Question

A sample of pure solid naphthalene (C10H8) weighing 0.6410 g is burned completely with oxygen to CO2(g) and H2O(,) in a constant-volume calorimeter at 25°C. The amount of heat evolved is observed to be 25.79 kJ. (a) Write and balance the chemical equation for the combustion reaction. (b) Calculate the standard change in internal energy (DU°) for the combustion of 1.000 mol naphthalene to CO2(g) and H2O(,). (c) Calculate the standard enthalpy change (DH°) for the same reaction as in part (b). (d) Calculate the standard enthalpy of formation per mole of naphthalene, using data for the standard enthalpies of formation of CO2(g) and H2O(,) from Appendix D.

Answer 1

Step-by-step explanation:

a) The balance the chemical equation for the combustion reaction.

`C_(10)H_8+12O_2\rightarrow 10CO_2+4H_2O`

b) The amount of heat evolved on combustion of naphthalene = Q = -25.79 kJ

Mass of naphthalene = 0.6410 g

Moles of naphthalene =
`(0.6410 g)/(128 g/mol)=0.005 mol`

0.005 moles of naphthalene gives 25.79 kilo joules of heat. then 1 mol will give:

`\Delta U^o=(Q)/(0.005 mol)=(-25.79 kJ)/(0.005 mol)=-5,158 kJ/mol=-5,158,000 J/mol`

The standard change in internal energy (ΔU°) for the combustion of 1.000 mol naphthalene is -5,158 kJ/mol.

c)
`\Delta H^o=\Delta U^o+n_gRT`

`\Delta H^o=-5,158,000 J/mol+(-2)* 8.314 J/mol K* 298.15 K`

`\Delta H^o=-5,162,957.64 J=-5,162.96 kJ/mol`

The standard enthalpy change (ΔH°) for the same reaction is -5,162.96 kJ/mol.

d) Standard enthalpy of formation per mole of naphthalene,

Enthlapy of formation of carbon dioxide ,
`\Delta H_(f,CO_2)= -393.509 kJ/mol`

Enthlapy of formation of water ,
`\Delta H_(f,H_2O)= -258.8kJ/mol`

`\Delta H=10* \Delta H_(f,CO_2)+4* \Delta H_(f,H_2O) -(\Delta H_(f,naph)+12* \Delta H_(f,O_2))`

`-5,162.96 kJ/mol=10* ( -393.509 kJ/mol) +4* (-258.8 kJ/mol) -(H_(f,naph)-12* 0kJ/mol)`

`H_(f,naph)=10* (-393.509 kJ/mol) +4* (-258.8 kJ/mol) +0kJ/mol+5,162.96 kJ/mol`

`H_(f,naph)=-192.67 kJ/mol`

The standard enthalpy of formation per mole of naphthalene is 192.67 kJ/mol.