Please I need the last part and I cannot solve it. presented by Sapling Learning

Question

Please I need the last part and I cannot solve it. presented by Sapling Learning The follawing equation represents the decomposition of a generic diatomic element in its standard state. Assume that the standard molar Gibbs energy of formation of X(g) is 4.80 kJ-mot" at 2000. K and -64 96 kJ mor" at 3000. K. Determine the value of K (the thermodynamic equilivium constant) at each mperature Number K at 2000, K= 0.749 Number K at 3000, K= 13.52 Assuming that A+Hrmn is independent of temperature, determine the value of AH.m from these data. Number kJ: mol .OPrevious ® Give Up&ViewSolution; Try Again O Next help Pravacy polioy terms of use y contact us

Explanation / Answer

consider the given reaction

0.5 X2 ---> X

we know that

dGo rxn = dGof products - dGof reactants

in this case

dGo rxn = ( dGof X) - ( 0.5 x dGof X2)

we know that

standard molar gibbs free energy of formation of elements in their standard state is zero

so

dGof X2 = 0

now

at 2000 K

dGo rxn = 4.8 - ( 0.5 x 0)

dGo rxn = 4.8 kJ /mol

now

we know that

dGo = -RT lnK

so

4.8 x 1000 = -8.314 x 2000 x ln K

K = 0.749

2) At 3000 K

dGo rxn = -64.96 - ( 0.5 x 0)

dGo rxn = -64.96 kJ/mol

now

dGo = -RT lnK

-64.96 x 1000 = -8.314 x 3000 x lnK

K = 13.52

3)

now

we know that

using clausius claperyon equation

ln (k2/k1) = (dH/R) ( 1/T1 - 1/T2)

in this case

k1 = 0.749

T1 = 2000 K

k2 = 13.52

T2 = 3000 K

so

ln ( 13.52 / 0.749) = (dH/8.314) ( 1/2000 - 1/3000)

dH = 144323

dH = 144.323 x 1000

dH = 144.323 kJ/mol

so

the value of dHo rxn = 144.323 kJ/mol

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