Question

The standard Gibbs Energy change for a gaseous reaction at 27 is X Kcal. If the equilibrium constant of a reaction is 100 and R is 2 \[cal{{K}^{-1}}mo{{l}^{-1}}\]. Then X is:
A.\[-2.7636\]
B. \[+2.7636\]
C. \[+807\]
D. \[-807\]

Answer 1

Hint: Use the formula for Gibbs Energy change which includes equilibrium constant, temperature and R. Then using the above given values find the value of X.

Formula Used: \[\Delta G=-RT\ln K\]
where \[\Delta G=\]change in Gibbs free energy
 \[T\text{ }=\text{ }temperature\text{ }in\text{ }kelvin\]
\[\begin{array}{*{35}{l}}
K\text{ }=\text{ }equilibrium\text{ }constant \\
R\text{ }=\text{ }ideal\text{ }gas\text{ }constant \\
\end{array}\]

Complete Step By Step Solution:
Gibbs free energy is the energy associated with a chemical reaction that can be used to do work. Negative Gibbs free energy means that the process is spontaneous and may proceed in the forward direction.
\[Given,\text{ }, K=\text{ }100, R=\text{ }2, T=\text{ }27\]
In kelvin \[T\text{ }=\text{ }273\text{ }+\text{ }27\text{ }=\text{ }300\text{ }K\]
Using the above formula we get, \[\Delta G=-RT\ln K\]
 \[X~~=\text{ }-2\]\[\times \]\[300\]\[\times \]\[100\]
\[=\text{ }-\text{ }600\] \[\times \]\[4.6052\]
\[=\text{ }-2763\text{ }cal\]
\[=\text{ }-2.763Kcal\]

So, the correct option is A.

Additional Information:
Gibbs Free Energy: The free energy of a system is the sum of its enthalpy \[\left( H \right)\] plus the product of the temperature (Kelvin) and the entropy \[\left( S \right)\] of the system. Enthalpy \[\left( H \right)\] is the sum of the internal energy \[\left( U \right)\] and the product of pressure and volume \[\left( PV \right)\] given by the equation:\[H=U+PV\] . When a process occurs at constant pressure, the heat evolved (either released or absorbed) is equal to the change in enthalpy. Gibbs available (free) energy of reaction is intensive. It's constant for the reaction (under the same conditions) regardless of the extent of your experiment.
If free energy decreases, the reaction can proceed. If the free energy increases, the reaction can't proceed. A reaction is favored if the free energy of the system decreases. A reaction is not favored if the free energy of the system increases.
The equilibrium constant, K, expresses the relationship between products and reactants of a reaction at equilibrium with respect to a specific unit.
The gas constant (also known as the molar gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol R . It is equivalent to the Boltzmann constant, but expressed in units of energy per temperature increment per mole.

Note: Study the concepts of Gibbs Free Energy, change in the energy, its thermodynamic relations with enthalpy, entropy and other relations. Its properties, meaning of negative and positive free energy. Reason of being called free energy, effect on the reaction and the factors leading to change in the gibbs free energy.