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, b, and c 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 plus b/2 T2
plus c/3 T3. Delta S is given
by delta S0 plus a log (T) plus b T plus c/2 T2. 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 values of a, b, and c 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.
Values of the constants a, b, and c 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). For
example, the weighted value of constant a is equal to minus 2 (2 moles of
Carbon) time 1.1 minus 1 (1 mole of hydrogen) time 6.88 plus 1 (1 mole of
acetylene) time 8.28 is equal to minus 0.8 calories per mole per degree
Kelvin. Similarly, the value of b and c
for the reaction mixture can be calculated.
With a, b, and c calculated for the reaction mixture,
integration constant delta H0 is equal to delta H298
minus (a ×298 plus b/2 ×2982 plus c/3 ×2983). This is equal to 54,395 calories per
mole. Delta H at any other temperature,
2573 in this case, is then calculated using the formula delta H0
plus aT plus b/2 T2 plus c/3 T3. Delta H is calculated to be 55,330 calories
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 14.074 calories per mole per degree Kelvin. So, the integration constant, delta S0,
is equal to delta S298 minus (a log (T) plus bT plus c/2 T2). This is equal to 18.378 calories 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) plus b T plus c/2 T2. Delta S is calculated to be 14.384 calories
per mole per degree Kelvin.
Delta G is thus equal to 55330 minus 2573×14.384 or 18,320
calories per mole.
This gives a value of K, exp(minus delta G/(RT)), as 0.0278.