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If I conduct a reaction say,

$$\ce{CaO(s) + H2O(l) \rightarrow Ca(OH)2 (aq)}$$

let us say , I want to measure the energy generated from the reaction.Will this energy I calculate equal the change in enthalpy of the reaction because it is exothermic or will it be equal to the change in Gibbs free energy because it is the maximum non-expansive work that can be obtained.

Also, suggest a method to calculate the energy say using a coffee-cup calorimeter, etc .

Conditions for the reaction: T = 298 K Case 1:constant volume Case 2:constant pressure

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  1. If you measure the heat absorbed or released by the process at constant volume, you're measuring $\Delta U$ (the change in internal energy). You'll need to measure the temperature change of the reaction when it's running in a rigid, sealed container---or, better, compute it from $\Delta H$ measured as follows.

  2. If you measure the heat absorbed or released by the process at constant pressure, you're measuring $\Delta H$ (the change in enthalpy). You can measure the temperature change of the reaction when it's running in a container open to the atmosphere, e. g. a coffee cup calorimeter.

  3. If you're measuring the nonexpansion work reversibly and at constant temperature and pressure, you're measuring $\Delta G$ (the change in Gibbs free energy). You can do your measurements in a container open to the atmosphere immersed in a constant temperature bath. The system must be closed in the sense that you aren't losing any reactants or products.

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Case 2: Gibb's free energy is used to determine if a reaction is spontaneous or not. If you want to determine how much energy is released, you look at the change in enthalpy. To determine the change in enthalpy, perform the reaction in a calorimeter and graph out the temperatures at different points in time. Once the reaction has settled let it cool for a bit so that you have a nice linear slope in your data. Use this slope to extrapolate backwards to the initial time of reaction to get the most precise result (this takes into account the heat loss over time). Alternatively, just take the peak temperature of your reaction as an approximation. That is your value of Q. Find a suitable equation off of this site and sub in your value.

Case 1: This is a bit trickier, but really only requires a slight change to the experiment, I leave it up to you to figure it out.

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