For reactions in condensed phases (liquids and solids), the difference between A

Question

For reactions in condensed phases (liquids and solids), the difference between All and A U is usually quite small. This statement holds for reactions carried out under atmospheric conditions. For certain geochemical processes, however, the external pressure may be so great that All and AU can differ by a significant amount. A well-known example is the slow conversion of graphite to diamond under Earth?s surface. Calculate triangle H - triangle U for the conversion of 1 mole of graphite to 1 mole of diamond at a pressure of 4.00 X 10^4 atm. The densities of graphite and diamond are 2.25 g/cm^3 and 3.52 g/cm^3, respectively. -0. 0722 kJ/mol

Explanation / Answer

we know that

dH - dU = pdV

given

1 mole of graphite and diamond

we know that

1 mole of graphite and diamond weighs 12 g

we know that

volume = mass / density

so

volume of graphite = mass of graphite / density of graphite

volume of graphite = 12 / 2.25

volume of graphite = 5.333 cm3

similarly

volume of diamond = 12 / 3.52

volume of diamond = 3.409 cm3

now the reaction is

graphite ----> diamond

so

dV = volume of diamond - volume of graphite

dV = 3.409 - 5.333

dV = -1.924 cm3

dV = -1.924 x 10-6 m3

now

given

pressure = 4 x 10^4 atm

pressure = 4 x 10^4 x 101325 pa

pressure (p)= 4.053 x 10^9 Pa

so

now

dH - dU = pdV

dH - dU = 4.053 x 10^9 x (-1.924 x 10-6)

dH - dU = -7797.97 J

dH - dU = -7.80 kJ

so

the dH - dU value is -7.8 kJ /mol

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