What is the value of change in internal energy at 1 atm in the process?
`H_(2)O(l,323K)rarrH_(2)O(g,423K)`
Given : `C_(v,m)(H_(2)O,l)=75.0JK^(-1) mol^(-1):" "C_(p,m)(H_(2)O,g)=33.314JK^(-1)mol^(-1)`
`DeltaH_(vap)"ar 373 K"=40.7KJ//mol`

Options

A. `52.91 kJ//mol`
B. `43086 kJ//mol`
C. `42.6kJ//mol`
D. `49.6kJ//mol`

Answer

C

Explanation

`H_(2)O(l,323 K) overset(Delta U_(1))rarr H_(2)O(l, 373 K)`
, `Delta U_(2)`
`H_(2)O(g, 323K) overset(Delta U_(3))larr H_(2)O(g, 373 K)`
`C_(V, m) (H_(2)O, g) = 33.314-8.314`
`Delta U_(2) = Delta n_(g)RT = 376`, `Delta U_("total") = Delta U_(1) + Delta U_(2) + U_(3)`
`= C_(v, m)(l)Delta T+Delta U_(vap) + C_(vap) + C_(vm)(g) Delta T`
`= (75 xx 50)/(1000) + 37.6 + (25 xx 50)/(1000) = 42.6 kJ//mol`