Sample Introductions from Five Chemistry Experiments Using Electronic Data Collection Technology
Synthesis of an Alum KAl(SO4)2×12H2O
Potassium aluminum sulfate dodecahydrate, KAl(SO4)2×12H2O, belongs to a class of inorganic compounds called alums (which is accented on the first syllable). The composition of alum is represented by the general formula M+M3+(SO4)2×12H2O. In this formula, M+ is a monoatomic ion such as Na+, K+, Tl+, or Ag+; or is NH4+. Although the name alum sounds as if the compound must contain aluminum, the M3+ might be from any of several main-group metals (p block elements) and transition metals (d block elements) that form triply charged ions: Al, Ti, V, Cr, Mn, Fe, Co, Ga, In, and Ir. Some examples are NaAl(SO4)2×12H2O, which is a component of some baking powders; NH4Al(SO4)2×12H2O, which is used in dyeing textiles; and KCr(SO4)2×12H2O, which is used in tanning leather.
The term double salt also describes KAl(SO4)2×12H2O. A double salt is an ionic compound that contains two different cations or two different anions. In aqueous solution, double salts give positive tests for all three of the ions they contain. KAl(SO4)2×12H2O would give positive tests for K+, Al3+, and SO42-.
Hydrate is another term that describes KAl(SO4)2×12H2O. A hydrate is a substance that contains a specific number of water molecules per formula unit in its solid form. Hydration is common with ionic compounds, for example Na2SO4×10H2O and CoCl2×6H2O. The water of hydration is included when calculating the compound’s formula mass. The water molecules are part of the crystal of a compound along with cations and anions, but they can break out of the crystal when it is heated. This dehydration might occur at a specific temperature characteristic of the particular compound. If the compound is heated in a relatively closed container, the escaping water might dissolve the remaining salt forming a liquid solution. Consequently, this combination of dehydration and dissolving looks like melting; the temperature range at which it occurs (the solid-to-liquid transition) can be measured in the same way that a melting point is measured.
Introduction to Spectroscopy
Much of what we know about the structures of atoms and molecules has been learned through experiments in which photons (electromagnetic radiation—visible light, microwaves, ultraviolet or infrared radiation, radio waves, etc.) are emitted or absorbed by the atoms or molecules. The energy of a photon is related to its frequency, n, and wavelength, l, according to
where h is Planck’s constant, and c is the speed of light. The energy of an emitted or absorbed photon corresponds to the change in energy the atom or molecule experiences.
Whether photons are absorbed or emitted is correlated with the type of energy change the atom or molecule is undergoing. Thus, for example, a molecule can be raised to an excited electronic state by absorbing a visible or ultraviolet photon. A molecule already in an excited electronic state can return to the unexcited, or ground state by emitting a visible or ultraviolet photon. The energies of photons in this portion of the electromagnetic spectrum correspond to the differences between the ground and excited electronic states. For changes in vibrational or rotational energy, infrared and microwave photons respectively, have energies corresponding to the differences between states. Careful analysis of the details of the radiation absorbed or emitted as a function of wavelength (the absorption or emission spectrum), coupled with the formulation of physical models to interpret and explain them, has provided a wealth of detailed information about atoms and molecules.
In addition to the structural information that can be gained, studies involving the absorption and emission of electromagnetic radiation have proven to be extremely useful in other practical ways. For example, even without knowing why particular wavelengths are absorbed or emitted, we can often use the observed spectra to identify the substances responsible. This is particularly true in the infrared region for organic molecules, where many vibrational spectra have been recorded and cataloged and can often serve as “fingerprints” to identify what is present. In a similar way, the specific wavelengths of visible and ultraviolet radiation emitted by atoms and ions in a flame or in an electrical discharge can provide an unambiguous means of identification. In fact, a number of elements were first discovered in this way, when previously unknown emissions were observed. Spectroscopic measurements are now routinely employed in the analysis of chemical samples.
Enthalpy of Reaction—Hess’s Law
Chemical changes are generally accompanied by energy changes; energy is absorbed or evolved, usually as heat. Breaking chemical bonds in reactants requires energy, and energy is released as new bonds form in products. Whether the combination of these steps absorbs or releases energy depends on the relative sizes of the energies associated with breaking and forming bonds.
The amount of heat involved in a reaction depends not only on what the reaction is, but also on the temperature at which the reaction occurs and whether the reaction occurs under conditions of constant pressure or constant volume. In the laboratory, many reactions are conveniently carried out at constant pressure in beakers or flasks that are open to the atmosphere. The amount of heat absorbed or released under this condition is the enthalpy change, DH, for the reaction, where
∆H = Hproducts -Hreactants
Enthalpy, H, can be thought of as the heat content of a substance; this heat is stored as potential energy in the form of bond, and other, energies. When atoms rearrange during a reaction, the heat content of the products is usually different from the heat content of the reactants. This difference in heat content appears as heat absorbed or released. This heat is generally indicated in Joules for the reaction as written. For example, in this experiment you will examine an acid-base neutralization in aqueous solution:
H3O+(aq) + OH-(aq) 2 H2O(l) ∆H =-55.8kJ
The enthalpy change for this reaction could be given in J/(mol of H3O+), or in J/(mol of OH-), or in J/(mol of H2O). To avoid confusion it is customary to report DH for the reaction with the numbers of moles of reactants and products simply as written. Thus, for reaction 9.2, in which 1 mole of H3O+ and 1 mole of OH- combine to form 2 moles of H2O, ∆H = -55.8 kJ, as shown.
