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The internal energy change in the conver...

The internal energy change in the conversion of `1.0` mole of the calcite form of `CaCO_3` to the aragonite form is `+0.21 KJ`. Calculate the enthalpy change when the pressure is `1.0 `bar, given the densities of the solids are `2.71 gcm^(-3)` and `2.93 gcm^(-3)` respectively.

Text Solution

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`DeltaH= DeltaU + P DeltaV`
Here, `DeltaU =+ 0.21kJmol^(-1)=0.21xx 10^(3)J mol^(-1)= 210J mol^(-1)`
`P =1 ` bar `=10^(5)` P
`DeltaV =`Molar volume of aragonite `-` Molar volume of calcite
`= ( 100)/( 2.93)- (100)/( 2.71) cm^(3) mol^(-1)` ` ( :'` Molar mass of`CaCO_(3) = 100 g mol^(-1))`
`= 100 (( 1)/( 2.93 )- (1)/( 2.71)) =100 xx ( -0.22)/(2.93xx2.71) = -2.77 cm^(3) mol^(-1) = - 2.77 xx 10^(-6) m^(3) mol^(-1)`
`:. DeltaH = 210 +10^(5) ( - 2.77 xx 10^(-6))=210- 0. 277 J = 209. 72 J mol^(-1)`
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