Predicting Outcomes of Experiments
The strong background given to MSE undergraduates in physical chemistry and thermodynamics should be exploited in predicting events which may occur in the laboratory. Using the fundamental laws developed in these courses, tabulated data can be used to predict potentially dangerous vapor pressures, whether or not reactions will occur, and whether the heats of reactions will approach explosive behavior. Useful tabulations may be found in the CRC Handbook of Chemistry and Physics, the JANAF thermochemical tables, and the North American Combustion Handbook. A few examples will be cited:
If we wish to melt copper in an evacuated and sealed fused silica ampoule, the vapor pressure of copper is negligible, and no dangerous pressures will build up. This is not true, however, for phosphorous, where as can be seen in Figure , the vapor pressure builds up appreciably with increasing temperature. From a standard glass science textbook, the tensile strength of silica glass is roughly 50 MPa, or 490 atm, thus the container will burst at 900°C, if not before. The figure was generated using the integrated form of the Clapeyron equation:
Where p is the equilibrium vapor pressure formed over the condensed phase in a closed system, R is the gas constant, DH is the heat of vaporization or sublimation of the condensed phase (assumed to vary insignficantly with temperature), T0 is the equilibrium boiling or sublimation temperature under atmospheric pressure, and T is temperature. For Figure , DH and T0 data were obtained from the CRC Handbook. In using equations such as this, it is important to understand the nuances of the terms and how they relate to a realistic experimental situation. These nuances can often only be elucidated by following the derivation of the expression and observing what simplifying or conditional assumptions were made.
The JANAF tables have very complete enthalpy and free energy tabulations. To predict whether a reaction will occur, the standard state Gibbs energy equation is useful:
DG° = -RT lnkp
where DG° is the standard state free energy change for a reaction, and kp is the equilibrium constant. For a equilibria
aA + bB = gC +
the value of DG° may be obtained from the standard state Gibbs energies of formation (products - reactants, each one multiplied by its stoichiometry constant) in the JANAF tables. The equilibrium constant for such a reaction is the ratio of product and reactant activities:
If gases are assumed ideal, the activities can be written as the pressure of the reaction constituent divided by its pressure in its standard state. For gases, the standard state is that it is pure and at one atmosphere. For condensed phases, the standard state requirement is simply that it is pure (thus the copper in brass is not in its standard state). Thus for all pure condensed phases, their activity is unity. As an example, consider what would happen if flowing CO2 atmosphere were used in a graphite furnace chamber. The equilibrium constant for CO2 + C = 2CO may be written:
Using tabulated data, this ratio is plotted as a function of temperature in Figure .
Figure 1: (left) Vapor pressures predicted by the integrated Clayperon equation.
Figure 2: (right) Equilibrium partial pressure ratio showing propensity of CO2 to react with graphite to form CO.
Clearly, around 800°C the carbon dioxide will react with the graphite chamber, making carbon monoxide. If the exit gas is vented into the room, the atmosphere in the room will be poisoned.
If a thermite reaction such as:
5Mg + TiO2 + B2O3 ® 5MgO + TiB
is to be investigated, the standard state enthalpies of formation in the JANAF tables can be used to determine a standard state enthalphy of reaction at 298 K of -1093.6 kJ/mol. The heat content tabulations on the same pages can be used to show that this reaction under adiabatic conditions will result in a product temperature of 2387°C. This certainly dictates the use of a highly refractory container for this reaction as well as other safety precautions.