Views: 29

Heat Capacity

Heat capacity is an intrinsic physical property of a substance that measures the amount of heat required to change that substance’s temperature by a given amount. In the International System of Units (SI), heat capacity is expressed in units of joules per kelvin (J∙K−1). Heat capacity is an extensive property, meaning that it is dependent upon the size/mass of the sample. For instance, a sample containing twice the amount of substance as another sample would require twice the amount of heat energy (Q) to achieve the same change in temperature (ΔT) as that required to change the temperature of the first sample.

Molar and Specific Heat Capacities

1. Molar Heat Capacity: Molar heat capacity (Cm) is the amount of heat energy required to change the temperature of one mole of a substance by 1 degree Celsius (or 1 Kelvin). It is calculated by dividing the heat capacity by the number of moles of the substance. The equation for molar heat capacity is:

   Cm = C/n

   where C is the heat capacity and n is the number of moles of the substance.

   Molar heat capacity is also an intensive property, similar to specific heat capacity, but it is expressed on a per-mole basis. It helps to compare the heat capacities of different substances, especially when dealing with chemical reactions or processes involving varying amounts of substances.

1. Specific Heat Capacity: Specific heat capacity (c) is defined as the amount of heat energy required to change the temperature of a unit mass (usually 1 gram or 1 kilogram) of a substance by 1 degree Celsius (or 1 Kelvin). The equation for specific heat capacity is:

   c = Q/(m * ΔT)

   where Q is the heat energy absorbed or released, m is the mass of the substance, and ΔT is the change in temperature.

   Specific heat capacity is an intensive property, meaning it is independent of the amount of substance present. It characterizes the thermal properties of a substance on a per-mass basis. Different substances have different specific heat capacities, and it helps determine how much heat energy is required to raise or lower the temperature of a given mass of a substance.

Heat, Enthalpy, and Temperature

Given the molar heat capacity or the specific heat for a pure substance, it is possible to calculate the amount of heat required to raise/lower that substance’s temperature by a given amount. The following two formulas apply:

               q=mcpΔT          

In these equations, m is the substance’s mass in grams (used when calculating with specific heat), and n is the number of moles of substance (used when calculating with molar heat capacity).

Example

The molar heat capacity of water, CP, is 75.2 Jmol∙K. How much heat is required to raise the temperature of 36 grams of water from 300 to 310 K?

We are given the molar heat capacity of water, so we need to convert the given mass of water to moles:

• 36 grams×1 mol H2O 
•                        18 g                =   2.0 mol H2O

Now we can plug our values into the formula that relates heat and heat capacity:

•                  q= nCPΔT
•                   q= (2.0mol)(75.2Jmol∙K)(10K)
•                    q = 1504 J

Enthalpy Change 

 The total enthalpy of a system cannot be measured directly because the internal energy contains components that are unknown, not easily accessible, or are not of interest in thermodynamics.

In practice, a change in enthalpy is the preferred expression for measurements at constant pressure, because it simplifies the description of energy transfer.

The enthalpy change of a reaction is the amount of heat absorbed or released as the reaction takes place, if it happens at a constant pressure.

The following equation can be used to calculate the enthalpy change:

           ΔH = M × C × -ΔT

Where

 M is the mass or volume of the solution being used to test the energy change, 

C is the Specific Heat Capacity of the solution, (for example the specific heat capacity of water is 4.1855 J g^-1 K^-1),

 ΔT is the change in temperature. The sign of ΔT is reversed to reflect the fact that ΔH represents the enthalpy change of the test substance not the surroundings.

Definition of Enthalpy

The precise definition of enthalpy (H) is the sum of the internal energy (U) plus the product of pressure (P) and volume (V). In symbols, this is:

           H = U + PV

A change in enthalpy (∆H) is therefore:

            ∆H = ∆U + ∆P∆V

Where:
      H – enthalpy

       U – internal energy of a system (sum of all types of energies  present in a substance)

      P – pressure

      V – volume

Where the delta symbol (∆) means “change in.” In practice, the pressure is held constant and the above equation is better shown as:

           ∆H = ∆U + P∆V

However, for a constant pressure, the change in enthalpy is simply the heat (q) transferred:

             ∆H = q

If (q) is positive, the reaction is endothermic (i.e., absorbs heat from its surroundings), and if it is negative, the reaction is exothermic (i.e., releases heat into its surroundings).

Enthalpy has units of kJ/mol or J/mol, or in general, energy/mass. The equations above are really related to the physics of heat flow and energy: thermodynamics.

Enthalpy is a property of a thermodynamic system, and is defined as the sum of the system’s internal energy and the product of its pressure and volume. The unit of measurement for enthalpy in the International System of Units (SI) is the joule .

There are 3 types of Standard Enthalpy Changes under the following standard conditions:

• M = 1mol/L
• P = 1bar = 1atm = 100kPa
• T = 298K = 25^oC (room temperature)

1. Standard Enthalpy Change of a Reaction– ∆H^o or ∆H_r^o or ∆H^o₂₉₈

To calculate the standard enthalpy change of a reaction, we use a simple formula:

          ∆H = H_products – H_reactants

Example:

          x AB + y CD = z EF + u GH

If resulting ∆H is positive – the reaction is endothermic (heat is absorbed during the reaction)

If the resulting ∆H is negative – the reaction is exothermic (heat is released during the reaction)

In endothermic reaction, heat is transferred from the surrounding to the system, therefore products have more energy than the reactants  thus ΔH is positive

In exothermic reaction, heat is transferred from the system to the surrounding , therefore products have less energy than the reactants  thus ΔH is negative

• Standard Enthalpy Change of Combustion– ∆H_C^o

Standard enthalpy change of combustion is the enthalpy change when 1 mole of a substance is completely burnt (combusted) in excess oxygen under standard conditions.

• Standard Enthalpy Change of Formation– ∆H_f^o

Standard enthalpy change of formation is the enthalpy change when 1 mole of a substance is formed from free elements in their most stable states under standard conditions.

Let’s consider the following sample problem to better understand the concept of enthalpy change:

Simple Enthalpy Change Calculation

The most basic way to calculate enthalpy change uses the enthalpy of the products and the reactants. If you know these quantities, use the following formula to work out the overall change:

                     ∆H = H_products − H_reactants

The addition of a sodium ion to a chloride ion to form sodium chloride is an example of a reaction you can calculate this way. Ionic sodium has an enthalpy of −239.7 kJ/mol, and chloride ion has enthalpy −167.4 kJ/mol. Sodium chloride (table salt) has an enthalpy of −411 kJ/mol. Inserting these values gives:

           ∆H = −411 kJ/mol – (−239.7 kJ/mol −167.4 kJ/mol)

                 = −411 kJ/mol – (−407.1 kJ/mol)

                = −411 kJ/mol + 407.1 kJ/mol = −3.9 kJ/mol

So the formation of salt releases almost 4 kJ of energy per mole