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General Chemistry Principles, Patterns, and Applications, 2011

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B To find ΔE using Equation 18.11, we need to calculate Δ(PV). The process is carried out at a constant<br />

pressure of 1.00 atm, so<br />

D(PV) = PDV = P(Vf -V)<br />

= (1.00 atm)(0.0180 L - 0.0197 L)<br />

= (-1.7 ´10 - 3 L ×atm)(101.3 J / L ×atm) = -0.0017 J<br />

C Substituting the calculated values of ΔH <strong>and</strong> PΔV into Equation 18.11,<br />

ΔE = ΔH − PΔV = 6010 J − (−0.0017 J) = 6010 J = 6.01 kJ<br />

Exercise<br />

At 298 K <strong>and</strong> 1 atm, the conversion of graphite to diamond requires the input of 1.850 kJ of heat per mole<br />

of carbon. The molar volumes of graphite <strong>and</strong> diamond are 0.00534 L <strong>and</strong> 0.00342 L, respectively.<br />

Calculate ΔH <strong>and</strong> ΔE for the conversion of C (graphite) to C (diamond) under these conditions.<br />

Answer: ΔH = 1.85 kJ/mol; ΔE = 1.85 kJ/mol<br />

The Relationship between ΔH <strong>and</strong> ΔE<br />

If ΔH for a reaction is known, we can use the change in the enthalpy of the system (Equation 18.11) to<br />

calculate its change in internal energy. When a reaction involves only solids, liquids, liquid solutions, or<br />

any combination of these, the volume does not change appreciably (ΔV = 0). Under these conditions, we<br />

can simplify Equation 18.11to ΔH = ΔE. If gases are involved, however, ΔH <strong>and</strong> ΔE can differ significantly.<br />

We can calculate ΔE from the measured value of ΔH by using the right side of Equation 18.11together with<br />

the ideal gas law, PV = nRT. Recognizing that Δ(PV) = Δ(nRT), we can rewrite Equation 18.11 as follows:<br />

Equation 18.12<br />

ΔH = ΔE + Δ(PV) = ΔE + Δ(nRT)<br />

At constant temperature, Δ(nRT) = RTΔn, where Δn is the difference between the final <strong>and</strong> initial<br />

numbers of moles of gas. Thus<br />

Equation 18.13<br />

ΔE = ΔH − RTΔn<br />

For reactions that result in a net production of gas, Δn > 0, so ΔE < ΔH. Conversely, endothermic<br />

reactions (ΔH > 0) that result in a net consumption of gas have Δn < 0 <strong>and</strong> ΔE > ΔH. The relationship<br />

between ΔH <strong>and</strong> ΔE for systems involving gases is illustrated in Example 4.<br />

Note the Pattern<br />

Saylor URL: http://www.saylor.org/books<br />

Saylor.org<br />

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