Question

What would be the value of Δ_rH° at 1000 K for the reaction: H₂(g) + Cl₂(g)---> 2HCl(g)

given Δ_rH°₂₉₈ = -184.614 kJ? Assume that the heat capacities are given in J/K.mol by:
C_p= 29.066 - 0.836x10^-3 T + 20.17x10^-7 T² for H₂ (g)

C_p= 31.696 + 10.144x10^-3 T - 40.38x10^-7 T²   for Cl₂ (g)

C_p= 28.166 + 1.810x10^-3 T + 15.47x10^-7 T²    for HCll (g)

Δ_rH°₁₀₀₀ K = ?

Answer 1

HRxn = Hformation + Hsensible heat 298K - > 1000 K

We can add

HRxn = 2 products - 1-1 reactants

Hsensible = 2*(28.166 + 1.810x10-3 T + 15.47x10-7 T2 ) - (31.696 + 10.144x10-3 T - 40.38x10-7 T2) - (29.066 - 0.836x10-3 T + 20.17x10-7 T2)

HRxn = 2*HCl = 2*(-184.614 ) = -369.228 kJ/mol

Now.

Htotal = Hrxn + Hsensible

Htotal = -369.228 +  2*(28.166 + 1.810x10-3 T + 15.47x10-7 T2 ) - (31.696 + 10.144x10-3 T - 40.38x10-7 T2) - (29.066 - 0.836x10-3 T + 20.17x10-7 T2)

simplify

Htotal = -369.228*10^3 +  2*(28.166 + (1.810*10^-3)*T + (15.47*10^-7)* T2 ) - (31.696 + (10.144*10^-3) T - (40.38*10^-7) T2) - (29.066 - (0.836*10^-3) T + (20.17*10^-7)* T2)

Htotal = -369.228 + (2*(28.166 - 31.696 -29.066 ) + T ( 2*(1.810*10^-3) - (10.144*10^-3) - (0.836*10^-3) ) + T^2 * (2*(15.47*10^-7) - (40.38*10^-7) -(20.17*10^-7) )

keep simplifying

Htotal = -369228 + (- 65.192 - 0.00736*T + -0.000002961 *T^2)*dT

Htotal = -369228 + - 65.192(Tf-Ti) - 0.00736/2*(Tf^2-Ti^2) + -0.000002961/3 *(Tf^3 - Ti^3) *dT

Htotal = -369228 + - 65.192*(Tf-Ti) - 0.00368**(Tf^2-Ti^2) - (9.87*10^-7) * (Tf^3- Ti^3)

substitute Tf = 1000, Ti = 298

Htotal = -369228 + - 65.192*(1000-298) - 0.00368*(1000^2-298^2) - (9.87*10^-7) * (1000^3- 298^3)

Htotal = -419306.86J/mol

HRxn = -419.30 kJ