Thermochemistry Definitions
How many Joules are in 1 L·atm?
101.3 Joules
Constant-pressure calorimetry
- Coffee-cup calorimetry: measures ΔHrxn and qsoln, which is the heat absorbed by or lost from the solution (which is acting as the surroundings): qsoln = msoln x Cs,soln x ΔT. - Assuming no heat is lost to the calorimeter, qrxn = -qsoln. - Since the reaction occurs under constant pressure, qrxn = qp = ΔHrxn, which is the heat of reaction of the specific amount of reactants that reacted. - If a chemical equation is reversed, then ΔHrxn changes signs. - Hess's Law: the change in enthalpy for a stepwise process is the sum of the enthalpy changes of the steps.
Pressure-volume work
- Energy transfer can occur via work (w) or heat (q). - Pressure-volume work occurs when the force is caused by a volume change against an external pressure: w = -PΔV, measured in L x atm. 1 L x atm = 101.3 J. - ΔV = Final volume - initial volume
Energy, work, and heat overview
- Energy: the capacity to do work; something an object has. - Work: the result of a force acting through a distance; way an object exchanges energy. - Heat: the flow of energy caused by a temperature change; way an object exchanges energy. - Thermal energy: the energy associated with the temperature of an object; a type of kinetic energy; always flows from high temp to low temp. - Kinetic energy: 0.5 x m x v^2, where m is measured in kg and v in m/s. - The SI unit of energy is J (kg x m^2/s^2). - Calories: the amount of energy needed to raise the temperature of 1 g of water by 1 degree Celsius. 1 cal = 4.184 J.
Enthalpy (H)
- Enthalpy (H): the sum of a system's internal energy and the product of its pressure and volume: H = E + PV. - Change in enthalpy (ΔH): ΔH = ΔE + PΔV. - Under constant pressure, ΔH = qp, where qp is the heat at constant pressure. - Enthalpy, like ΔE, is a state function. ΔE is a measure of all the energy (heat and work) a system exchanges with its surroundings, while ΔH is a measure of only the heat exchanged under conditions of constant pressure. For reactions that don't exchange much work wit the surroundings (don't cause a large change in reaction volume), ΔH and ΔE are nearly identical in value. But for reactions that produce or consume large amounts of gas (have large volume changes), ΔE and ΔH have slightly different values. - Positive ΔH = heat flows into the system; endothermic reaction; absorbs heat from the surroundings. - Negative ΔH = heat flows into the system; exothermic reaction; gives off heat to the surroundings.
Additional information
- Generally, the size of a temperature increase is proportional to the amount of heat released by an exothermic reaction. - ΔH is the amount of heat absorbed or evolved in the reaction under conditions of constant pressure. - Kinetic energy is the total thermal energy of the system, while internal energy is the sum of system's potential and kinetic energy. - In exothermic reactions, potential energy is converted to thermal energy. In an endothermic reaction, the products have higher potential energy than the reactants and absorb thermal energy. - Bomb calorimetry: measures ΔE, occurs at constant volume; energy change that occurs all takes the form of heat (q). - Coffee-cup calorimetry: measures ΔH, occurs at constant pressure; amount of energy released as heat may be smaller because some of the energy may be used to do work (w).
Heat and work
- Heat: the exchange of thermal energy between a system and its surroundings caused by a temperature difference; transfer stops when a system and its surroundings reach the same temperature (thermal equilibrium). - Temperature: a measure of thermal energy within a sample of matter. - When a system absorbs heat, its temperature changes by ΔT. The heat absorbed by a system and its corresponding change are directly proportional, and the constant of proportionality between q and ΔT is the system's heat capacity (C). - Heat capacity (C): a measure of a system's ability to absorb thermal energy without undergoing a large change in temperature; the higher the heat capacity, the smaller the change in temperature for a give amount of absorbed heat. Also defined as the quantity of heat needed to change a system's temperature by 1 degree Celsius. C = q/ΔT. Measured in J/degree Celsius. Is an extensive property, so it depends on the amount of substance being heated. - q = C x ΔT.
