Experiment Two: Freezing Point Depression

AP Lab Report 2: Freezing Point Depression Lance Schell, Colin Livasy, Erin Tatman, and Niral Rajyaguru Park Hill South High School Block One Advanced Placement (AP) Chemistry January 20, 2009 Abstract In this lab, the purpose was to use the freezing point depression method to determine the molecular weight of benzoic acid. This was done by determining the freezing point of lauric acid and that of a lauric-benzoic acid solution; then finding the molality of the solution, and moles of benzoic acid. The results of the experiment confirmed our hypothesis that the freezing point would decrease as more benzoic acid was added to the solution. This was because the addition of solute (benzoic acid) lowers the vapor pressure of the solution. As the vapor pressure lowers, the freezing point also lowers because the addition of benzoic acid increases the number of particles and H+ ions in solution which causes the freezing point to be lower. In the results of the experiment, the molar mass (MM) was found to be 93 grams per mole, which differed from the established value of 122.13 grams per mole by a 24% error. The molar mass was found from the moles of lauric acid and a lauric-benzoic acid mixture existing in the experiment. Errors existing in this experiment could include impurities in the benzoic acid – lauric acid mixture, contamination and “crossing” the two solutions in the main beaker commonly used to heat the substances, and the exact presence of liquid versus solid (i.e. the solutions both had relatively disadvantageous freezing points, and any amount of time at room temperature causes the two forms [solid and liquid] to coexist which would lead to a change in the experimental values). Adding benzoic acid to the lauric acid in the benzoic-lauric acid mixture, the kinetic energy of the solution was “inhibited”, evident of a lower vapor pressure and subsequent decreasing freezing / melting point.

Introduction Freezing point depression may easily be defined as a vertical medium in reference to boiling point elevation. The general definition is the effect of lowering the freezing (or melting) point of a substance due to an increased amount of solute added to the solvent (such as adding salt to pure water) in that the solute decreases the amount of vapor pressure, increasing both the boiling point (known as boiling point elevation), and lowering the freezing point (freezing point depression).1 The two differing effects are known collectively as colligative properties, and the only way to return to pure solvent back to its original chemical potential is to decrease the temperature, which is achievable through freezing point depression.1 The idea was founded by the National Institute of Technology, whose charter was approved by the US Congress, 1901.2 Freezing point depression has a wide variety of uses in the world of today. First year college students first learn of colligative properties before moving on to more specific entities, some dealing with colligative properties, while some did not deal with colligative properties.3 Thinking of shipments requiring dry ice to contain a certain temperature (usually cold), one could infer that freezing point depression would be useful in this type of situation. According to the Chemical Rubber Company’s Guide to Chemistry and Physics, dry ice (solid carbon dioxide) has a sublimation point of -78.5 °C at which point the solid turns directly into a gas.4 The solid obviously is less warm (as there is no such thing as “cold”) than water or ice, and is a good cooling agent. The temperature of dry ice’s sublimation point can be readily modified using the freezing point depression method. Changing the amount of carbon dioxide gas (or even changing the pressure used to pressurize the gas) would change the point at which the solid sublimates. During the manufacturing process of dry ice, one can find out how much liquid carbon dioxide is present (moles of liquid carbon dioxide) by using the molality portion of

freezing point depression. Using that information, the amount of solid carbon dioxide could be estimated. This is especially important in industries needing an exact amount of dry ice and varying quantities, saving both time and money in the business realm. Molar mass, amount of solute or solvent, and temperature (varying, original, and final) can all be calculated using the fundamentals of freezing point depression.5 Experimental This lab concerning freezing point depression is from the procedure documented in the handout from Vernier Software.6 Data / Calculations The first step to finding the molality, is finding the freezing temperature depression, ΔT. To do this, one would take the temperature initial and the temperature final and subtract. 𝛥𝑇 = 𝑇𝑓 − 𝑇𝑖 𝛥𝑇 = 38.973 °𝐶 − 44.276 °𝐶 ∆𝑇 = −5.303 °𝐶 Next, molality is calculated using the Kf value of lauric acid of 3.9 °C-kg/mol. ∆𝑇 = 𝐾𝑓 ∙ 𝑚 5.303 ℃ = 3.9 ℃ 𝑘𝑔 𝑚𝑜𝑙 −1 ∙ 𝑚 𝑚 = 1.4 𝑚𝑜𝑙 𝑘𝑔−1 Next, moles of benzoic acid are needed. To do this, one would use the same equation as shown above, except substituting in for m, moles of solute over kg of solvent. This way, one can

solve for the moles of the solute, benzoic acid. The first step in doing so is converting the grams of lauric acid as the solvent, into kilograms.

