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# Reactivity and Reactions Help (page 2)

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By — McGraw-Hill Professional
Updated on Aug 16, 2011

## Bond-Dissociation Energies

The bond-dissociation energy is the energy needed for the endothermic homolysis of a covalent bond A:B → A · + · B; ΔH is positive for these reactions. Bond formation, the reverse of this reaction, is exothermic and the ΔH values are negative. Stronger bonds require more energy to break, so they have larger ΔH values. The ΔH of a reaction is the sum of all the (positive) ΔH values for bond cleavages PLUS the sum of all the (negative) ΔH values for bond formations.

ΔH = ΔH(bonds broken) + ΔH(bonds formed)

## Rates of Reactions

The rate of a reaction is how quickly reactants disappear or products appear. For the general reaction dA + eB + fC + gD, the rate is given by a rate equation:

Rate = k[A]x[B]y

where k is the rate constant at the given temperature, T, and [A] and [B] are molar concentrations (mol/L).

## Chemical Equilibrium

Every chemical reaction can proceed in either direction, even if it goes in one direction only to a microscopic extent. A state of equilibrium is reached when the concentrations of reactants and products no longer change because the reverse and forward reactions are taking place at the same rate. The equilibrium constant, Keq, is defined in terms of molar concentrations as indicated by the square brackets.

The ΔG of a reaction is related to Keq by the expression ΔG = –RT lnK, where R is the gas constant (R= 8.314 Jmol–1K–1) and T is the absolute temperature (in K).

## Transition State Theory and Energy Diagrams

When reactants have collided with sufficient energy of activation (Ea or ΔG) and with the proper orientation, they pass through a transition state in which some bonds are breaking while others are forming. The transition state is the highest energy state between reactants and products. The relationship of the transition state (TS) to the reactants (R) and products (P) is shown by the energy diagram below, which corresponds to a one-step exothermic reaction A+B →C+D. At equilibrium, formation of molecules of lower energy is favored. In this reaction, the products (C+ D) are favored. The reaction rate is actually related to the free energy of activation, ΔG, where ΔG = ΔH – TΔS.

## Brønsted Acids and Bases

In the Brønsted definition, an acid donates a proton and a base accepts a proton. The strengths of acids and bases are measured by the extent to which they lose or gain protons, respectively. In these reactions, acids are converted to their conjugate bases and bases to their conjugate acids. Acid-base reactions go in the direction of forming the weaker acid and the weaker base. The strongest acids have the weakest conjugate bases, and the strongest bases have the weakest conjugate acids. The stronger an acid, the larger its ionization constant Ka and the smaller its pKa value.

For the acid HA, HA →H+ + A,

Ka = [H+][A]/[HA]

pKa = –logKa

## Lewis Acids and Bases

A Lewis acid (electrophile) shares an electron pair furnished by a Lewis base (nucleophile) to form a covalent (coordinate) bond. The Lewis concept is especially useful in explaining the acidity of an aprotic acid (no available proton), such as BF3.

Practice problems for these concepts can be found at: Reactivity and Reactions Practice Problems

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