Introduction
Enthalpy of hydration is the energy change for converting 1 mol of an anhydrous substance to 1 mol of the hydrated substance. In order to find this number, it is necessary to first calculate the enthalpy of dissolution for each substance separately, and then find the different between the two. The enthalpy of dissolution is the energy change of dissolving 1 mol of a substance in water. It is calculated using temperature changes in the water, heat capacity of the substance, and the weight of the mixture. For this experiment, MgSO4 and MgSO4 ∙ 7 H2O were used and the enthalpy of hydration between the two was calculated.
Experimental
A Styrofoam cup and stirring bar were first obtained and weighed together. This mass was recorded. 100.0 mL of deionized water was measured with a graduated cylinder and then put into the cup with the stirring bar. The cup was again weighed and this new mass was recorded. The cup was then placed on a mixing plate set on medium to high and its temperature was recorded every 30 second for 4.5 minutes. An unknown amount of MgSO4 salt was added to the cup. The cup kept on the mixing plate set on medium to high and its temperature was recorded every minute for 15 minutes. Finally, the cup was weighed and its final mass was recorded. This process was repeated placing the MgSO4 with MgSO4 ∙ 7 H2O.
Results
| Measurement | MgSO4 ∙ 7 H2O Trial | MgSO4 Trial |
| Mass of cup and stirring bar (g) | 7.85 | 7.41 |
| Mass of cup, stirring bar, and water (g) | 107.21 | 106.70 |
| Mass of water (g) | 99.36 | 99.29 |
| Mass of cup, stirring bar, water, and salt (g) | 119.50 | 113.06 |
| Mass of Mg salt (g) | 12.29 | 6.36 |
| Molar mass of solute (g) | 246.476 | 120.369 |
| Moles of solute added (mol) | 0.04986 | 0.0528 |
| Mass of salt and water (g) | 111.68 | 105.65 |
| Initial temperature at time of mixing (ºC) | 20.90 | 21.60 |
| Extrapolated final temperature of reaction mixture (ºC) | 19.27 | 32.65 |
| ΔT = Tfinal – Tinitial (ºC) | -1.63 | 12.05 |
| Heat Capacity of reaction mixture (J/(gºC)) | 3.84 | 3.84 |
| Heat transferred during dissolution, Q (Joule) | 699. | -4890. |
| ΔHdissolution (J/mole) | 14000. (14.0 kJ) | -92600. (-92.6 kJ) |
Enthalpy of Hydration: -106.6 kJ
| Time (minutes) | Temperature of MgSO4 ∙ 7 H2O solution (ºC) | Temperature of MgSO4 solution (ºC) |
| 0.0 | n/a | n/a |
| 0.5 | 20.90 | 21.63 |
| 1.0 | 20.90 | 21.63 |
| 1.5 | 20.90 | 21.63 |
| 2.0 | 20.90 | 21.62 |
| 2.5 | 20.90 | 21.60 |
| 3.0 | 20.90 | 21.60 |
| 3.5 | 20.90 | 21.59 |
| 4.0 | 20.89 | 21.57 |
| 4.5 | 20.89 | 21.57 |
| 5.0 (salt added) | n/a | n/a |
| 5.5 | 19.57 | 26.50 |
| 6.0 | 19.30 | 27.18 |
| 7.0 | 19.29 | 28.72 |
| 8.0 | 19.30 | 29.12 |
| 9.0 | 19.32 | 29.50 |
| 10.0 | 19.35 | 31.20 |
| 11.0 | 19.38 | 31.65 |
| 12.0 | 19.40 | 31.60 |
| 13.0 | 19.42 | 31.44 |
| 14.0 | 19.49 | 31.28 |
| 15.0 | 19.50 | 31.10 |
| 16.0 | 19.51 | 30.91 |
| 17.0 | 19.58 | 30.76 |
| 18.0 | 19.60 | 30.58 |
| 19.0 | 19.65 | 30.43 |
| 20.0 | 19.69 | 30.23 |
Calculations
To find the mass of water used, I subtracted the weight of the cup with just the stirring rod from the weight of the cup with the stirring rod and water. To find the weight of the salt used, I subtracted the weight of the cup, stirring rod, and water from the final weight of the cup. In order to find the moles of solute used, I divided the mass of the salt by its molar mass. To find the change in temperature, I subtracted the initial temperature from the final temperature. In order to find Q, the heat capacity of the reaction mixture, I used the equation Q = – (mass of mixture) * (heat capacity of mixture) * (ΔT). To find the ΔHdissolution, I used the equation ΔH = Q / (number of moles of solute). Lastly, to calculate the enthalpy of hydration, I subtracted the ΔHdissolution of the MgSO4 ∙ 7 H2O from the ΔHdissolution of the MgSO4.
Discussion/Conclusions
I was surprised that while the MgSO4 salt heated the water, the MgSO4 ∙ 7 H2O salt cooled the water down. It was interesting that two substances very close in chemical makeup could have such different reactions in water. My graph for the temperature change of water with MgSO4 seems to only gradually jump in temperature after adding the salt. I believe this is because my lab partner forgot to turn the mixer on, so the salt was not completely mixing at first. Other than that, the procedure went well. The enthalpy of hydration of -106.6 kJ seems fairly high. Water takes 4.184 kJ to be raised only 1 ºC, so 106.6 kJ seems like a lot of energy.
