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Niobium crystallises as body centered cube (BCC) and has density of 8*55kg//dm^(3). Calculate the atomic radius of niobium. (Given : Atomic mass of niobium = 93). Write one statement of first law of thermodynamics and its mathematical expression. Write the reactions involved in the zone of reduction in blest furnace during extraction of iron. |
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Answer» SOLUTION :Density of Niobium (Nb) crystal is `=8*55kg//dm^(3)` Crystalline structure is bec. Atomic mass no. of Nb =93 g/mol. Avogadro number `=N_(A)=6*022xx10^(23)mol^(-1)` Atomic radius of Niobium = ? In bcc unit cells, there are 8 atoms at 8 -coners and 1 atoms at body centre. `:.` Number of Nb atoms. `=(1)/(8)xx8+1=1+1=2` Mass of one Nb atom `=(a^(2))/(6*022xx10^(23))` `=1*5544xx10^(-22)` `=3*088xx10^(-22)kg` Mass of unit cell = Mass of 2 Nb atoms `=4*088xx10^(-22)`g If a is edge LENGTH of bcc unit cell Volume of unit cell `=^(3)` Density `=("Mass of unit cell")/("Volume of unit cell")` `d=(3*088xx10^(-22))/(a^(3))` `:.""a^(3)=(3*088xx10^(-22))/(d)` `=(3*088xx10^(-22))/(8.55)` `=0*361xx10^(-22)dm^(3)` `=36*1xx10^(-24)dm^(3)` `a=(36*1xx1-^(-24))^(1//3)` `=3*33xx10^(-8)dm` If r is the radius of 1 Nb atom. then in bcc structure `r=(sqrt(3))/(4)a` `=(sqrt(3))/(4)xx3*33xx10^(-8)` `=1*43xx10^(-8)dm` `or""~~14*3nm` (where, 1 dm `=10^(-9)` nm) Hence, the atomic radius of niobium is `14*3` nm. The first law of thermodynamics states that Energy can NEITHER be created nor be destroyed. The total energy of an isolated system (cannot exchange energy with its surroundings) remains the same. Mathematical expression : In a system that exchanges both heat and mechanical work with its surroundings, the total energy or the energy change is described by taking both - heat and work in it's account. `U_(2)-U_(1)=DeltaY=q+W` `q=DeltaU-W` `DeltaU=q+W` This is the mathematical expression for first law of thermodyamics, from the point of view of conservation of energy. This expression justifies first law of thermodynamics. where, `U_(2)andU_(1)` =Energies of system in the final and initial states, respectively `DeltaU` =Change in internal energy q=heat absorbed or evolved by the system W = Work DONE by the system or the system. Reactions involved in the of reduction : `3Fe_(2)O_(3)+COto2Fe_(3)O_(4)+CO_(2)` `Fe_(3)O_(4)+COto3FeO+CO_(2)` `FeO+COtoFe+CO_(2)`. |
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