HEAT CAPACITY CALCULATIONSHEAT CAPACITY CALCULATIONSCALCULATION OF PV WORKCALCULATION OF PV WORKCALCULATION OF PV WORKCALCULATION OF PV WORKCALCULATION OF PV WORKCALORIMETRYCALORIMETRYCONSTANT VOLUME PROCESSESCONSTANT PRESSURE PROCESSESCALORIMETRYTHERMOCHEMISTRYTHERMOCHEMISTRYTHERMOCHEMISTRYTHE STANDARD STATETHE STANDARD STATETHE STANDARD STATETHERMOCHEMICAL CALCULATIONSTHERMOCHEMICAL CALCULATIONSTHERMOCHEMICAL CALCULATIONSTHERMOCHEMICAL CALCULATIONSTHERMOCHEMICAL CALCULATIONSTHERMOCHEMICAL CALCULATIONSTHERMOCHEMICAL CALCULATIONSTHERMOCHEMICAL CALCULATIONSTHERMOCHEMICAL CALCULATIONSTHERMOCHEMICAL CALCULATIONSTHERMOCHEMISTRYTHERMOCHEMISTRYTHERMOCHEMISTRYTHERMOCHEMISTRYTHERMOCHEMISTRYTHERMOCHEMISTRY1HEAT CAPACITY CALCULATIONSTHERE ARE ABOUT 1OO MILLION SUCH WATER HEATERS IN THE US. IF ALL THE ENERGY IN ALL THOSE WATER HEATERS WERE TRANSFERRED ASHEAT TO THE EARTH ESTIMATE HOW MUCH THE TEMPERATURE RISE OF THE EARTH WOULD BE. NOTE: TABLE 10-1 PROVIDES ALL THE INFORMA-TION YOU NEED EXCEPT FOR THE MASS OF THEEARTH, WHICH IS 6 X 1024kg. GChem 1404 • JJValentini2HEAT CAPACITY CALCULATIONSTHE ANSWERWE HAVE q = 6.3 x 106cal PER WATER HEATERFOR 108WATER HEATERS q = 6.3 x 1014cal∆TEARTH= q/(mEARTHx cs,EARTH)= (6.3 x 1014cal)/[(6 X 1027g)(≈0. 1 cal K-1g-1)]≈ 1 x 10-12KESTIMATE FROM TABLE 10-1GChem 1404 • JJValentini3CALCULATION OF PV WORKwwaa--bb--cc= w= wbb--cc= = --PPbcbcx (Vx (Vcc--VVbb))= = --9 kPa x (4 9 kPa x (4 --1) m1) m33= = --27 kJ27 kJPext= 29 kPaPext= 9 kPawwaa--dd--cc= w= waa--dd= = --PPadadx (Vx (Vdd--VVaa))= = --29 kPa x (4 29 kPa x (4 --1) m1) m33= = --87 kJ87 kJGChem 1404 • JJValentini4CALCULATION OF PV WORKCALCULATION OF PV WORKIN THE EXAMPLE WE JUST CONSIDERED CALCULATE THE HEAT q FOR EACH STEP FOR A SYSTEM IN WHICH OXYGEN IS THE GAS, BEHAVING IDEALLY.GChem 1404 • JJValentini5CALCULATION OF PV WORKTHE ANSWERTHE SYSTEM HAS NOT BEEN DEFINEDSUFFICIENTLY TO DO THIS CALCULATION, SINCE WE NEED TO SPECIFY THREE VARIABLES TO DEFINE THE STATE OF THE SYSTEM AND HERE WE HAVE SPECIFIED ONLY TWO. BUT, THE FIRST LAW ALLOWSYOU TO SAY THAT THE SUM OF THE WORK DONE AND THE HEAT ABSORBED MUST BE THE SAME FOR EACH PATH, SINCE THE INITIAL AND FINAL STATES OF THE SYSTEM ARE THE SAME FOR ALL THREE PATHS.GChem 1404 • JJValentini6CALCULATION OF PV WORKCALCULATION OF PV WORKYOUR 7-YEAR-OLD NEPHEW IS HAVING A BIRTHDAY PARTY. YOU ARE ASKED TO BLOW UP 75 BALLOONS. EACH BALLOON IS NO BIGGER THAN YOUR THUMB WHEN YOU START, BUT IS A SPHERE OF DIAMETER 25 CM WHEN INFLATED. HOW MUCH WORK WILL YOU PERFORM IN DOING THIS IF YOU ASSUME THAT THE BALLOON IS PERFECTLY ELASTIC?GChem 1404 • JJValentini7CALCULATION OF PV WORKTHE ANSWERWHAT IS THE SYSTEM HERE? YOU ARE. SO, THE WORK, w, SHOULD BE NEGATIVE. NOW w = - P x ∆V AS ALWAYS.WE HAVE P = 1.01 x 105Pa AND FOR EACH BALLOON ∆V = 4/3 π r3= 8.2 x 10-3m3.THE TOTAL WORK FOR 75 BALLOONS IS:w = - (1.01 x 105Pa) x (8.2 x 10-3m3) X 75= - 6.2 X 104J.GChem 1404 • JJValentini8CALORIMETRYTHE CALORIMETERWHAT DOES THE CALORIMETERCALORIMETERMEASURE? ∆THOW IS THIS TEMPERATURE CHANGE RELATED TO q?q = mcalorimeterx cs, calorimeterx ∆TGChem 1404 • JJValentini9CALORIMETRYWHAT DOES q TELL US? q IS NOT A STATE FUNCTION.IT