Chemical reactions involve energy changes that can make or break bonds. This topic dives into how we measure and predict these changes using tools like Hess's Law and calorimetry.
Understanding energy changes helps us figure out if reactions will happen on their own. We'll explore how temperature and concentration affect whether a reaction is spontaneous or needs a push to get going.
Hess's Law and Enthalpy of Formation
Calculating Heat of Reaction using Hess's Law
- Hess's law states that the enthalpy change of a reaction is independent of the pathway taken from reactants to products, and depends only on the initial and final states of the system
- To calculate the heat of reaction using Hess's law, break down the reaction into a series of steps, each with a known enthalpy change
- Sum these enthalpy changes to give the overall enthalpy change for the reaction
- Example: Calculate the enthalpy change for the reaction $A + B \rightarrow C$ by summing the enthalpy changes of the steps $A \rightarrow D$, $D \rightarrow E$, and $E + B \rightarrow C$
Standard Enthalpy of Formation and Calculating Heat of Reaction
- The standard enthalpy of formation ($\Delta H^\circ_f$) is the enthalpy change that occurs when one mole of a compound is formed from its constituent elements in their standard states at 1 atm pressure and a specified temperature (usually 25°C)
- Calculate the enthalpy change of a reaction using standard enthalpies of formation by subtracting the sum of the standard enthalpies of formation of the reactants from the sum of the standard enthalpies of formation of the products
- Example: For the reaction $2H_2(g) + O_2(g) \rightarrow 2H_2O(l)$, subtract the sum of $\Delta H^\circ_f$ for $H_2(g)$ and $O_2(g)$ from the $\Delta H^\circ_f$ for $H_2O(l)$
Bond Dissociation Energies and Enthalpy Change
Bond Dissociation Energy
- Bond dissociation energy (BDE) is the energy required to break a specific bond in a molecule, forming two radical fragments, with all other bonds remaining intact
- BDE assumes that the energy required to break a bond is independent of the molecule in which it occurs
- BDE also assumes that the energy released when a bond is formed is equal to the energy required to break it
- Example: The BDE of the C-H bond in methane ($CH_4$) is 439 kJ/mol
Predicting Enthalpy Change using Bond Dissociation Energies
- Estimate the enthalpy change of a reaction by calculating the difference between the sum of the BDEs of the bonds broken in the reactants and the sum of the BDEs of the bonds formed in the products
- Example: For the reaction $CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O$, sum the BDEs of the bonds broken in $CH_4$ and $O_2$, then subtract the sum of the BDEs of the bonds formed in $CO_2$ and $H_2O$
Calorimetry and Energy Changes
Calorimetry Concepts
- Calorimetry is the measurement of heat transfer in a chemical reaction or physical process
- A calorimeter is an insulated device used to measure the heat released or absorbed during a chemical reaction or physical change
- The heat capacity of a calorimeter ($C_{cal}$) is the amount of heat required to raise the temperature of the calorimeter by one degree Celsius
- The heat capacity of a substance ($C_s$) is the amount of heat required to raise the temperature of one gram of the substance by one degree Celsius
Calculating Enthalpy Change using Calorimetry
- Calculate the change in enthalpy ($\Delta H$) of a reaction using the equation: $q = m \times C_s \times \Delta T$, where $q$ is the heat energy transferred, $m$ is the mass of the substance, and $\Delta T$ is the change in temperature
- Example: In a calorimeter, 50 g of water is heated from 20°C to 30°C. Given the specific heat capacity of water is 4.18 J/g°C, calculate the heat energy transferred
Spontaneity of Reactions: Temperature vs Concentration
Factors Affecting Spontaneity
- Spontaneity refers to the tendency of a process to occur without external intervention
- The spontaneity of a reaction is determined by the change in Gibbs free energy ($\Delta G$), which is a function of the change in enthalpy ($\Delta H$), the change in entropy ($\Delta S$), and the temperature ($T$) of the system: $\Delta G = \Delta H - T\Delta S$
- A reaction is spontaneous when $\Delta G$ is negative, non-spontaneous when $\Delta G$ is positive, and at equilibrium when $\Delta G$ is zero
Temperature and Concentration Effects on Spontaneity
- Temperature affects spontaneity by influencing the magnitude of the $T\Delta S$ term. At higher temperatures, the $T\Delta S$ term becomes more significant, favoring reactions that increase entropy
- Example: The decomposition of calcium carbonate ($CaCO_3$) to form calcium oxide ($CaO$) and carbon dioxide ($CO_2$) becomes spontaneous at high temperatures due to the increase in entropy
- Concentration affects spontaneity by influencing the entropy of the system. Reactions that proceed from high concentration to low concentration (diffusion) are generally spontaneous, as they result in an increase in entropy
- Example: The diffusion of a drop of ink in water is a spontaneous process driven by the increase in entropy as the ink molecules spread out from a region of high concentration to a region of low concentration