CHMY 373 2019 – Problem Set 3 Due: Friday Feb. 1 Reminder: See previous problem sets and/or the syllabus for rules regarding problem sets. Reading: Chapter 19.7‐19.12, Simon & McQuarrie 1. What’s the difference between and ? Does it make a big difference whether our device for measuring heat capacity a “calorimeter” is isobaric or isochoric? a. Derive the difference between and ∆ starting from the expression for the definition of enthalpy: Hint: the result you are looking for has the form: ∆ where , , and are measurable variables of state from the subset and both calorimeters are “closed” systems. , , b. Using the expression derived above, find ∆ for an ideal gas. c. Rearrange the expression derived in part a to obtain a much simpler general expression in terms of the isothermal compressibility, , and the coefficient of thermal expansion, , which we have previously defined as: 1 , 1 , d. Write the expression derived in part c in intensive form as ∆ per mole . 2. Joule‐Thomson Inversion: real gases exhibit two distinct regions in their phase diagram corresponding to different heat transfer effects upon Joule‐Thomson expansion which we have seen is an “isenthalpic” or constant enthalpy process . , determines this behavior: when is The sign of the Joule‐Thomson coefficient, positive, cooling occurs upon expansion. This is the effect we are most familiar with, and almost all gases exhibit cooling upon expansion at ambient temperature. However, at very high temperatures for most gases , is negative, and heating occurs upon expansion. The temperature at which this property changes is the Joule‐Thomson inversion temperature, . For a van der Waals gas, the Joule‐Thomson coefficient turns out to be: 2 2 a. Assume the isobaric heat capacity is independent of temperature. Derive an expression for the Joule‐Thomson inversion temperature, , of a van der Waals gas. b. Simplify the inversion temperature derived in part a by assuming the system to be in the “dilute limit.” c. Determine the Joule‐Thomson inversion temperature in K for argon using the van der Waals equation of state. d. Will argon undergo heating or cooling if expanded isenthalpically at room temperature? e. Determine the Joule‐Thomson inversion temperature in K for helium using the van der Waals equation of state. f. Will helium undergo heating or cooling if expanded isenthalpically at room temperature? g. A brand new high‐pressure hydrogen gas cylinder filled to 200 bar has just been delivered to your laboratory to replace the empty one, but someone forgot to note which cylinder was empty and both now stand side by side and look identical. Upon lifting the two cylinders, it’s too hard to tell which is the full one and which is empty. Is it safe to quickly open the valve referred to as the “packing nut” at the top of both cylinders without attaching a regulator to see which is full? In other words, if isenthalpic expansion is assumed, will a temperature difference ≫20 °C occur we usually start to feel burns at above ~45 °C or below ~‐60°C in the case of the full cylinder? 3. Calculate the average bond enthalpy in units of kJ mol of the Si H bonds in disilane gas Si H from the following data provided in units of kcal mol : ‐ ‐ ‐ ‐ ‐ ‐ the standard molar enthalpy of combustion of Si H gas to 2 SiO2 solid and liquid water is ‐637.23 kcal mol the standard enthalpy of formation of SiO solid is ‐205.00 kcal mol the standard enthalpy of formation of H O liquid is ‐68.32 kcal mol Si → Si ∆ ○, 88.04 kcal mol H →H ∆ ○ , 52.09 kcal mol the bond enthalpy of the Si Si bond in disilane is 24.38 kcal mol 4. The standard enthalpies of combustion of ethanol liquid and methyl ether liquid at 25 °C are ‐1235 kJ mol and ‐1247 kJ mol , respectively. Determine the isomerization enthalpy ∆ ○ , for the following reaction: CH OCH → CH CH OH 5. A 1.00 g sample of liquid benzene, C H , is burned in pure oxygen in a “Parr bomb calorimeter” a closed, rigid calorimeter . The initial temperature is 25 °C and the observed temperature increase is 1.681 °C. The heat capacity of the calorimeter assembly heavy metal components is known to be 23.80 kJ K . Assuming ideal gas behavior of the reaction products, find: per mole and per gram of liquid benzene, and a. Δ b. Δ per mole and per gram of liquid benzene. c. Comment on the significance of the difference between Δ and Δ in this experiment.