Acetylene is produced at 2573 degrees Kelvin or 2200 degrees
centigrade. Two moles of carbon (s)
react with one mole of hydrogen to produce one mole of acetylene.
Energy of formation (delta G) and enthalpy of formation
(delta F) values are given at 298 degrees K for this reaction. Heat capacity is given as a function of
temperature described as a plus b T plus c T2. Values of a are
provided for carbon, hydrogen and acetylene.
What is the value of equilibrium constant at this temperature?
Solution:
Delta G is equal to minus RT log (K), where delta G is given
by delta H minus T delta S. Delta H is
given by delta H0 plus aT. Delta S is given by delta S0 plus
a log (T). There is only one unknown, so
these constants, delta H0 or delta S0 can be found by
using the values provided at 298 degrees Kelvin. However, we need to find value of a for the
reaction mixture. Then, we can calculate
delta H and delta S at 2573 degrees Kelvin, thus enabling us to find the value
of delta G and K.
Value of the constant a for the
reaction mixture is calculated by writing the chemical reaction and calculating
the weighted value. It is conventional
to consider the value positive for the products (as being produced) and
negative for the reactants (as being consumed).
The weighted value of constant a is equal to minus 2 (2 moles of Carbon)
time 20.934 minus 1 (1 mole of hydrogen) time 26.231 plus 1 (1 mole of
acetylene) time 70.188 is equal to 2.089 joules per mole per degree
Kelvin.
With a calculated for the reaction mixture, integration
constant delta H0 is equal to delta H298 minus (a ×298). This is equal to 2.2628×105 joules
per mole. Delta H at any other
temperature, 2573 in this case, is then calculated using the formula delta H0
plus aT. Delta
H is calculated to be 2.317×105 joules per mole.
Delta S at 298 degrees can be obtained using the values of
delta H and delta G at 298 degree Kelvin.
Delta S is given as (delta H minus delta G)/T and its value is 58.294 joules per mole per degree Kelvin. So, the integration constant, delta S0,
is equal to delta S298 minus a log (T). This is equal to 47.023 joules per mole per
degree Kelvin. Delta S at any
temperature, 2573 in this case, is thus calculated using the formula delta S0
plus a log(T).
Delta S is calculated to be 63.428 joules per mole per degree Kelvin.
Delta G is thus equal to 2.317×105 minus 2573×58.294
or 6.845×104 joules per mole.
This gives a value of K, exp(minus
delta G/(RT)), as 0.0409. Note that R is
8.32 joules per mole per degree Kelvin.