Calorimeter Constant

 

All chemical reactions involve changes in energy as a result of bond breaking and bond formation during the chemical change.  This energy change is an important parameter when studying chemical reactions and is normally measured in an insulated vessel called a calorimeter.  When using a calorimeter, the chemical reagents being studied are mixed directly in the calorimeter with the temperature recorded both before and after the reaction.  If the mass of the material is also recorded, then the change in the energy occurring in the calorimeter can be calculated by the relationship:

 

Δq  =  m • Δt • c_p

 

where Δq is the change in energy, m is the mass of the solution, Δt is the temperature change of the solution, and c_p is the specific heat of the solution.  Since most reactions are carried out in dilute water solutions, the specific heat of the solution is assumed to be the same as that of water (1.00 cal/g°C  or 4.185 J/g°C).

 

The underlying principle utilized in calorimetry is the law of Conservation of Energy.  The basic premise of this principle is that “energy can neither be created nor destroyed but may be converted from one form to another.”  In other words, the heat lost (or gained) by the chemical reaction is equal to the heat gained (or lost) by the solution in the calorimeter.

 

In this experiment we are going to simply mix hot and cold water, determine the change in the temperature, and compare the total amount of energy lost with the total amount of energy gained.  If the Law of Conservation of Energy is valid, then

 

Δq_{hot water  =}  Δq_{cold water}

 

where Δq_{hot water}  is the energy lost by the hot water and the Δq_{cold water} is the energy gained by the cold water.  Unfortunately, no system is perfect and some of the energy transferred is absorbed by the calorimeter.  Therefore, the actual relationship for the Law of Conservation of Energy in this experiment should be:

 

Δq_{hot water  =}  Δq_{cold water}  +  Δq_calorimeter

 

The purpose of this experiment is to verify the Law of Conservation of Energy and to determine the amount of energy absorbed or lost by the calorimeter called the calorimeter constant.  Calorimeter constants are unique to each calorimeter and must be determined experimentally.  they are usually express in calories or Joules per degree Celsius.  That is, calorimeter constants represent the amount of energy absorbed or lost by the calorimeter for every one degree change in the temperature.  The equation to be used:

 

calorimeter constant =  | Δq _{hot water}  -   Δq _{cold water} |

                                                                  _______________________

                                                                                   Δt

 

The change in energy of both the hot and cold water is calculated from the mass of the water, the specific heat of water, and the difference in the temperature of the water in each calorimeter before and after mixing.  By measuring these values, the calorimeter constant can be determined and utilized in each subsequent experiment which uses the calorimeters. 

 

Procedure:

P1.  Label the two calorimeters “cold water” and “warm water”.  Mass each.  Add 8 mL of the cold tap water to the calorimeter labeled for cold water and find its mass.  Add 8 mL of the warm tap water to the calorimeter labeled for the warm water and find its mass.

 

P2.  Stir the water in the calorimeter frequently and when the temperature has been constant over several five-second intervals, record the temperature in each calorimeter to the nearest 0.1 °C.  Pour the cold water into the warm water and record the resulting temperature of the mixture.

 

P3.  Thoroughly dry each of the calorimeters, re-weigh, and repeat the experiment another time.

 

Calculations and Questions:

Q1a.  Calculate the mass of the water in each calorimeter.

 

Q1b.  Calculate the changes in temperature, Δt_cold and Δt_warm of the water in each calorimeter by subtracting the final temperature, t_final from the initial temperature of both the cold and warm water.

Δt_cold = t_cold  -  t_final

 

Δt_warm = t_warm  -  t_final

 

Q2.  Calculate the energy gained by the cold water by multiplying the mass of the cold water (Q1a) by the specific heat capacity of water (c_p = 1.00 cal/g°C), by the change in temperature of the cold water (Q1b).

 

Δq _{cold water  =} m_cold • Δt_cold • c_p

 

Q3.  Repeat for the warm water.

 

Δq _{hot water  =}  m_warm •Δt_warm • c_p

 

Q4a.  Calculate the absolute difference between the energy lost by the warm water (Q2), and the energy gained by the cold water (Q3).

 

Q4b.  Calculate the calorimeter constant in cal/°C by dividing the absolute difference in energy (Q4a) by the temperature change in the warm water (Q1b).

 

calorimeter constant =  | Δq_warm  -   Δq_cold |

                                                                       _________________

                                                                                   Δt_warm

 

 

 

 

Q4c.  Repeat the experiment and calculate the average calorimeter constant in

cal/ °C.  Record your average value on the chalkboard.   Then repeat the experiment with Styrofoam cups and record your values on the board.

 

 

Q5.  The Law of Conservation of Energy states that “energy can neither be created nor destroyed but may be converted from one form to another”.  According to your calculations, has energy been conserved?  That is, is the heat lost by the warm water equal to the heat gained by the cold water?  Explain your answer in terms of your calculated results.

 

Tips:

1)     It is important that the calorimeter be completely dry form one trial to the next.  A dry calorimeter should have almost exactly the same mass at the start of each trial.

2)    Covers are not needed for the pink micro-scale calorimeters.  For this experiment they will not be used on the Styrofoam cups since equilibrium is established in just a few seconds.