IS PATH DEPENDENT. WE MUST CONNECT q TO A STATE FUNCTIONSTATE FUNCTION. THE FIRST LAW (∆E = q + w∆E = q + w) PROVIDES THECONNECTION.GChem 1404 • JJValentini10CONSTANT VOLUME PROCESSESWHAT DOES q TELL US WHEN V IS CONSTANT?THE FIRST LAW SAYS: ∆E = q + w∆E = q + w.WHEN THE ONLY WORK POSSIBLE IS PV WORKAND V IS CONSTANT WE HAVE w = 0.FOR ANY CONSTANTFOR ANY CONSTANT--VOLUME PROCESS UNDER VOLUME PROCESS UNDER CONDITIONS FOR WHICH ONLY PV WORK ISCONDITIONS FOR WHICH ONLY PV WORK ISPOSSIBLE ∆E = q.POSSIBLE ∆E = q.GChem 1404 • JJValentini11CONSTANT PRESSURE PROCESSESWHAT DOES q TELL US WHEN P IS CONSTANT?INTRODUCE A NEW STATE FUNCTION:H = E + PV H = E + PV SO∆H = ∆E + ∆(PV)∆H = ∆E + ∆(PV).WHEN P IS CONSTANT ∆H = ∆E + (P x ∆V).WHEN ONLY PV WORK IS POSSIBLE ∆E = q + w = q - (P x ∆V), SO THEN ∆H = q - (P X ∆V) + (P x ∆V) = q.FOR ANY CONSTANTFOR ANY CONSTANT--PRESSURE PROCESS UNDER PRESSURE PROCESS UNDER CONDITIONS FOR WHICH ONLY PV WORK ISCONDITIONS FOR WHICH ONLY PV WORK ISPOSSIBLE ∆H = q.POSSIBLE ∆H = q.GChem 1404 • JJValentini12CALORIMETRYCALORIMETRY IS THE EXPERIMENTAL BASISOF THERMOCHEMISTRYq CAN BE RELATED TO A STATE FUNCTIONFOR BOTH CONSTANT-VOLUME AND CONSTANT-PRESSURE CONDITIONS.CONSTANTCONSTANT--VOLUME PROCESSES TAKE PLACE VOLUME PROCESSES TAKE PLACE IN A RIDID, CLOSED CONTAINER AND ∆E = q.IN A RIDID, CLOSED CONTAINER AND ∆E = q.CONSTANTCONSTANT--PRESSURE PROCESSES TAKE PLACE PRESSURE PROCESSES TAKE PLACE IN AN OPEN CONTAINER AND ∆H = q.IN AN OPEN CONTAINER AND ∆H = q.GChem 1404 • JJValentini13THERMOCHEMISTRYCHEMICAL AND PHYSICAL CHANGE EVERY CHEMICALTRANSFORMATION IS CHARACTERIZED BY PRECISE VALUES OF ∆E AND ∆H. EVERY PHYSICALTRANSFORMATION IS CHARACTERIZED BY PRECISE VALUES OF ∆E AND ∆H.GChem 1404 • JJValentini14THERMOCHEMISTRYCOMPUTING ∆H AND ∆E FOR ANY REACTION1. WRITE A BALANCED CHEMICAL REACTION, KEEPING TRACK OF PHYSICAL STATE.2. RE-WRITE THIS REACTION AS A SUM OF STEPS TO MAKE USE OF AVAILABLE THERMOCHEMICAL DATA FOR ∆H OR ∆E.3. ADD THE ∆H OR ∆E FOR ALL STEPS TO COMPUTE ∆H OR ∆E FOR THE REACTION.GChem 1404 • JJValentini15THERMOCHEMISTRYCOMPUTING ∆H AND ∆E FOR ANY REACTIONTHE MOST COMMONLY AVAILABLE THERMOCHEMICAL DATA ARE:STANDARD ENTHALPY OF FORMATIONSTANDARD ENTHALPY OF FORMATIONBOND ENTHALPYBOND ENTHALPYSTANDARD ENTHALPY OF PHASE CHANGESTANDARD ENTHALPY OF PHASE CHANGEGChem 1404 • JJValentini16THE STANDARD STATETHERMOCHEMICAL CALCULATIONSARE BASED ON THE STANDARD STATEENTHALPIES OF SUBSTANCES DEPEND ON TEMPERATURE, PRESSURE, AND PHYSICAL STATE.THE STANDARD STATE IS USED TO PROVIDE ATHE STANDARD STATE IS USED TO PROVIDE ACONSISTENT BASIS FOR ∆H CALCULATIONS.CONSISTENT BASIS FOR ∆H CALCULATIONS.GChem 1404 • JJValentini17THE STANDARD STATETHERMOCHEMICAL CALCULATIONSARE BASED ON THE STANDARD STATEFOR SOLIDS AND LIQUIDS THE STANDARD FOR SOLIDS AND LIQUIDS THE STANDARD STATE IS THE STATE OF THE PURE SOLID OR STATE IS THE STATE OF THE PURE SOLID OR LIQUID UNDER A PRESSURE OF 1 ATMOSPHERE LIQUID UNDER A PRESSURE OF 1 ATMOSPHERE AT A STATED TEMPERATURE.AT A STATED TEMPERATURE.FOR GASES THE STANDARD STATE IS THE FOR GASES THE STANDARD STATE IS THE GASEOUS PHASE UNDER A PRESSURE OF GASEOUS PHASE UNDER A PRESSURE