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A sample of 64.0 g of methane, CH4 (molecular mass 16.0 g/mol, assume ideal gas behaviour))...

A sample of 64.0 g of methane, CH4 (molecular mass 16.0 g/mol, assume ideal gas behaviour)) at 300 K and with an initial pressure V1 = 1.00 m3 is compressed isothermally and reversibly to a final volume of 2.00L. Calculate DU, DH, w, and q

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Answer #1

During isothermal expansion or compression U =0 and H =0

[When the temperature is constant P1V1=P2V2 or PV = constant. Thus H = U + (PV),

H = 0+0 =0]

a) Work done in isothermal reversible compression W= 2.303 nRT log (V2/V1)

where n = no.of moles of gas = 64g/16g mol-1 = 4 moles

          R = 8.314 J/K mol

           T= 300K

W = 2.303 * 4 moles* 8.314 J/K mol * 300K * log ( 2.00L/1000L)                  (since 1m3 = 1000litres)

    = - 62013.1 J

   = -62.013kJ

q = -w , hence q = 62.013KJ

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