General Chemistry

Rate Determination and Activation Energy

An important part of the kinetic analysis of a chemical reaction is to determine the activation energy, E_a. Activation energy can be defined as the energy necessary to initiate an otherwise spontaneous chemical reaction so that it will continue to react without the need for additional energy. An example of activation energy is the combustion of paper. The reaction of cellulose and oxygen is spontaneous, but you need to initiate the combustion by adding activation energy from a lit match.

In this experiment you will investigate the reaction of crystal violet with sodium hydroxide. Crystal violet, in aqueous solution, is often used as an indicator in biochemical testing. The reaction of this organic molecule with sodium hydroxide can be simplified by abbreviating the chemical formula for crystal violet as CV.

${\text{C}}{{\text{V}}^{\text{ + }}}{\text{ }}{\text{(aq) + O}}{{\text{H}}^{\text{ - }}}{\text{ (aq)}} \to {\text{CVOH (aq)}}$

As the reaction proceeds, the violet-colored CV⁺ reactant will slowly change to a colorless product, following the typical behavior of an indicator. You will measure the color change with a Vernier Colorimeter or a Vernier Spectrometer. You can assume that absorbance is directly proportional to the concentration of crystal violet according to Beer’s law.

The molar concentration of the sodium hydroxide, NaOH, solution will be much greater than the concentration of crystal violet. This ensures that the reaction, which is first order with respect to crystal violet, will be first order overall (with respect to all reactants) throughout the experiment. You will monitor the reaction at different temperatures, while keeping the initial concentrations of the reactants the same for each trial. In this way, you will observe and measure the effect of temperature change on the rate of the reaction. From this information you will be able to calculate the activation energy, E_a, or the reaction.

Vapor Pressure and Heat of Vaporization

When a liquid is placed in a container, and the container is sealed tightly, a portion of the liquid will evaporate. The newly formed gas molecules exert pressure in the container, while some of the gas condenses back into the liquid state. If the temperature inside the container is held constant, then at some point equilibrium will be reached. At equilibrium, the rate of condensation is equal to the rate of evaporation. The pressure at equilibrium is called vapor pressure, and will remain constant as long as the temperature in the container does not change.

In mathematical terms, the relationship between the vapor pressure of a liquid and temperature is described in the Clausius-Clayperon equation,

$\ln P = \frac{{ - \Delta {H_{vap}}}} {R}\left( {\frac{1} {T}} \right) + C$

where ln P is the natural logarithm of the vapor pressure, ΔH_vap is the heat of vaporization, R is the universal gas constant (8.31 J/mol•K), T is the absolute, or Kelvin, temperature, and C is a constant not related to heat capacity. Thus, the Clausius-Clayperon equation not only describes how vapor pressure is affected by temperature, but it relates these factors to the heat of vaporization of a liquid. ΔH_vap is the amount of energy required to cause the evaporation of one mole of liquid at constant pressure.

Determining the Half-Life of an Isotope

One type of nuclear reaction is called radioactive decay, in which an unstable isotope of an element changes spontaneously and emits radiation. The mathematical description of this process is shown below.

$R(t) = {R_0}{e^{ - \lambda t}}$

In this equation, λ is the decay constant, commonly measured in s^–1 (or another appropriate unit of reciprocal time) similar to the rate law constant, k, in kinetics analyses. R₀ is the activity (rate of decay) at t = 0. The SI unit of activity is the bequerel (Bq), defined as one decay per second. This equation shows that radioactive decay is a first-order kinetic process.

One important measure of the rate at which a radioactive substance decays is called half-life, or t_1/2. Half-life is the amount of time needed for one half of a given quantity of a substance to decay. Half-lives as short as 10^–6 second and as long as 10⁹ years are common.

In this experiment, you will use a source called an isogenerator to produce a sample of radioactive barium. The isogenerator contains cesium-137, which decays to produce barium-137. The newly made barium nucleus is initially in a long-lived excited state, which eventually decays by emitting a gamma photon and becomes stable. By measuring the decay of a sample of barium-137, you will be able to calculate its half-life.

Follow all local procedures for handling radioactive materials. Follow any special use instructions included with your isogenerator.

Potentiometric Titration of Hydrogen Peroxide

One method of determining the concentration of a hydrogen peroxide, H₂O₂, solution is by titration with a solution of potassium permanganate, KMnO₄, of known concentration. The reaction is oxidation-reduction and proceeds as shown below, in net ionic form.

${\text{5 }}{{\text{H}}_{\text{2}}}{{\text{O}}_{\text{2}}}{\text{ (aq) + 2 Mn}}{{\text{O}}_{\text{4}}}^{{\text{ - }}}{\text{ (aq) + 6 }}{{\text{H}}^{{\text{ + }}}}{\text{ (aq)}} \to {\text{ 5 }}{{\text{O}}_{\text{2}}}{\text{ (g) + 2 M}}{{\text{n}}^{{\text{2 + }}}}{\text{ (aq) + 8 }}{{\text{H}}_{\text{2}}}{\text{O (l)}}$

In this experiment, you will use an ORP (Oxidation-Reduction Potential) Sensor to measure the potential of the reaction. Your data will look like an acid-base titration curve. The volume of KMnO₄ titrant used at the equivalence point will be used to determine the concentration of the H₂O₂ solution. Your sample of H₂O₂ will come from a bottle of ordinary, over-the-counter hydrogen peroxide purchased at a grocery or a drug store. The concentration of this product is labeled as 3% mass/volume, which is ~0.9 M.