Summary of Calculations for Coffee Cup Calorimeter Experiment

 

Purpose: To measure DH for each of the processes below:

 

           

NH4NO3(s)  NH4NO3(aq)

(1)

HCl(aq, 12 M)  HCl(aq, )

(2)

H2O(s) ® H2O(l)

(3)

 

 

                       

           

Calculations:

 

 Heats of Solution (Processses (1) and (2))

 

Let q be the heat of the process, then

-q  = heat absorbed by solution + heat absorbed by Calorimeter

 

(4)

-q = msolnCp,soln(Tf - Ti) + CCAL (Tf -Ti)

(5)

 

In equation (5):

msoln = mass of solution in grams = mass of water + mass of solute

Cp,soln = specific heat of the solution, assumed to be the same as water, 4.184 J/(oC-g)

CCAL = heat capacity of the calorimeter, to be measured.

Ti and Tf are the initial and final temperatures, respectively, of the of the solution and the calorimeter.

 

To calculate DH for processes (1) and (2) use

 

Calculation of CCAL, the heat capacity of the calorimeter

 

heat lost by hot water = heat gained by calorimeter + heat gained by cold water

 

(6)

-  mw, h Cp, w(Tf – Th) = CCAL(Tf – Tc) + mw, c Cp,w(Tf – Tc)

(7)

 

Finally,

(8)

 

In Equations (7) and (8), mw, h and mw, c are the masses of the hot and cold water, respectively; Th and Tc are the respective initial temperatures of the hot and cold water;  Tf  is the temperature of the mixed hot and cold water at the time of mixing, and Cp,w is the specific heat of water.

 

The heat of fusion of water

 

When ice is dropped into the room temperature water in the calorimeter, it melts, and the water from the melted ice is heated from the melting point of 0 oC to the final temperature, Tf.  The process is represented by the following equations:

 

H2O(s, 0 oC) ® H2O(l, 0 oC)

DH = DHfus

 

(9)

H2O(l, 0 oC) ® H2O(l, Tf oC)

 

(10)

 

The heat for this process comes from the water initially at room temperature water and the calorimeter:

 

ht. lost by rm. temp. water + ht. lost by CAL = ht. of fusion + ht. gained by cold water

 

-[mw,RT Cp,w(Tf –Ti) + CCAL(Tf – Ti)] = qfus + miceCp,w(Tf –0 o)

(11)

 

In equation (11), mw,RT, mice are the masses of the water initially at room temperature and the ice, respectively;  Tf and Ti are the initial and final temperature of the calorimeter and water, and qfus is the heat of fusion.  The enthalpy of fusion, in J/mol is calculated from:

 

(12)