Answer:
The reactions free energy [tex]\Delta G = -49.36 kJ[/tex]
Explanation:
From the question we are told that
The pressure of (NO) is [tex]P_{NO} = 9.20 \ atm[/tex]
The pressure of (Cl) gas is [tex]P_{Cl} = 9.15 \ atm[/tex]
The pressure of nitrosly chloride (NOCl) is [tex]P_{(NOCl)} = 7.70 \ atm[/tex]
The reaction is
[tex]2NO_{(g)} + Cl_2 (g)[/tex] ⇆ [tex]2 NOCl_{(g)}[/tex]
From the reaction we can mathematically evaluate the [tex]\Delta G^o[/tex] (Standard state free energy ) as
[tex]\Delta G^o = 2 \Delta G^o _{NOCl} - \Delta G^o _{Cl_2} - 2 \Delta G^o _{NO}[/tex]
The Standard state free energy for NO is constant with a value
[tex]\Delta G^o _{NO} = 86.55 kJ/mol[/tex]
The Standard state free energy for [tex]Cl_2[/tex] is constant with a value
[tex]\Delta G^o _{Cl_2} = 0kJ/mol[/tex]
The Standard state free energy for [tex]NOCl[/tex] is constant with a value
[tex]\Delta G^o _{NOCl} =66.1kJ/mol[/tex]
Now substituting this into the equation
[tex]\Delta G^o = 2 * 66.1 - 0 - 2 * 87.6[/tex]
[tex]= -43 kJ/mol[/tex]
The pressure constant is evaluated as
[tex]Q = \frac{Pressure \ of \ product }{ Pressure \ of \ reactant }[/tex]
Substituting values
[tex]Q = \frac{(7.7)^2 }{(9.2)^2 (9.15) } = \frac{59.29}{774.456}[/tex]
[tex]= 0.0765[/tex]
The free energy for this reaction is evaluated as
[tex]\Delta G = \Delta G^o + RT ln Q[/tex]
Where R is gas constant with a value of [tex]R = 8.314 J / K \cdot mol[/tex]
T is temperature in K with a given value of [tex]T = 25+273 = 298 K[/tex]
Substituting value
[tex]\Delta G = -43 *10^{3} + 8.314 *298 * ln [0.0765][/tex]
[tex]= -43-6.36[/tex]
[tex]\Delta G = -49.36 kJ[/tex]
