the fall in pressure by application of the gas laws if the volumes of the vessel and of the solid are known or it can be determined directly as the increase in weight of the solid in the case where the spring balance is used. 

The equilibrium concentration in seawater is described by Henry s Law, which relates the partial pressure of the gas to its concentration (see Chapter 5 and Waser, 1966). Using the appropriate values of Henry s Law constant, Kh, and the partial pressures of gases in the atmosphere, the equilibrium concentrations of several gases are given in Table 10-11 for 0°C and 24°C. 

In Boyle s work the pressure was subsequently plotted as a function of the reciprocal of the volume, as calculated here in the third column of Thble 1. The graph of P vs. l/V is shown in Fig. lb. This result provided convincing evidence of the relation given by Eq. (3), the mathematical statement of Boyle s law. Clearly, the slope of the straight tine given in Fig. 1 b yields a value of C(T) at die temperature of the measurements [Eq. (3)] and hence a value of the gas constant 17. However, the significance of the temperature was not understood at the time of Boyle s observations. 

It is convenient and useful to express the Boltzmann distribution law in two forms a quantum form and a classical form. The quantum form of the law, in its application to atoms and molecules, may be expressed as follows The relative probabilities of various quantum states of a system in equilibrium with its environment at absolute temperature T, each state being represented by a complete set of values of the quantum numbers, are proportional to the Boltzmann factor e Wn/kT, in which n represents the set of quantum numbers, Wn is the energy of the quantized state, and k is the Boltzmann constant, with value 1.3804 X 10 16 erg deg 1. The Boltzmann constant k is the gas-law constant R divided by Avogadro s number that is, it is the gas-law constant per molecule. 

All three of the gas laws discussed in the previous section can be combined into a single statement called the ideal gas law, which describes how the volume of a gas is affected by changes in pressure, temperature, and amount. When the values of any three of the variables P, V, T, and n are known, the value of the fourth can be calculated using the ideal gas law. The constant R in the equation is called the gas constant and has the same value for all gases. 

NH3 and to a lesser extent mono-, di-, and trimethylamines are the only significant gaseous bases in the atmosphere, and there has been considerable interest in whether the oceans are a source or sink of these gases. Early attempt to assess the air-sea flux from concentration measurements are probably suspect because of the ease with which sample contamination can occur during laboratory processing and analysis. It should be noted here that due to its high solubihty (low value of Henry s law constant), the air-water transfer of NH3 (and the methylamines for the same reason) is under gas phase control (see Section 6.03.2.1.1). The first reliable measurements were probably from the North and South Pacific and indicated that the flux of NH3 from sea to air is of a size similar to that for emission of DMS (Quinn et al., 1990, 1988). Indeed, the authors showed that this similarity was mirrored in the molar ratio of (non-sea-salt) sulfate to ammonium (1.3 0.7) in atmospheric aerosol particles collected on the cruise, indicating that for clean marine air remote from terrestrial sources, the emission of DMS and NH3 from the sea appears to control the composition of the aerosol. 

Nitrogen monoxide gas and chlorine gas react according to the equation 2NO + CI2 — 2NOC1. Use the following data to determine the rate law for the reaction by the method of initial rates. Also, calculate the value of the specific rate constant. 

Now that solubility and vapor pressure have been defined, consider how a volatile chemical partitions, or distributes itself, between water and air phases at equilibrium. In general, a partition coefficient is the ratio of the concentrations of a chemical in two different phases, such as water and air, under equilibrium conditions. The Henry s law constant, H (or KH), is a partition coefficient usually defined as the ratio of a chemical s concentration in air to its concentration in water at equilibrium. [Occasionally, a Henry s law constant is interpreted in an inverse fashion, as the ratio of a chemical s concentration in water to its concentration in air see, e.g., Stumm and Morgan (1981, p. 179). Note that in that table, KH is equivalent to 1/H as H is defined above ] Values of Henry s law constants are tabulated in a variety of sources (Lyman et al, 1990 Howard, 1989, 1991 Mackay and Shiu, 1981 Hine and Mookerjee, 1975) Table 1-3 lists constants for some common environmental chemicals. When H is not tabulated directly, it can be estimated by dividing the vapor pressure of a chemical at a particular temperature by its aqueous solubility at that temperature. (Think about the simultaneous equilibrium among phases that would occur for a pure chemical in contact with both aqueous and gas phases.) Henry s law constants generally increase with increased temperature, primarily due to the significant temperature dependency of chemical vapor pressures as previously mentioned, solubility is much less affected by the changes in temperature normally found in the environment. 

How do the values of the power-law flow behaviour and consistency indices depend upon temperature Estimate the activation energy of viscous flow (E) from these data by fitting them to the equation m = moexpffi/RJ) where mo and E are constants and R is the universal gas constant. 

The value of p can be calculated by solving the mass transfer equation in the gas phase and the value of p can be calc lated from vapor-liquid equilibrium data. It is important to realize that, in order to calculate ip, one does not need to know the value of Henry s law constant in the reactive medium. 

From this expression, any value can be calculated if the other five are known. Note that each of the gas laws can be obtained from the combined gas law when the proper variable is constant. For example, Boyle s law is obtained when the temperature is constant. Because Tj =T2, and T2 will cancel out on both sides of the combined gas law equation, giving Boyle s law. 

Values of Henry s law constant k =plc, where p is the partial pressure of the solute in the gas above the solution and c is the concentration of the solute) is a quantity frequently apphed in the thermodynamic description of dilute aqueous solutions, which is used in environmental chemistry and atmospheric physics as a major criterion for describing air-water partitioning of solutes at near ambient conditions. It plays amajor role in evaluating the transport of pollutants between atmosphere and aquatic systems, rainwater and aerosols. The octanol-water partition coefficient is a dimensionless number defined as the ratio of the compound s concentration in a known volume of octan-l-ol (Cq) to its concentration in a known volume of water (c ) after the octan-l-ol and water have reached equihbrium. It has been found to be related to water solubility, soil/sediment absorption coefficients and bioconcentration factors of pollutants for aquatic life. The adsorption coefficient normalised to the organic carbon content of the soil (sediment) is a useful indicator of the binding capacity of... 

The solubilities were expressed as Bunsen coefficients a for temperatures of 20 and 25°C. I shall deal only with the values for 20°C because of ready access to density data. To adjust for pressure, those workers used Henry s law in the form m = kp,m being the mass of gas. To convert the Bunsen coefficient into values of Henry s law constant expressed as mole liter atm , a gram-mole volume of 22,260 cm was used, allowance thereby being made for deviation from the ideal gas law in the example of carbon dioxide. 

For quite a number of gases, Henry s law holds very well when the partial pressure of the solute is less than about 100 kPa (I atm). For partial pressures of the solute gas greater than 100 kPa, H seldom is independent of the partial pressure of the solute gas, and a given value of H can be used over only a narrow range of partial pressures. There is a strongly nonlinear variation of Heniy s-law constants with temperature as discussed by Schulze and Prausnitz [2nd. Eng. Chem. Fun-dam., 20,175 (1981)]. Consultation of this reference is recommended before considering temperature extrapolations of Henry s-law data. 

---