Question

Acetylene, C2H2, can be converted to ethane, C2H6, by a process known as hydrogenation. The reaction is C2H2(g)+2H2(g)?C2H6(g)

Given the following data, what is the value of Kp for this reaction?

Substance	?G?f (kJ/mol)
C2H2(g)	209.2
H2(g)	0
C2H6(g)	?32.89

In Part A, we saw that ?G?=?242.1 kJ for the hydrogenation of acetylene under standard conditions (all pressures equal to 1 atm and the common reference temperature 298 K ). In Part B, you will determine the ?G for the reaction under a given set of nonstandard conditions

At 25?C the reaction from Part A has a composition as shown in the table below.

Substance	Pressure (atm)
C2H2(g)	3.85
H2(g)	4.45
C2H6(g)	1.25

Answer 1

Concepts and reason

For chemical reaction, the chemical equilibrium is a state of system. The equilibrium constant for a chemical reaction is a certain value at equilibrium state, which depends on concentrations of species involved and the thermodynamic variables such pressure, temperature and volume at equilibrium state. The equilibrium constant can be calculated using the relation between the Gibbs free energy change and equilibrium constant.

Gibbs free energy change of system for any given set of conditions (non-standard state) that can be calculated by using the and reaction quotient, .

Fundamentals

The relation between the standard Gibbs free energy change and equilibrium constant is given below:

Here,

The standard Gibbs free energy change is .

The equilibrium constant in terms of partial pressure is .

The temperature of the system is .

The universal gas constant is .

Reaction quotient: For the given reaction, the reaction quotient determines the direction of the reaction. It is the ratio of activities (partial pressures) of products by reactants.

For a general reaction,

Here,

The square bracket represents concentration of species.

The partial pressure of the gas is denoted by the symbol, .

The relation between Gibbs energy at non-standard conditions and Gibbs energy at standard conditions with reaction quotient for a given set of conditions is given below:

Here,

The Gibbs free energy change is .

The standard Gibbs free energy change is .

The reaction quotient is .

The temperature of the system is .

The universal gas constant is .

(A)

Substitute the values in the relation of the standard Gibbs free energy change and equilibrium constant

(B)

The partial pressure values for each of the reaction species is given below:

Substance	Pressure (atm)
	3.85
	4.45
	1.25

The reaction quotient is calculated below:

At non-standard conditions, the Gibbs free energy change is calculated below:

Ans: Part A

The value of for the given reaction is .