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Lecture 10 Conservation of Energy – Enthalpy and Heat Capacity

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Lecture 10 Conservation of Energy – Enthalpy and Heat Capacity Lecture 9 Conservation of Energy – Enthalpy and Heat Capacity Reading: Lecture 9, today: Chapter 6, section A Lecture 10, Wednesday: Chapter 6, section B MCB65 2/12/15 1 Energy in biological systems Example of a reaction releasing energy: Example of a reaction performing work: Heat Work Thermodynamics helps us understand and describe these types of biological processes. MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 2 Thermodynamics In this course, we will discuss thermodynamics as it applies to biological molecules We will first cover concepts of classical thermodynamics, which cover macroscopic properties (temperature, volume, pressure, etc) We will then bring in concepts of statistical mechanics, which will enable us to relate the macroscopic properties to the microscopic view of biological molecules in action MCB65 2/12/15 3 Classical Thermodynamics DG = DH – TDS What is thermodynamics? Science of heat and temperature Laws governing the conversion of thermal energy into mechanical, electrical or other forms of energy Concerns bulk properties like pressure, temperature, volume Not based on a specific description of molecules Helps us predict the direction and extent of chemical and biological reactions (but not the rate) MCB65 2/12/15 4 Math – make sure you understand We’re entering the more math-intensive part of the course Work it through on your own as you do the readings and review the lecture If there are things that you don’t know or don’t understand, use the resources available to you Ask in class, section, office hours Review your math textbooks No need to get stuck on a concept because the math used doesn’t make sense to you! MCB65 2/12/15 5 Laws of Thermodynamics The first law of thermodynamics, which mandates conservation of energy. The second law of thermodynamics, which states that the entropy of the universe always increases. MCB65 2/12/15 6 Today’s goals Develop elements of the First law of thermodynamics – conservation of energy Delineate the system under observation Understand the concepts of heat and work Define Enthalpy, H MCB65 2/12/15 7 Defining the field of observation – the closed system is most useful in biology Closed system most commonly used to study chemical reactions Closed MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 8 Defining the field of observation Two other types of systems are more extreme: Open Isolated Three different kinds of systems: open, isolated, or closed MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 9 Change in energy of a system . U = Energy of the system ΔU = U(final) – U(initial) Negative ΔU means an exothermic reaction Positive ΔU means endothermic reaction How do we measure these changes in energy? MCB65 2/12/15 10 Calorimetry Calorimetry is a method to study energetic changes, commonly used in biochemistry Measures the heat released or taken up by a chemical reaction under study Isothermal titration calorimetry (ITC) How much heat to keep the temperature constant? Differential scanning calorimetry (DSC) How much heat to increase the temperature by a given amount? MCB65 2/12/15 11 Isothermal Titration Calorimetry Uses a closed system The instrument has a feedback loop that maintains constant temperature in the system (both reference and test cells). Records how much more or less energy is required each time more reagent is added from the syringe. MCB65 Figure adapted from The Molecules of Life (© Garland Science 2008) 2/12/15 12 ITC to measure binding of NC protein to RNA NC protein needle buffer dropwise injection RNA Packaging sequence from MLV virus binding to the nucleocapsid (NC) MCB65 D’Souza and Summers (2004) Nature 2/12/15 13 ITC – an example Binding reaction is exothermic and maintaining temperature requires less energy during an injection Packaging sequence from MLV virus binding to the nucleocapsid (NC) MCB65 D’souza and Summers (2004) Nature 2/12/15 15 Extensive and intensive properties Doubling the system size Doubles the energy released Energy is an extensive property of a system Depends on its size Amount of material is often Volume? specified for extensive Temperature? properties, e.g. kJ mol-1 Density? MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 16 Energy transfer as heat or work Heat Work Energy transferred as work is “stored” and can be brought back into the system Mechanical Chemical Electrical … MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 17 Example of a chemical