Calorimetry

You may see a much simpler, but less accurate calorimeter in the laboratory, which, by its construction is necessarily constant pressure:

Constant volume calorimetry measure the internal Energy change between reactants and products, but constant pressure calorimetery measures directly the Enthalpy change during the reaction.  These two heats are slightly different when gases are evolved or consumed during the transformation. (Gases evolved expand if at constant pressure and thus do Work in the surroundings. This energy must come from somewhere...)

Both constant volume and constant pressure instruments use the fact that the heat evolved from the reaction heats up a working substance (usually a water bath) with a known heat capacity. Thus a measurement of the temperature rise in the surroundings (calorimeter body) allows a determination of the heat crossing the boundary.

We usually assume that the heat capacity of a substance at constant volume, C_p, or the heat capacity at constant volume, C_V, are roughly independent over a small range of temperatures (or at least the range of temperatures in the Calorimeter).

• The Heat Capacity of a substance is extensive, and can be quoted as
•     the molar heat capacity (heat capacity per mole of substance)
•     or the specific heat (heat capacity per gram of substance)
• The Heat Capacity of any substance is positive.
• The Heat Capacity is discontinuous at phase transitions.
• The Heat Capacity of a solid is in general less than that for a liquid, which is less than that for a gas.
• The values of the Heat Capacity at constant Volume, C_V, and the Heat Capacity at constant pressure, C_p, for a given substance are are almost exactly equal, if the substance is a solid or a liquid.  C_p and C_V are not equal for a gas;  The difference between C_p and C_V is the capacity of the gas to expand and do work and is equal to R per mole (R is the universal gas constant)  {C_p = C_V+R for an ideal gas}  For solids and liquids, the subscript p or V is usually dropped.
• Q = m C DT
• if m is moles and C is molar Heat Capacity
• if m is mass (grams) and C is the Specific Heat
• is positive for a temperature increase because the system has undergone an endothermic change of state

A constant pressure calorimeter where the water bath has a mass of 150 grams.  1.00 g of diamond is burned to produce CO₂ and Water.  If the water bath in the Calorimeter is initially at 22 ^oC, what is the final temperature of the Calorimeter?

First, let's write a balanced chemical reaction for the combustion
C _(diamond) + O_{2 (gas)} = CO_{2 (gas)}

Next, the molar heat of reaction comes from the Heats of  Formation of the products minus the reactants.

DH_rxn = -393.5 kJ/mol - (1.88 kJ/mol + 0) = -395.4 kJ/mol

The actual heat released by 1.00g /12.011 g/mol = 8.326 x 10^-2 mol of diamond is

Q = (-395.4 kJ/mol) (8.326 x 10^-2 mol) = -3.292 x 10⁴ J

The temperature rise is the heat provided to the water (-Q) divided by the mass times the specific heat of water

DT = 3.292 x 10⁴ J/ ((150. g)(4.184 J/K.g) = 52.5 K

The final temperature of the water bath is then

T_final = 22 + 52.5 = 74.5 ^oC
 

If 0.500 gram of another substance, H₂CO, is burned in the same Calorimeter, and the temperature of the bath in the calorimeter (150 g H₂0) changes from 24.0 to 39.2 ^oC, what is the molar heat of formation of the H₂CO?

Again, lets see what kind of reaction we should have in the reactor

H₂CO _(gas) + O_{2 (gas)} = CO_{2 (gas)} + H₂O _(l)
So the Heat of that reaction for 0.500 g / 30.03 g/mol = 1.665 x 10^-2 mol of formaldehyde raised the temperature of 150. g of water by 15.2 K.  That means the heat released by that amount of reaction liberated:

-Q = (150 g)(4.184 J/g.K)(15.2 K) = 9.540 kJ

of heat.  One mole of reaction would liberate

-Q = 9.540 kJ/(1.665 x 10^-2 mol) = 572.9 kJ/mole

which is the heat of combustion, DH_comb, of formaldehyde.

The heat of formation of formaldehyde, DH_form{formaldehyde}, is related to the heat of combustion as:

DH_comb = DH_form{water (l)} + DH_form{CO_{2 (gas)}} - DH_form{formaldehyde}

So
-572.9 kJ/mol = -285.8 kJ/mol + -393.5 kJ/mol - DH_form{formaldehyde}

or
DH_form{formaldehyde} = -106.4 kJ/mol

This number is a little low, according to the The National Institute of Standards and Technology (NIST), which can be searched on the web at http://webbook.nist.gov/chemistry/

Sometimes the metal reaction vessel containers heat capacity is also included in the calculation, but the entire calorimeter can be calibrated with the combustion of any substance whose heat of formation is known.