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Geological conditions are sometimes so extreme that quantities neglected in normal laboratory experiments take on an overriding importance. For example, consider the formation of diamond under geo-physically typical conditions. The density of graphite is $2.4 g / c m^{3}$ and that of diamond is $3.6 g / c m^{3}$ at a certain temperature and 500 k bar. By how much does $Δ U_{t r a n s}$ differs from $Δ H_{t r a n s}$ for the graphite to diamond transition?

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0.83 kJ/mol

83.33 J/mol

83.33 kJ/mol

$8.33 \times 10^{7}$ kJ/mol

answer is A.

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Detailed Solution

$Δ H - Δ U = P . Δ V = P [V_{D} - V_{G}]$

$= 500 \times 10^{3} \times 10^{5} \frac{N}{M^{2}} [\frac{12}{3.6} - \frac{12}{2.4}] \times 10^{- 6} m^{3} = - 8.33 \times 10^{4} J / m o l$

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