hw4_solutions_F

# hw4_solutions_F - 1(5 The equation of state of a material...

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1(5) . The equation of state of a material is given by 2 0 V Va Pb T =− + , where V 0 , a , and b are constants. Derive the equation for the change of the chemical potential of this material, 0 (,) ( ,) PT P T µµ , when its pressure is raised from P 0 to P . 0 3 3 00 0 0 ( ) ( ) (/ 3 ) ( ) P P VdP V bT P P a P P −= = + 2(10) . Obtaining very high vacuum inside an aluminum container is ultimately limited by the fact that some of the atoms of Al escape the bulk of the metal and form the vapor phase. Calculate the pressure of aluminum vapor that is in equilibrium with Al(s) at T=298K using the value (Al(g)) f G =285.7 kJ/mol for Al(g) at P=1atm and T=298K. To simplify your calculations, neglect the pressure dependence of the chemical potential of Al(s) . The equilibrium pressure is determined by the condition (,) gs = We can write this as 0 0 0 l n (/ ) (,) ( ) s s PT RT PP PT V P P µ +≈ + , where P 0 =1atm. This gives 0 / 51 exp 8.3 10 f GPTR T sg PP P e a t m RT −∆  == ×   The equation 0 f G PT for Al(g) is obtained the same way we have found heats of reaction from formation enthalpies in thermochemistry (this can be done for any quantity that is a function of state).

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hw4_solutions_F - 1(5 The equation of state of a material...

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