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A Verification of Hess's Law

H in Various NaOH and HCl(aq) Reactions

Our experiment verified Hess's Law by measuring the heat of reaction in coffee cup calorimeters. We used solid NaOH, aqueous NaOH, and hydrochloric acid to test Hess's Law. The heat from the dissociation of NaOH was -47.2 and -54.6 for the heat of reaction between NaOH(aq) and HCl(aq). Using our empirical values we predicted a heat of -101.8 and we found it to be -118.4 . The data affirmed our hypothesis.

Introduction

Coffee cup calorimetry allows the empirical determination of the change in enthalpy of a reaction. Enthalpy, normally Q + PV where Q is the change in heat, P is pressure, and V is volume, can be simply measured as the change in temperature - Q = mcT where m is the mass, c is the heat capacity, and T is the change in temperature - because the pressure remains constant.

Measuring the heat of dissociation in NaOH(s) NaOH(aq) along with heat of the acid-base reaction between sodium hydroxide and hydrochloric acid allowed us to calculate, via Hess's Law, the heat of the reaction NaOH(s) + HCl(aq) H2O(l) + NaCl(aq). Our lab empirically calculated the heats of all three reactions. We thus hypothesized that the heats of the reactions could be added to predict the heat of the third reaction.

Materials and Methods

We used styrofoam cups with a modified paper plate lid as our calorimeter. Our first task was to find the heat capacity of the calorimeter by combining room temperature water and hot water. Next we dissolved NaOH pellets into room temperature water and measured the temperature change. The temperature was read every 30 seconds, starting the 10 second after the pellets were added. Using the temperature readings, we could find a temperature the highest temperature and thus the point where the exothermic reaction stopped giving enough heat to counteract cooling. Our last sample was the aqueous NaOH and HCl reaction. Because of the speed of this reaction, we measured temperatures every 10 seconds.

The cups and the thermometer were rinsed after each reaction so that none of the residual reactants would bias the results of the next one.

Because we were working with acids and bases, standard clothing protocols were followed. Spill kits were also nearby so that any spill could be dealt with promptly. A disposal flask was also present to collect the aqueous NaOH. A Bunsen burner was used to heat the water for the heat capacity of the calorimeter sample. The Bunsen burner protocol was adhered to and the flame remained ignited only for the duration necessary.

Results


 Time (s)     Warm Water       NaOH(s)  NaOH(aq)    NaOH(s) + HCl(aq) 

       10         43.0°C                  17.1°C               18.0°C 

       40         40.7°C                  18.0°C               19.0°C 

       70         40.1°C                  18.7°C               21.9°C 

      100         40.0°C                  19.0°C               24.0°C 

      130         39.7°C                  19.7°C               25.5°C 

      160         39.5°C                  20.0°C               26.9°C 

      190         39.1°C                  21.1°C               28.0°C 

      220                                 21.7°C               29.0°C 

      250                                 20.5°C               29.3°C 

      280                                 20.9°C               29.3°C 



The initial temperature for all the samples was 16°C. The warm water temperature was 67°C. All temperatures were measured as best as possible. The markings on the thermometer used would normally only allow readings 0.5°C.


 Time (s)    NaOH(s) + HCl(aq) 

       10               21.5°C 

       20               22.5°C 

       30               23.0°C 

       40               23.0°C 



The temperature of the NaOH was 17°C and the HCl(aq) was 16.5°C. The initial temperature of the calorimeter was 17°C. All temperatures were measured as best as possible. The markings on the thermometer used would normally only allow readings 0.5°C.

First we calculated the heat capacity of the calorimeter. We took the perfect case, where the two equal amounts of water should even out to the average of their temperatures, and compared it to the less perfect case where the calorimeter takes some of that heat and uses it. To get the instant temperature when the calorimeter "reacts" with all of the inputs, we regressed the data points collected after 40 seconds, thus allowing 40 seconds of mixing before the reading, to the y-axis. The y-intercept should give us what our calorimeter would have read had we been the supernatural lab scientists who could mix the solution fast enough and read the thermometer quickly enough to get the instantaneous temperature reading from the two samples. The difference instant temperature reading and the theoretical temperature tells us change in temperature due to the heat capacity of the calorimeter.

Tavg = = 41.5°C

Ttheoretical = 41.0°C [Calculated by computer with all the points but the 10 second reading]

Twater = 0.5°C

mwatercTwater = CcalorimeterTcalorimeter = Q

(0.5 °C) = C(41.0°C - 16.0°C)

Ccalorimeter = 5.97

Our next reaction was the dissociation of NaOH. We placed 2.09 g of NaOH into the calorimeter with some water. The reaction heats the water and we made readings every 30 seconds until the temperature went down. A similar procedure was followed for NaOH dissolving in hydrochloric acid and NaOH(aq) reacting with the acid.

To analyze the data, we found the maximum temperature and found T. Finding the total mass of the solution was approximated by using 1.00 for water and 1.03 for the aqueous solutions. The heat capacities of the solutions was assumed to be 4.18 . Now we have enough data to find Q for the reaction:

Qreaction = Qcalorimeter + Qsolution

= CcalorimeterT + mcT

= (5.7°C) + (102 g)(5.7°C)

= 2.47 kJ

Now by dividing by the number of moles reacted, we can find the H of the reaction:

= H = = -47.2

To verify Hess's Law, we proceeded to add the two reaction of the dissociation of sodium hydroxide and the reaction between aqueous sodium hydroxide and hydrochloric acid. This resulted in an empirically derived, in other words using our empirical values to derive the expected value for the solid sodium hydroxide reacting with hydrochloric acid, H of -101.8 . Our actual reaction resulted in a H of -118 . This represents a 16% error from our empirically derived, expected value.


Reaction                                        Percent Error  

Dissolving NaOH                                 6.1%           

Solid NaOH and hydrochloric acid (empirical)    11%            

Solid NaOH and hydrochloric acid (empirically   -3.7%          
derived)                                                       

Aqueous NaOH and hydrochloric acid              -1.8%          



All values are compared to the standard accepted values given in the prelab.

It is important to note that the temperature variations were only about 6°C. Our thermometers were marked only for integral Celsius degrees. This poses a problem because the biases of the temperature reader will call out certain numbers like 5.7°C more than 5.6°C or 5.8°C. All three values are possible, especially when one considers the parallax effect of the thermometer scale printed on the outside of the glass.

Discussion

Our data affirms the hypothesis that the heat from two reactions may be summed up to predict the heat of the third reaction. Our data concurs with established values for the reactions tested.

The error in the solid NaOH and hydrochloric acid solution is somewhat disturbing. We should consider the precision of our measurements. Readings definitely could be made within 0.2°C if proper precautions are taken against parallax. When one goes through the calculations again this time with the change in temperature set to the maximal possible reading error (+0.4°C because we can err for both the starting and ending temperature), the value of H is calculated and is off by about 7%. In contrast, the compensation made for the calorimeter's heat capacity is by comparison only about 1.5%.

Other insignificant errors could include, the heat present in the solid NaOH, and the assumption that the heat capacity of the aqueous solutions equaled that of water.