Select the correct enthalpy at corresponding temperature using following datas
(i) Heat capacity of solid from 0K to normal melting point 200K
`C_(p.m)(s)=0.035T" "JK^(-1)"mol"^(-1)`
`(ii)` Enthalpy of fusion `=7.5 KJ"mol"^(-1)`
`(iii)` Enthalpy of vaporisation `=30KJ "mol"^(-1)`
`(iv)` Heat capacity of liquid form 200K to normal boiling point 300K
`C_(p.m)(l)=60+0.016T " "JK^(-1)"mol"^(-1)`
`(v)` Heat capacity of gas from 300 K to 600 K at 1 atm
`C_(p.m)(g)=50.0" " JK^(-1)"mol"^(-1)`

Options

A. `S_(200(s))`=7
B. `S_(300(l))`=70.43
C. `S_(300(g))=170.43`
D. `S_(600(g)) = 205.09`

Answer

A, B, C, D

Explanation

`S_(200(0)) = underset(0)overset(200)int (C_(p) dT)/(T) =7 J"mol"^(-1)K^(-1)`
`S_(200(f))=7 + (7500)/(200) =44.5 J "mol"^(-1)K^(-1)`
`S_(300(f)) = 44.5 + underset(200)overset(300)int (C_(p) dT)/(T)=44.5 + 60 "In" (300)/(200) + 1.6= 70.43 J "mol"^(-1)K^(-1)`
`S_(300(g)) = 70.43 + (30000)/(300) = 170.43 J "mol"^(-1) K^(-1)`
`S_(800(g)) = 170.43 "In" 50 "In" (600)/(300)=205.09 JK^(-1)"mol"^(-1)`