Question

3. What is the change in chemical potential (Au) of gaseous methane for a pressure change from 1.0 to 20.0 bar at 298 K?

Answer 1

write the relation between change in chemical potential and pressure at constant temperature as follows:

∆μ = ­_p2p1PdV

PdV 'p2

          = ­_p2p1Pd(RT/p)

Pd(RT/p) p2

      = ­_{p2p1PRT-1P2dp}

PRT(-dp p2

     ∆μ = -RT ln (P_­2­ /P_­1)----------(1)

here ∆μ is change in chemical potential R is gas constant T is temperature P­_1­ is initial pressure and P_­2­ is final pressure

P­_1­ is initial pressure = 1.0 bar

P_­2­ is final pressure   = 20.0 bar

T is temperature =298 K

R is gas constant = 8.314 J/molK

substitute all the required values in equation (1) to find the change in chemical potential

     ∆μ = -RT ln (P_­2­ /P_­1)

           = -8.314 J/molK X (298 K) X ln(20/1)

           = -7422.14 J/mol

therefore the required change in chemical potential is   -7422.14 J/mol

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