reaction producing work Figure from The Molecules of Life (© Garland Science 2008) Expansion work – energy could be returned to the system by pushing the piston back down MCB65 2/12/15 18 First Law of Thermodynamics Law of conservation of energy dU = dUsystem + dUsurroundings = 0 dU is an infinitesimally small change in energy dUsystem = -dUsurroundings A change in energy in the system should always be matched by a change in energy in the surroundings MCB65 2/12/15 19 Change in energy through heat and work dUsystem can come about through heat and/or work q denotes heat and w denotes work Change in energy of the system can be written out as: dUsystem = dq + dw Increment of heat = dq Increment of work = dw MCB65 2/12/15 20 Sign conventions Changes that increase the Usystem have a positive sign negative sign if they decrease the Usystem dUsystem = dq + dw “positive in, dw will have negative out” negative value Here, heat transferred to the system increases its energy, therefore dq will be positive Work done by the system to move the piston up decreases its energy, therefore dw will be negative MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 21 Reactions under constant volume have no expansion work dUsystem = dq + dw If there is no change in volume, then dw = 0 and dUsystem = dq MCB65 2/12/15 22 Biological reactions - under constant pressure dUsystem = dq + dw If a reaction produces a gas, the gas will cause expansion work of magnitude PEXTdV: negative because the dUsystem = dq − PEXTdV work is done by the system The heat transferred to the system will be: dq = dUsystem + PEXTdV When the volume changes in reactions at constant pressure, the heat transferred to the system is NOT equal to the change in energy MCB65 2/12/15 23 Defining Enthalpy Hsystem = Usystem + PVsystem H = Enthalpy Enthalpy is the total energy of a system, the sum of its internal energy (U) and the energy required to make room for it in its surroundings (PV) Change in enthalpy is then: dHsystem = dUsystem + PdVsystem + VsystemdP For biological reactions, which happen under constant pressure, VsystemdP = 0: dHsystem = dUsystem + PdVsystem And therefore dHsystem = dq (at constant pressure) MCB65 2/12/15 24 Enthalpy is useful in biology Under constant pressure: dHsystem = dUsystem + PdVsystem Most biological reactions do not cause a change in volume and therefore PdVsystem = 0 and dHsystem = dUsystem That is why enthalpy is such an important concept – change in enthalpy often reflects change in energy, and is easy to measure E.g. protein + ligand ↔ protein-ligand complex By measuring dq (e.g. through ITC), we can determine the difference in energy between bound and unbound MCB65 2/12/15 25 State variables State variables are properties of the system that are independent of the history of the system U = Energy P = Pressure V = Volume H = Enthalpy q = Heat “path” or “process” w = Work functions MCB65 2/12/15 27 Energy vs. direction of spontaneous change But those are single, macroscopic objects. What about molecular reactions and populations of molecules? MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 28 Energy vs. direction of spontaneous change Setting up the experiment: Reminder: Ideal Gas Law PV = nRT Reminder: An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The idea of an ideal gas is often used in thermodynamics to develop concepts with minimal real life complications MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 29 Adiabatic - In the absence of heat exchange Starting from dU = dq + dw In this case, dq = 0 therefore dU = dw dw is negative because the gas does work on the piston For an ideal gas U = kinetic energy = (3/2)nRT (Box 6.3) dU = (3/2)nRdT therefore dU and dT are negative and temperature decreases and the kinetic energy of the gas also decreases MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 30 Isothermal expansion Here dU = dq + dw = 0 because T = constant Ideal gas: dU = (3/2)nRdT In this case, dq = -dw Even though dU = 0, there is a change in the system. What is driving this change? MCB65 Figure from The Molecules of Life (© Garland Science 2008) 2/12/15 31 Some key concepts First law of thermodynamics: energy (U) is conserved Heat transferred to the system (dq) has a (+) value Work done by the system (dw) has a (-) value Change in enthalpy (dH) = change in heat (dq) at constant pressure Extensive properties depend on the size of the observed system whereas intensive properties do not State variables depend only on the current state of the system, not its history It’s important to fully delineate the system under observation MCB65 2/12/15 32.
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