Internal energy
- Internal energy is the sum of the kinetic and potential energies of all the particles that make up a system; it is a state function. - State function: value depends only on the state of the system, not on how the system arrived at that state; specified by temperature, pressure, concentration, and physical state. The value of a change in a state function is always the difference between the final and initial values; it's irrelevant of the path taken. - Internal energy (ΔE) = Efinal - Einitial, or ΔE = Eproducts - Ereactants. - ΔEsys = -ΔEsurr - If the reactants have a higher internal energy than the products, then ΔEsys is negative and energy flows out of the system into the surroundings. If the reactants have a lower internal energy than the products, then ΔEsys is positive and energy flows into the system form the surroundings.
Specific heat capacity (Cs) and molar heat capacity
- Specific heat capacity (Cs): the measure of the intrinsic capacity of a substance to absorb heat; the amount of heat needed to raise 1 g of a substance by 1 degree Celsius; measured in J/g x degree Celsius. Is an intensive property, so depends on type of material, not how much of it. - Molar heat capacity (or heat capacity): the amount of heat needed to raise 1 mol of the substance by 1 degree Celsius; measured in J/mol x degree Celsius; intensive property.
System and surroundings
- System: the particles/objects under observation. - Surroundings: everything with which the system can exchange energy. - If a system loses energy, the surroundings gain the exact same amount of energy, and vice versa.
Enthalpies of reaction
- The standard for enthalpy has 3 parts: (1) Standard state. For a gas, the pure gas has a pressure of exactly 1 atm. For a liquid or solid the standard state is the pure substance in its most stable form at a pressure of 1 atm and at the temperature of interest (often 25 degree Celsius). For a substance in solution the standard state is a concentration of exactly 1 M. (2) Standard enthalpy change (ΔH°): the change in enthalpy for a process when all reactants and products are in their standard states; the degree sign indicates standard states. (3) Standard enthalpy of formation (ΔH°f): For a pure compound the change in enthalpy when 1 mole of the compound forms from its constituent elements in their standard states. Fro a prunes element in its standard state, ΔH°f = 0. Most compounds have a negative ΔH°f. ΔH°f is measured in kJ/mol.
Calorimetry
- When a reaction is carried out at a constant volume, the heat evolved (or given off) is called the heat at constant volume (qv) and is equal to ΔErxn: ΔErxn = q (because w = 0 at constant volume) - Calorimetry: used to measure the thermal energy exchanged between the reaction (system) and the surroundings; the magnitude of the temperature change is dependent on the magnitude of ΔE for the reaction and on the heat capacity of the surroundings. - Bomb calorimetry: equipment used to measure ΔE for combustion reactions; has constant volume. qcal = Ccal x ΔT, where Ccal (measured in kJ/degree Celsius) is the heat capacity of the entire calorimeter assembly. If no heat escapes the assembly, then the amount of heat gained by the calorimeter is equal and opposite to that released by the reaction: qcal = -qrxn. - qrxn = qv = ΔErxn (measured in kJ). - Under these conditions (sealed container, constant volume), energy is only evolved as heat.
Signs
- q (heat) positive = system gains thermal energy - q (heat) negative = system loses thermal energy - w (work) positive = work is done on the system - w (work) negative = work is done by the system - ΔE positive = energy flows into the system - ΔE negative = energy flows out of the system
Heat equation
- q = m x Cs x ΔT - q is equal to the heat (J), m is equal to the mass (g), Cs is equal to the specific heat capacity (J/g x degree Celsius) x temperature change (degree Celsius) - qsys = -qsurr, therefore msys x Cs,sys x ΔTsys = -msurr x Cs,surr x ΔTsurr
Internal energy equation
- ΔE = q (heat) + w (work) - ΔE depends only on the system's initial and final kinetic energy (it's a state function), while q and w depend on the details of a system's journey.
