The transition Sn(s, gray) ⇌ Sn(s, white) is in equilibrium at 18°C and 1 atm pressure. If ΔS = 8.811K mol for the transition at 18°C and if the densities are 5.75 g/cm3 for gray tin and 7.28 g/cm3 for white tin, calculate the transition temperature under 100 atm pressure

Asked by sayantan.chem2 | 6th Aug, 2019, 05:07: PM

Expert Answer:

Transition temperature can be find out by using formulae-
dP over dT equals fraction numerator increment straight S over denominator increment straight V end fraction
dP over dT equals fraction numerator increment straight S over denominator begin display style straight M over straight d subscript 1 minus straight M over straight d subscript 2 end style end fraction
straight d subscript 1 comma space end subscript straight d subscript 2 space are space density space of space gray space Tin
straight T subscript 2 equals ? space space space space space straight T subscript 1 equals 273 plus 18 equals 291 space straight K

fraction numerator left parenthesis 100 minus 1 right parenthesis over denominator left parenthesis straight T subscript 2 minus 291 right parenthesis end fraction equals fraction numerator 8.811 over denominator left parenthesis begin display style fraction numerator 118.71 over denominator 5.75 end fraction end style minus begin display style fraction numerator 118.71 over denominator 7.28 end fraction end style right parenthesis end fraction
fraction numerator 99 over denominator 8.811 end fraction left parenthesis fraction numerator 118.71 over denominator 5.75 end fraction minus fraction numerator 118.71 over denominator 7.28 end fraction right parenthesis space equals space straight T subscript 2 minus 291
fraction numerator begin display style 99 end style over denominator begin display style 8.811 end style end fraction left parenthesis 20.64 minus 16.306 right parenthesis plus 291 equals straight T subscript 2
straight T subscript 2 space equals 339.68 space straight K
space space space space space space equals space 339.68 minus 273
space space space space space space space equals 66.68 space straight C presuperscript straight o

Answered by Ravi | 12th Aug, 2019, 06:47: PM