For CaCO3(s) -> CaO(s) + CO2(g), Delta H_298=+178.0 kJ. Heat capacities (in J mol^-1K^-1, assumed constant): CaCO3=83.5, CaO=42.0, CO2=37.1. Estimate Delta H at 800 K.

JEE Main levelSingle correct optionDifficulty 2 of 3td136

For $CaCO X_{3} (s) CaO (s) + CO X_{2} (g)$ , $Δ H_{298} = + 178.0 kJ$ . Heat capacities (in $J mo l^{- 1} K^{- 1}$ , assumed constant): $CaCO X_{3} = 83.5$ , $CaO = 42.0$ , $CO X_{2} = 37.1$ . Estimate $Δ H$ at $800 K$ .

Kirchhoff:

Δ H_{T_{2}} = Δ H_{T_{1}} + Δ C_{P} (T_{2} - T_{1})

Δ C_{P} = (42.0 + 37.1) - 83.5 = - 4.4 J K^{- 1}

Δ H_{800} = 178.0 + (- 4.4) (502) /1000 = 178.0 - 2.21 = + 175.8 kJ

. The value

+ 180.2

comes from the wrong sign of

Δ C_{P}

, and

+ 174.5

from using

800

instead of

502 K

for

Δ T