Important equations
- ΔE(J) = q(J) + w(J) - q (J) = m(g) + Cs(J/g x degree Celsius) + ΔT (degree Celsius) - w(J) = -P(atm)ΔV(L x atm) 101.3 J = 1 L x atm - ΔErxn = qv - qcal = Ccal x ΔT qcal = -qrxn qrxn = qv = ΔErxn - ΔH = qp - qsoln = msoln x Cs,soln x ΔT qrxn = -qsoln qrxn = qp = ΔHrxn -
Enthalpy of reaction
- ΔHrxn is the enthalpy change for a reaction (also called enthalpy of reaction or heat of reaction), and it's an extensive property, so the amount of heat generated or absorbed during a chemical reaction depends on the amounts of reactants. The magnitude of ΔHrxn is for the stoichiometric amounts of reactants and products for the reaction has written. Measured in kJ.
heat capacity (C)
A measure of the system's ability to absorb thermal energy without undergoing a large change in temperature; Specifically, it's the quantity of heat required to change its temperature by 1 °C.
Standard State for a gas, liquid, solid, and substance in solution
Gas: At a pressure of exactly 1 atm. Liquid or Solid: At a pressure of 1 atm and at 25 °C. Substance in Solution: A concentration of exactly 1 M.
Hess's Law
If a chemical equation can be expressed as the sum of a series of steps, then ΔH for the overall equation is the sum of the heats of reaction for each step.
kinetic energy equation
KE = 1/2m(v^2)mass is in kgvelocity is in m/s
specific heat capacity (Cs)
The measure of the intrinsic capacity of a substance to absorb heat; Specifically, the amount of heat required to raise the temperature of 1 gram of the substance by 1 °C.
thermal equilibrium
The point at which there is no additional net transfer of heat between a system and its surroundings.
enthalpy (H)
The sum of the internal energy of a system and the product of its pressure and volume; the energy associated with the breaking and forming of bonds in a chemical reaction.
The first law of thermodynamics
The total energy of the universe is constant. In other words, since energy is neither created nor destroyed, and since the universe does not exchange energy with anything else, its energy content does not change.
pressure-volume work
The work that occurs when a volume change takes place against an external pressure.
If a chemical reaction is multiplied by a number, what happens to the ΔH of that reaction?
The ΔH gets multiplied by that same number. A + 2B → C ΔH1 2A + 4B → 2C ΔH2 = (2 x ΔH1)
Standard Enthalpy Change for a Reaction ΔH°rxn
To calculate ΔH°rxn, subtract the [enthalpies of formation of the reactants multiplied by their stoichiometric coefficients] from the [enthalpies of formation of the products multiplied by their stoichiometric coefficients].
law of conservation of energy
energy can be neither created nor destroyed; it can be transferred from one object to another, and it can assume different forms
relationship between q of water and q of metal
m(water) x Cs(water) x ΔT(water) = -m(met) x Cs(met) x ΔT(met)
Equation for q using specific heat
q = m x Cs x ΔT q: Heat in Joules m: Mass in grams Cs: Specific Heat Capacity in J/g°C T: Temperature change in °C
Bomb Calorimeter Equation
q(cal)=C(cal)×ΔT q: heat in Joules C(cal): heat capacity of the calorimeter ΔT: the temperature change
molar heat capacity
the amount of heat required to raise the temperature of 1 mole of a substance by 1 °C.
thermochemistry
the study of the relationships between chemistry and energy
internal energy (E)
the sum of the kinetic and potential energies of all of the particles that compose the system.
q (heat) is positive when
the system gains thermal energy
q (heat) is negative when
the system loses thermal energy
pressure-volume work equation
w = -P(ext) ΔVP: Pressure in atm V: Volume in liters
w (work) is negative when
work is done BY the system
w (work) is positive when
work is done ON the system
The formula describing energy in terms of heat and work
ΔE = q + w
When energy flows from the system to the surroundings, describe ΔE of the system and the surroundings
ΔE of the system is negative,ΔE of the surroundings is positive
When energy flows from the surroundings to the system, describe ΔE of the system and the surroundings
ΔE of the system is positive,ΔE of the surroundings is negative
ΔE
ΔE= (E products) − (E reactants)
how is enthalpy related to heat?
ΔH = ΔE + PΔV= (q + w) + (-w) **both of those relationships are defined earlier:E = q + ww = -PΔV ** Therefore,ΔH = q + w - wΔH = q
