4. (a) Derive an expression for the half-life of the reactant in a first-order process in terms of the rate constant k. (b) Find the natural lifetime for first-order reactions corresponding to half-life = 26.5 years. (20%)

2. Assume that the mole fraction of carbon dioxide in the earth' s atmosphere is 0.000306.(a) Estimate the mean free path between intermolecular collisions in the atmosphere at sea level if the temperature is 298 K.b) Estimate the number of collisions with other carbon dioxide molecules per second undergone by a carbon dioxide molecule under the conditions in (a). (20%)

4. (a) Derive an expression for the half-life of the reactant in a first-order process in terms of the rate constant k. (b) Find the natural lifetime for first-order reactions corresponding to half-life = 26.5 years. (20%)

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