Energy and the first law of thermodynamics

 

Energy and the first law of thermodynamics

The concept of energy is a fundamental and familiar one in all the sciences. In simple terms, the energy of a body represents its ability to do work, and work itself is a force acting over a distance.

Chemical systems can have both kinetic energy (energy of motion) and potential energy (stored energy). The kinetic energy possessed by any collection of molecules in a solid, liquid, or gas is known as its thermal energy. Since liquids expand when they have more thermal energy, a liquid column of mercury, for example, will rise higher in an evacuated tube as it becomes warmer. In this way a thermometer can be used to measure the thermal energy, or temperature, of a system. The temperature at which all molecular motion comes to a halt is known as absolute zero.

Energy also may be stored in atoms or molecules as potential energy. When protons and neutrons combine to form the nucleus of a certain element, the reduction in potential energy is matched by the production of a huge quantity of kinetic energy. Consider, for instance, the formation of the deuterium nucleus from one proton and one neutron. The fundamental mass unit of the chemist is the mole, which represents the mass, in grams, of 6.02 × 1023 individual particles, whether they be atoms or molecules. One mole of protons has a mass of 1.007825 grams and one mole of neutrons has a mass of 1.008665 grams. By simple addition the mass of one mole of deuterium atoms (ignoring the negligible mass of one mole of electrons) should be 2.016490 grams. The measured mass is 0.00239 gram less than this. The missing mass is known as the binding energy of the nucleus and represents the mass equivalent of the energy released by nucleus formation. By using Einstein’s formula for the conversion of mass to energy (E = mc2), one can calculate the energy equivalent of 0.00239 gram as 2.15 × 108 kilojoules. This is approximately 240,000 times greater than the energy released by the combustion of one mole of methane. Such studies of the energetics of atom formation and interconversion are part of a specialty known as nuclear chemistry.

The energy released by the combustion of methane is about 900 kilojoules per mole. Although much less than the energy released by nuclear reactions, the energy given off by a chemical process such as combustion is great enough to be perceived as heat and light. Energy is released in so-called exothermic reactions because the chemical bonds in the product molecules, carbon dioxide and water, are stronger and stabler than those in the reactant molecules, methane and oxygen. The chemical potential energy of the system has decreased, and most of the released energy appears as heat, while some appears as radiant energy, or light. The heat produced by such a combustion reaction will raise the temperature of the surrounding air and, at constant pressure, increase its volume. This expansion of air results in work being done. In the cylinder of an internal-combustion engine, for example, the combustion of gasoline results in hot gases that expand against a moving piston. The motion of the piston turns a crankshaft, which then propels the vehicle. In this case, chemical potential energy has been converted to thermal energy, some of which produces useful work. This process illustrates a statement of the conservation of energy known as the first law of thermodynamics. This law states that, for an exothermic reaction, the energy released by the chemical system is equal to the heat gained by the surroundings plus the work performed. By measuring the heat and work quantities that accompany chemical reactions, it is possible to ascertain the energy differences between the reactants and the products of various reactions. In this manner, the potential energy stored in a variety of molecules can be determined, and the energy changes that accompany chemical reactions can be calculated.

Studies of molecular structure

 

Studies of molecular structure

The chemical properties of a substance are a function of its structure, and the techniques of X-ray crystallography now enable chemists to determine the precise atomic arrangement of complex molecules. A molecule is an ordered assembly of atoms. Each atom in a molecule is connected to one or more neighbouring atoms by a chemical bond. The length of bonds and the angles between adjacent bonds are all important in describing molecular structure, and a comprehensive theory of chemical bonding is one of the major achievements of modern chemistry. Fundamental to bonding theory is the atomic–molecular concept.

Atoms and elements

As far as general chemistry is concerned, atoms are composed of the three fundamental particles: the proton, the neutron, and the electron. Although the proton and the neutron are themselves composed of smaller units, their substructure has little impact on chemical transformation. As was explained in an earlier section, the proton carries a charge of +1, and the number of protons in an atomic nucleus distinguishes one type of chemical atom from another. The simplest atom of all, hydrogen, has a nucleus composed of a single proton. The neutron has very nearly the same mass as the proton, but it has no charge. Neutrons are contained with protons in the nucleus of all atoms other than hydrogen. The atom with one proton and one neutron in its nucleus is called deuterium. Because it has only one proton, deuterium exhibits the same chemical properties as hydrogen but has a different mass. Hydrogen and deuterium are examples of related atoms called isotopes. The third atomic particle, the electron, has a charge of -1, but its mass is 1,836 times smaller than that of a proton. The electron occupies a region of space outside the nucleus termed an orbital. Some orbitals are spherical with the nucleus at the centre. Because electrons have so little mass and move about at speeds close to half that of light, they exhibit the same wave–particle duality as photons of light. This means that some of the properties of an electron are best described by considering the electron to be a particle, while other properties are consistent with the behaviour of a standing wave. The energy of a standing wave, such as a vibrating string, is distributed over the region of space defined by the two fixed ends and the up-and-down extremes of vibration. Such a wave does not exist in a fixed region of space as does a particle. Early models of atomic structure envisioned the electron as a particle orbiting the nucleus, but electron orbitals are now interpreted as the regions of space occupied by standing waves called wave functions. These wave functions represent the regions of space around the nucleus in which the probability of finding an electron is high. They play an important role in bonding theory, as will be discussed later.

Each proton in an atomic nucleus requires an electron for electrical neutrality. Thus, as the number of protons in a nucleus increases, so too does the number of electrons. The electrons, alone or in pairs, occupy orbitals increasingly distant from the nucleus. Electrons farther from the nucleus are attracted less strongly by the protons in the nucleus, and they can be removed more easily from the atom. The energy required to move an electron from one orbital to another, or from one orbital to free space, gives a measure of the energy level of the orbitals. These energies have been found to have distinct, fixed values; they are said to be quantized. The energy differences between orbitals give rise to the characteristic patterns of light absorption or emission that are unique to each chemical atom.

A new chemical atom—that is, an element—results each time another proton is added to an atomic nucleus. Consecutive addition of protons generates the whole range of elements known to exist in the universe. Compounds are formed when two or more different elements combine through atomic bonding. Such bond formation is a consequence of electron pairing and constitutes the foundation of all structural chemistry.