Note that the enthalpy change, ∆H = Hproducts - Hreactants, is positive if heat is absorbed; that is, if Hproducts > Hreactants, the reaction is endothermic. The enthalpy change is negative if heat is released. If Hproducts < Hreactants, the reaction is exothermic.
Behavior of Gases
A large number of substances of considerable chemical interest are gases. For example, CO2 is currently in the news because it is thought to be partly responsible for global warming. One important part of deciding whether or not this is so is to study the behavior of pure CO2. (Another important aspect is to understand its behavior in the atmosphere—what part of the atmosphere does it reside in? How long does it remain there without reacting with some other atmospheric component or floating off into space?, etc.)
Studying the behavior of individual gases was historically a very difficult problem because one needs to isolate and contain the sample in the face of the tendency of gases to occupy the entire volume available to them. The first reliable apparatus for doing this was the pneumatic trough described by Hales (1677–1761) in 1727. (See Figure 12-1) A gas was generated by decomposing a substance in the fire. For example, one such reaction might be:
CaCO3(s) CO2(g) + CaO(s) (12-1)
A gun barrel was originally used to connect the decomposition vessel to a vessel filled with water. The gas emitted passed through the barrel and exerted pressure to displace the water. After all the water was displaced, one had a pure sample of the gas (mixed with water vapor). The vessel could be capped under water and turned right side up.
Studies on many different gases revealed that their physical properties were independent of the identity of the gas, at least at ordinary pressures and temperatures. This behavior is summarized in the Ideal Gas Law:
where P = pressure, V = volume, n = number of moles of gas, R = ideal gas constant and T = temperature in Kelvins. The Ideal Gas Law was, of course, formulated from studies in which one quantity at a time was varied and the effect on some other quantity was noted. For example, Boyle (1627–1691) studied the change in volume of a sample of gas as its pressure was varied (n and T stayed constant). Amontons (1663–1705) studied how the pressure of a gas changed as the temperature was varied (n and V stayed constant). Charles (1746–1823) measured the effect on the volume of a gas as the temperature T was changed (n and P stayed constant).Dalton (1766–1844) formulated his law describing the fact that gases in a mixture behave independently of one another. For example, each gas exerts its pressure independently so that
where the subscripts 1, 2, 3, ... refer to the different gases in the mixture.
As a result of this behavior, we can study the physical properties of gases by using air, even though air is a mixture of gases. The purpose of this experiment is to investigate the physical properties of gases. The interesting point is how much gases do in fact conform to ideal gas behavior under conditions of low pressure and moderate temperature found in the laboratory.
In this experiment, we will explore the variation of pressure with volume (as described in Boyle’s Law) and the variation of pressure with temperature (as described in Amontons’ Law).
Vapor Pressure and Heat of Vaporization
Any liquid evaporates to at least a slight extent; that is, some molecules leave the surface of the liquid and become vapor. As molecules in the vapor phase move about randomly, some strike the surface of the liquid and again become part of the liquid phase; vapor condenses. If a liquid is in a closed container, vapor cannot escape and eventually a state of equilibrium is reached in which vaporization and condensation occur at the same rate; there is no change in the number of molecules in either the liquid phase or the vapor phase. The vapor, like any gas, exerts pressure. When the liquid and vapor phases of a substance are in equilibrium, this pressure is called the vapor pressure of the liquid; it is the maximum pressure that can be exerted by the vapor phase of a substance at a particular temperature. It is possible to tell when this equilibrium between phases has been reached, because the volume of liquid no longer decreases and the pressure exerted by the vapor no longer increases. In this experiment, you will determine when equilibrium has been established between the liquid and vapor phases of a substance by measuring the pressure exerted by the vapor.
The magnitude of a liquid’s vapor pressure reflects the ability of molecules to escape from the surface of the liquid. In the liquid phase, molecules exert attractive forces on one another and energy is required to overcome these forces in order for the molecules to leave the liquid and to become part of the vapor phase. Temperature is a measure of the average kinetic energy of the molecules, and as temperature increases more molecules possess the energy required for escape. In addition, the vapor molecules will possess a higher average kinetic energy and will exert a greater pressure on the walls of the container, as described by Amonton’s Law (Experiment 12). Consequently, vapor pressure increases as temperature increases. In this experiment, you will measure the vapor pressure of one liquid at a number of temperatures.
After you have made measurements showing how the vapor pressure of a liquid is related to temperature, you will use these measurements to calculate the energy needed to overcome intermolecular attractions in the liquid. The molar heat of vaporization, DHvap, is the heat necessary to change one mole of liquid into one mole of vapor at a constant temperature. The mathematical relationship between vapor pressure and molar heat of vaporization is given by the Clausius-Clapeyron equation:
where Pvapor is the vapor pressure, R is the gas constant, T is the temperature in Kelvins, and C is a constant. Equation 14-1 has the form of the equation for a straight line, y = mx + b. Here, y = ln Pvapor (unitless) and x = 1/T, in units of K-1. When the natural logarithm of vapor pressure is plotted against the reciprocal of Kelvin temperature, a straight line results. The y intercept b corresponds to the constant C in Equation 14-1; you will not be concerned with this constant. The slope of the line therefore equals -∆Hvap/R. After the slope of the line is calculated from the graph, the value of DHvap can be calculated. This determination of the heat of vaporization is an example of how scientists determine a quantity that is not easy to measure (∆Hvap) by using measurements that are easy to make (pressure and temperature) and then applying an equation that relates these, usually in a linear fashion.