# Midterm 1


## Problem 1

a) For each reaction mechanism, there is a corresponding rate law for that reaction and for each rate law there is a corresponding mechanism.

b) The half-life of first order reactions is independent from the initial concentration.

c) An intermediate population increases the rate of the reaction by increasing the rate constant of the reaction.

d) Temperature plays no significant role in determining a molecule's average kinetic energy.

e) The pre-exponential constant in the Arrhenius equation is a measure for the probability of a collision that occurs with sufficient energy and orientation to result in product formation.

f) A simple definition for the order of a reaction is that it is the number of reactant species involved in the reaction.

g) The potential energy surface for a reaction can be used to identify and quantify the transition state for that reaction.

h) Classical mechanics is a powerful theory to describe the emission of light from excited hydrogen atoms

i) The steric facor for an elementary reaction reduces the effective molecularity of that reaction.

j) Graham's law of effusion was derived from the assumption that the average speed of a gas particle is independent of its molecular mass.

## Problem 2a

a) Draw a simple energy profile for an exothermic reaction in which 100kJ/mol is evolved, and which has an activation energy of 50 kJ/mol.

b) Draw a simple energy profile for an endothermic reaction in which 50 kJ/mol is absorbed and which has an activation energy of 100 kJ/mol.

c) Why do reaction have an activation energy and how does the exothermic or endothermic properties of the reaction affect it (if at all)?

## Problem 2b

Calculate the rate law for the following acid-catalyzed reaction:

$CH_3COCH_3 + Br_2 \overset{H^+}{\longrightarrow} CH_3COCH_2Br + H^+ + Br^-$

 Expt. # ﻿$$[CH_3COCH_3]_o$$/ M $$[Br_2]_o$$ /M $$[H^+]_o$$ /M Rate of Disappearance Br2/ M*s-1 1 0.3 0.05 0.05 $$5.7 \times 10^{-5}$$ 2 0.3 0.1 0.05 $$5.7 \times 10^{-5}$$ 3 0.3 0.05 0.05 $$1.2 \times 10^{-4}$$ 4 0.4 0.05 0.2 $$3.1 \times 10^{-4}$$

## Problem 3

A reaction is known to exhibit first order kinetics. At 300 K the concentration of reactant is reduced to one half of its initial value after 5000 s. In contrast, at 310 K the concentration is halved after 1000 s. Use this information to calculate:

a) the rate constant for the reaction at 300 K

b) the time required for the reactant concentration to red reduced to one quarter of its initial value at 310 K.

c) the activation energy of the reaction.

## Problem 4

a) Compare and contraast two discussed techniques to experimentally determine reaction order and rate constants for a generic reaction. Be as specific as possible including equations.

b) Calculate the mean free path between HF gas molecules at 500 K and 1 atm. The diameter of the HF molecules may be taken to be 3.50 angstroms ($$10^{-10}$$).

## Problem 5

A) Answer the follwoing questions regarding the Maxwell-Boltzmann distribution below for a thermalized gas at two temperatures:

a) True or false: temperature T1 is higher than temperature T2?

b) True of false: at lower temperatures the maximum of the graph shifts to the left?

c) Which axis that represents kinetic energy (Vertical, horizontal, or none)?

d) True or False: at lower temperatures the maximum of the graph shifts to the left?

e) True or false: the y-axis on the graph represents the number of particles with a particular velocity?

f) True or False: the area under each curve is the same?

g) True or False: both curves pass through the origin of both axes at (0,0)?

h) True or False: at higher temperatures the maximum of the graph is greater in height?

B) Consider the reaction coordinate diagram shown below for the next four questions.

a) Which one of the marked points in the diagram corresponds to a transition state?

b) Which one of the marked points in the diagram corresponds to a reaction intermediate?

c) How many elementary steps are involved in this reaction?

d) Which is the slow (rate determining) step in the reverse reaction (right to left) (First, second, third, fourth, or fifth)?

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