Respuesta :
Answer:
The value of equilibrium constant at 2000 C is [tex]6.045\times 10^{-4}[/tex].
Explanation:
To calculate [tex]\Delta H_{vap}[/tex] of the reaction, we use Van't Hoff equation, which is:
[tex]\ln(\frac{K_2}{K_1})=\frac{\Delta H^o}{R}[\frac{1}{T_1}-\frac{1}{T_2}][/tex]
where,
[tex]K_1[/tex] = vapor pressure at temperature [tex]T_1[/tex]
[tex]K_2[/tex] = vapor pressure at temperature [tex]T_2[/tex]
[tex]\Delta H^o[/tex] = Enthalpy change of the reaction= ?
R = Gas constant = 8.314 J/mol K
We have :
[tex]N_2+O_2\rightarrow 2NO[/tex]
Enthalpy of formation of nitrogen gas ,[tex]\Delta H_{f,N_2}= 0kJ/mol[/tex]
Enthalpy of formation of oxygen gas ,[tex]\Delta H_{f,O_2}= 0 kJ/mol[/tex]
Enthalpy of formation of NO gas ,[tex]]\Delta H^o= 90.3 kJ/mol[/tex]
Enthalpy of the reaction = [tex]\Delta H^o[/tex]
[tex]\Delta H^o=2\times \Delta H^o - (1\times \Delta H_{f,N_2}+1\times \Delta H_{f,O_2})[/tex]
[tex]\Delta H^o=2\times 90.3 kJ/mol - 1\times 0 kJ/mol =1\times 0kJ/mol[/tex]
[tex]\Delta H^o=180.6 kJ/mol = 180,600 J/mol[/tex]
Equilibrium constant at 25°C = [tex]K_1=1.95\times 10^{-31}[/tex]
Equilibrium constant at 2,000°C = [tex]K_2=?[/tex]
[tex]T_1=25^oC=298.15 K, T_2= 2000^oC=2273.15 K[/tex]
By using Van't Hoff equation, te [tex]K_2[/tex] can be calculated:
[tex]\ln(\frac{K_2}{1.95\times 10^{-31}})=\frac{180,600J/mol}{8.314 J/mol K}[\frac{1}{298.15 K}-\frac{1}{2273.15 K}][/tex]
[tex]K_2=6.045\times 10^{-4}[/tex]
The value of equilibrium constant at 2000 C is [tex]6.045\times 10^{-4}[/tex].
