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The molar heat capacity of ethane is represented in the temperature range 298 K to 400 K by the empirical expression Cp,m/ (J K-1 mol-1) = 14.73 + 0.1272(T/K). The corresponding expressions for C(s) and H2 (g) are given in Table 2.2. Calculate the standard enthalpy of formation of ethane at 350 K from its value at 298 K.

The standard enthalpy of formation of the metallocene bis (benzene) chromium was measured in a calorimeter. It was found for the reaction Cr (C6H6)2(s) →Cr(s) + 2 C6H6 (g) that ∆Uo (583 K) = +8.0 kJ mol-1. Find the corresponding reaction enthalpy and estimate the standard enthalpy of formation of the compound at 583 K. The constant-pressure molar heat capacity of benzene is 136.1 J K-1 mol-1 in its liquid range and 81.67 J K-I mol-1 as a gas.

It is possible to investigate the thermo chemical properties of hydrocarbons with molecular modeling methods.

(a) Use electronic structure software to predict ∆cHo values for the alkane’s methane through pentane. To calculate ∆cHo values, estimate the standard enthalpy of formation of CnH2 (n+l) (g) by performing semi-empirical calculations (for example, AMI or PM3 methods) and use experimental standard enthalpy of formation values for CO2 (g) and H20 (I).

(b) Compare your estimated values with the experimental values of ∆cHo (Table 2.5) and comment on the reliability of the molecular modeling method.

(c) Test the extent to which the relation ∆cHo= k {(M/ (g mol-1)} n holds and find the numerical values for k and n.

(a) Use electronic structure software to predict ∆cHo values for the alkane’s methane through pentane. To calculate ∆cHo values, estimate the standard enthalpy of formation of CnH2 (n+l) (g) by performing semi-empirical calculations (for example, AMI or PM3 methods) and use experimental standard enthalpy of formation values for CO2 (g) and H20 (I).

(b) Compare your estimated values with the experimental values of ∆cHo (Table 2.5) and comment on the reliability of the molecular modeling method.

(c) Test the extent to which the relation ∆cHo= k {(M/ (g mol-1)} n holds and find the numerical values for k and n.

Since their discovery in 1985, fullerenes have received the attention of many chemical researchers. Kolesov et al. reported the standard enthalpy of combustion and of formation of crystalline C60 based on calorimetric measurements (V.P. Kolesov, S.M. Pirnenova, V.K. Pavlovich, N.B. Tamm, and A.A. Kurskaya,J. Chem. Thermodynamics 28, 1121 (1996)). In one of their runs, they found the standard specific internal energy of combustion to be -36.0334 kJ g-1 at 298.15 K Compute ∆_{c}H^{o} and ∆_{f}H^{o} of C60.

Silylene (SiH2) is a key intermediate in the thermal decomposition of silicon hydrides such as silane (SiH4) and disilane (Si2H6). Moffat et al. (H.K.

Moffat, K.F. Jensen, and R.W. Carr, J. Phys. Chem. 95,145 (1991)) report ∆fHo SiH2) = +274 kJ mol-1. If ∆rHo (SiH4) = +34.3 k] mol-1 and ∆fHo(Si1H6)= +80.3 k] mol-1: (CRC Handbook (2004)), compute the standard enthalpies of the following reactions:

(a) SiH4 (g) →7 SiH2 (g) + H2 (g)

(b) Si2H6 (g) ---7 SiH2) + SiH4 (g)

Moffat, K.F. Jensen, and R.W. Carr, J. Phys. Chem. 95,145 (1991)) report ∆fHo SiH2) = +274 kJ mol-1. If ∆rHo (SiH4) = +34.3 k] mol-1 and ∆fHo(Si1H6)= +80.3 k] mol-1: (CRC Handbook (2004)), compute the standard enthalpies of the following reactions:

(a) SiH4 (g) →7 SiH2 (g) + H2 (g)

(b) Si2H6 (g) ---7 SiH2) + SiH4 (g)

The constant -volume heat capacity of a gas can be measured by observing the decrease in temperature when it expands adiabatically and reversibly. If the decrease in pressure is also measured, we can use it to infer the value of y= Cp/Cv and hence, by combining the two values, deduce the constant-pressure heat capacity. A fluorocarbon gas was allowed to expand reversibly and adiabatically to twice its volume; as a result, the temperature fell from 298.15 K to 248.44 K and its pressure fell from 202.94 kPa to 81.840 kPa. Evaluate Cp'

Take nitrogen to be a van der Waals gas with a = 1.352 dm6 atm mol-2 and b = 0.0387 dm3 mol-1, and calculate ∆Hm when the pressure on the gas is decreased from 500 atm to 1.00 atm at 300 K. For a van der Waals gas, .u= {(2a/RD - b}/Cp,m Assume Cp•m = 7/2 R.

(a) What is the total differential of z = x2 + 2y2 - 2xy+ 2x- 4y - 8?

(b) Show that ∂2z/∂y∂x = ∂2z/∂x∂y for this function.

(c) Let z= xy- y + in x + 2. Find dz and show that it is exact.

(b) Show that ∂2z/∂y∂x = ∂2z/∂x∂y for this function.

(c) Let z= xy- y + in x + 2. Find dz and show that it is exact.

(a) Derive the relation Cv= - (∂U/∂V)T (∂V/∂T)u from the expression for the total differential of U(T, V) and

(b) Starting from the expression for the total differential of H(T,p), express (∂H/∂p)T in terms of Cp and the Joule- Thomson coefficient, μ.

(b) Starting from the expression for the total differential of H(T,p), express (∂H/∂p)T in terms of Cp and the Joule- Thomson coefficient, μ.

(a) By direct differentiation of H = U + P V, obtain a relation between (∂H/∂U)p and (∂U/∂V)p

(b) Confirm that (∂H/∂U)p = I + p(∂V/∂U)p by expressing (∂H/∂U)p as the ratio of two derivatives with respect to volume and then using the definition of enthalpy.

(b) Confirm that (∂H/∂U)p = I + p(∂V/∂U)p by expressing (∂H/∂U)p as the ratio of two derivatives with respect to volume and then using the definition of enthalpy.

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