Physical Chemistry I
Physical Chemistry I CH 431
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This 4 page Class Notes was uploaded by Sienna Shields on Thursday October 15, 2015. The Class Notes belongs to CH 431 at North Carolina State University taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/224004/ch-431-north-carolina-state-university in Chemistry at North Carolina State University.
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Date Created: 10/15/15
Chemistry 431 Lecture 6 Heat Capacity State and Path Functions NC State University 9 12008 Question Which expression correctly gives the work of expansion V2 gt V1 V2 A nRTIn V B nRTIn v2 C nR In V2 D nR In The measurement of heat We must care Jlly distinguish between heat and temperature When we add heat to the system its temperature increases We can use measurement of the temperature to determine how much heat has been added However we need to know the heat capacity of the system in order to do this Heat supplied Heatcapadty Temperature rise The heat capacity is called C Ifwe perform a heat exchange at constant volume then we designate the heat capacity as CV Ifthe process occurs at constant pressure we call the heat capacity CF Calorimetry The science ofheat measurement is called calorimetry A calorimeter consists of a container in a heat bath Aphysical or chemical process occurs in the container and heat is added or removed from the heat bath The temperature increases or decreases as result By knowing the heat ca acit ofthe bath we can measure the amount ofheat that has been added or removed from the system Energy in the form at heat ows unto the bath 0va Cyp Calorimetry In the studies ofbiological systems there are two important ty es ofcalorimet 1 Differential scanning calorimetry D80 2 Isothermal titration calorimetry ITC In DSC the temperature is increased at a constant heating rate and the heat capacity is measured D80 is used for determining the parameters associated with phase transitions eg protein unfolding denaturation DNA hybridization etc In ITC the temperature is held constant while one component is added to another The heat ofinteraction eg binding is measured using this method ITC is widely used to determine the enthalpy ofbinding eg for proteinprotein and proteindrug interactions among other types of biological applications Molar and Specific Heat Capacities We use molar heat capacities for pure substances As the name implies the units are JmoIK forthe molar heat capacity We write the molar heat capacity at constant volume as CW For mixtures we cannot use a molar heat capacity and so we use the speci c heat capacity which is the heat capacity per gram ofmaterial with units of JgK Calculating the internal energy change We have seen that the internal energy depends only on temperature For example for a change ofpressure and temperature at constant volume we saw that AU qV since the work is zero for a constant volume process Thus at constant volume AU qv CVAT But in fact when we consider the origin ofthe internal energy in the kinetic theory ofgases we realizet at UnRAT CVAT and therefore cV gnR and cw R 9 12008 The heat capacity at constant pressure For a constant pressure step we saw in the last lecture that 7 qv PAV By analogy with the constant volume process F and therefore 09M CVAT PAV CPAT CVAT nRAT CF CV nR so that c gnR and 0 R Definition ofthe enthalpy Based on these considerations we can see that there is a new state function the energy at constant pressure This state function is known as the enthalpy H The enthalpy change is AH qF CFAT and can rewrite the relationship from the previous slide as AH AU PAV We have also de ned the relationship between the internal energy and the enthalpy The PAV term represents the work of expansion or compression done against the atmosphere during a chemical reaction We use enthalpy instead of internal energy under normal conditions because it includes this work automatically Heat Capacity for a Diatomic Molecule For a diatomic molecule there is contribution from rotations as well as translations This means that as heat is added to the system the rotational levels can be populated in addition to an increase in molecular speed The kinetic theor of gases considers only the speed An approximate rule is that we obtain a contribution to the heat capacity CV of 12nR for each degree of 39eedom We saw that for a monatomic gas the heat capacity was V 2n A diatomic gas has two rotational degrees of 39eedom and so the heat capacity is approximately CV 52nR What does this say about CF Well the relationship between CP and CV holds for all gases so CP 72nR for a diatomic ideal gas Question What is the internal energy of a monatomic gas A U 2R 3 B U jRT i C U 2nR i D U 2nRT Question lfthe heat capacity of a diatomic gas is 52nR what is the internal energy of a diatomic ideal gas u R B u gnRT c u gnR D u gnRT Adiabatic Processes lfa process occurs in an isolated system then no heat can transferred between the system and surroundings the heat transferred q is zero ie q 0 Therefor AU w We call such processes adiabatic cools adiabatically Expressed in differential format 6 chT PdV Here we have used the de nitions of the internal energy in terms ofthe heat capacity and the work in pressurevolume terms be In this case 51 Actually this special case is ofgreat importance For example column of air rises in the atmosphere it expands and 9 12008 Adiabatic Processes Using the form on the previous page we can derive h dU 6w ch7 PdV chT Tdv dT cVT R V udT JWdV c 7 R i J T V V T2 V2 Cvlnf annV t e relationship between the volume change and temperature Adiabatic Processes Using the form on the previous page we can derive the relationship between the volume change and temperature L lnT1 CVanZ 23 T2 for an ideal monatomic gas 2 25 T2 7mg for an ideal diatomic gas 2 This expression is great practical value since you can predict the temperature of air as it rises This phenomenon leads to rain over mountains and cooling that affects ecosystems at high elevation Qu estIo n Which statement is true for an adiabatic compression B AU q w C AU w D AU q w Question Which statement is true for an adiabatic expansion A The temperature increases as gas expands B The temperature decreases as gas expands C The temperature remains constant D The work done is equal to the heat transferred Path Functions We have seen that work and heat are path functions The magnitude of the work and heat depends not just on the nal values ofthe T and P but also on the path taken We can summarize the paths and their implications in the table below IE m AT o w Constant V Constant P ma w PAV p CAT Adiabatic EE AU w State Functions At present we have introduced two state functions Internal Energy AU halpy A State functions do not depend on the path only on the value ofthe variables We can make the analogy with elevation The potential energy at an elevation h which we call Vh does not depend on how we got to that elevation If we compare Why in Raleigh to Vhz on Mt Mitchell the difference Vhz Why is the same regardless ofwhether we drive 9 12008 Question Enthalpy is a state function therefore it depends only on A the temperature and pressure B the elevation C the work of expansion in a reaction D the volume
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