For certain heterogeneous reactions in which a solid reactant is involved

CHEMISTRY · Multi-part · A Level · Chemistry · Kinetics · Kinetics

Problem

For certain heterogeneous reactions in which a solid reactant is involved, the rate can be expressed empirically as

\text{rate} = k\,A\,e^{-\frac{E_a}{R\,T}}

where

A

is the total exposed surface area of the solid (in

\text{m}^2

E_a

is the activation energy (in

J\,\text{mol}^{-1}

T

is the absolute temperature, and

k

is a proportionality constant that is independent of both

A

and

T

. A chemist studies the reaction of iron(III) oxide with carbon monoxide:

Fe_2O_3(s) + 3\,CO(g) \rightarrow 2\,Fe(s) + 3\,CO_2(g)

Two sets of pellets identical in mass and composition but different in particle diameter are prepared. • Set X: average diameter

4.0\,\text{mm}

, total surface area

0.020\,\text{m}^2

• Set Y: average diameter

2.0\,\text{mm}

, total surface area

0.040\,\text{m}^2

Both sets are reacted in a flow reactor under a CO(g) partial pressure that remains constant and sufficiently large to keep the gas concentration effectively unchanged during the initial stage of the reaction. Data Table:

Set	Temperature (K)	Initial Rate ( $\text{mol}\,\text{s}^{-1}$ )
X	$700\,\text{K}$	$2.5\times10^{-5}$
Y	$700\,\text{K}$	$5.1\times10^{-5}$
X	$750\,\text{K}$	$7.2\times10^{-5}$

Answer the following. (1) Part 1: (a) Using the data for

700\,\text{K}

, determine the numerical factor by which the rate changes when the surface area is doubled while temperature is held constant. (2) Part 2: (b) Using the data for Set X at

700\,\text{K}

and

750\,\text{K}

, calculate the value of the activation energy

E_a

\text{kJ}\,\text{mol}^{-1}

. Assume

k

and

A

are constant for a given pellet set. (3) Part 3: (c) Predict the initial rate (to two significant figures) for Set Y at

750\,\text{K}

. Show all reasoning, explicitly indicating how both surface area and temperature effects are combined. (4) Part 4: (d) Evaluate whether the empirical rate expression provided at the beginning adequately accounts for all factors that could influence the observed rate in this system. Support your evaluation with one argument based on kinetic theory and one argument based on possible experimental limitations.

Related theory

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