![]() ![]() This equation only works at constant pressure since enthalpy equals heat only at constant pressure. Since a change in entropy (and enthalpy) for a system creates an accompanying change in entropy for the surroundings we can use the formula: ΔSsur = -ΔHsyt/T, where ΔHsyt is the change in enthalpy for the system, and T is temperature in kelvins. The change in enthalpy for a reaction we can determine experimentally using calorimetry. But we can relate the change in the surrounding’s entropy to another thermodynamic quantity we know well, the enthalpy change of the system. Measuring the change in entropy for a system is relatively easy, but measuring the change in entropy for the surroundings is less easy to do directly. Using this formula we can judge if a reaction is spontaneous or not based on whether its change in entropy, and the surrounding accompanying change in entropy, facilitates a positive or negative change in entropy for the universe (following the second law). Together we get a formula for the overall change of entropy based on the system and surroundings: ΔSuniv = ΔSsyt + ΔSsur, where ΔSsyt is the change in the entropy of the system and ΔSsur is the change in the entropy of the surroundings. And the entropy of the surroundings (everything but the system itself) also being influenced by the entropy of the system. So we can imagine a reaction as a system whose entropy we care about. Usually when we do chemistry though we’re concerned not so much directly with the entropy of the universe, but rather the entropy change which accompanies a chemical reaction. This is why gas particles spread out in a container instead of concentrate themselves into a small area. The law and the formula essentially state that the universe naturally prefers greater levels of entropy and allows any process which causes a positive increase, but prohibits any process which causes a negative increase. A spontaneous process is one which happens naturally without the need of outside energy or work to help it along. So W is measuring how many energetically equivalent microstates a system can organize its energy into to get the same macrostate (or the system as we can observe it on a human scale).Īnother formula uses the second law of thermodynamics: ΔSuniv > 0, which put into words states that any spontaneous process increases the entropy of the universe (creates a positive change). A microstate is a particular way to order energy. Boltzmann’s formula uses a more mathematical approach to entropy by using W. The unit for entropy is the same as Boltzmann’s constant which means that entropy can also be understood as how many energy can be dispersed at a certain temperature since entropy is temperature dependent. ![]() One equation is Boltzmann’s equation: S = k*ln(W), where S is entropy (the usual variable for entropy), k is Boltzmann’s constant which is equal to the gas constant divided by Avogadro’s number which is approximately equal to 1.38 x 10^(-23) J/K, and W is the number of microstates which is a unitless quantity. There are several because entropy can be explained and used in a variety of ways. Since entropy is primarily dealing with energy, it’s intrinsically a thermodynamic property (there isn’t a non-thermodynamic entropy).Īs far as a formula for entropy, well there isn’t just one. Here we further explore the nature of this state function and define it mathematically.First it’s helpful to properly define entropy, which is a measurement of how dispersed matter and energy are in a certain region at a particular temperature. In Chapter 13, we introduced the concept of entropy in relation to solution formation. To help explain why these phenomena proceed spontaneously in only one direction requires an additional state function called entropy (S), a thermodynamic property of all substances that is proportional to their degree of "disorder". Moreover, the molecules of a gas remain evenly distributed throughout the entire volume of a glass bulb and never spontaneously assemble in only one portion of the available volume. For example, after a cube of sugar has dissolved in a glass of water so that the sucrose molecules are uniformly dispersed in a dilute solution, they never spontaneously come back together in solution to form a sugar cube. For a full video: see Thus enthalpy is not the only factor that determines whether a process is spontaneous. When water is placed on a block of wood under the flask, the highly endothermic reaction that takes place in the flask freezes water that has been placed under the beaker, so the flask becomes frozen to the wood. The reaction of barium hydroxide with ammonium thiocyanate is spontaneous but highly endothermic, so water, one product of the reaction, quickly freezes into slush. ![]()
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