8.2181 𝑔 𝑙𝑎𝑢𝑟𝑖𝑐 𝑎𝑐𝑖𝑑 𝑥

1 𝑘𝑔 = .0082181 𝑘𝑔 𝑙𝑎𝑢𝑟𝑖𝑐 𝑎𝑐𝑖𝑑 1000 𝑔

Then, one can proceed with the equation.

∆𝑇 = 𝐾𝑓 𝑥

𝑚𝑜𝑙𝑒𝑠 𝑠𝑜𝑙𝑢𝑡𝑒 𝑘𝑔 𝑠𝑜𝑙𝑣𝑒𝑛𝑡

5.303 °𝐶 = 3.9 °𝐶 𝑘𝑔 𝑚𝑜𝑙 −1 𝑥

𝑚𝑜𝑙𝑒𝑠 𝑠𝑜𝑙𝑢𝑡𝑒 . 0082181 𝑘𝑔 𝑠𝑜𝑙𝑣𝑒𝑛𝑡

5.303 ℃ 𝑥 0.0082181 𝑘𝑔 = 3.9 ℃ 𝑘𝑔 𝑚𝑜𝑙 −1 𝑚𝑜𝑙 𝑠𝑜𝑙𝑢𝑡𝑒 . 001 𝑚𝑜𝑙 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 𝑠𝑜𝑙𝑢𝑡𝑒 The next step is finding the experimental molecular weight of benzoic acid in g/mol using the original mass of benzoic acid from the data table and the moles of benzoic acid that was calculated in the previous step.

𝑀𝑀 =

𝑀𝑀 =

𝑔𝑟𝑎𝑚𝑠 𝑠𝑜𝑙𝑢𝑡𝑒 𝑚𝑜𝑙𝑒𝑠 𝑠𝑜𝑙𝑢𝑡𝑒

1.0192 𝑔𝑟𝑎𝑚𝑠 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 . 011 𝑚𝑜𝑙𝑒𝑠 𝑏𝑒𝑛𝑧𝑜𝑖𝑐 𝑎𝑐𝑖𝑑 𝑀𝑀 = 93 𝑔 𝑚𝑜𝑙 −1

Now, by using the experimental molecular weight just calculated, one can find the percent error. This can be done by taking the actual molecular weight minus the experimental weight and then divided by the actual molecular weight times 100.

𝐴𝑐𝑡𝑢𝑎𝑙 𝑌𝑖𝑒𝑙𝑑 − 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑌𝑖𝑒𝑙𝑑 𝑥 100% = 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 𝐴𝑐𝑡𝑢𝑎𝑙 𝑌𝑖𝑒𝑙𝑑 122.13 𝑔 𝑚𝑜𝑙 −1 − 93 𝑔 𝑚𝑜𝑙 −1 122.13 𝑔 𝑚𝑜𝑙 −1 29 𝑔 𝑚𝑜𝑙 −1 𝑥 100% = 24% 𝑒𝑟𝑟𝑜𝑟 122.13 𝑔 𝑚𝑜𝑙 −1 Conclusion The addition of the benzoic acid solute to the lauric acid solution causes the vapor pressure to decrease. This decrease in vapor pressure and increase in solute present causes the freezing point to become lower when mixed in the solution. The H+ ions within the benzoic acid cause the freezing point to lower because the ions act to disrupt the bonds between the particles. The percent error was calculated to be relatively low (around 24%). Errors that contributed to the percent error could include (as previously stated), impurities in the benzoic-lauric acid mixture, “crossing” of the two in the main beaker commonly used to heat the solutions, and the coexistence of solid and liquid forms of the solutions. Adding benzoic acid to the lauric acid in the benzoic-lauric acid mixture, the kinetic energy of the solution was “inhibited” evident of a lower vapor pressure and subsequent decreasing freezing/melting point.

Table Mass of lauric acid Mass of benzoic acid Freezing point of pure lauric acid Freezing point of the benzoic acidlauric acid mixture

8.2181 g 1.0192 g 44.276 °C 38.973 °C

Freezing temperature depression ( ∆t ) -5.303 °C Molality, m 1.4 mol/kg Moles of benzoic acid .011 mol Molecular weight of benzoic acid (experimental)

93 g/mol

Molecular weight of benzoic acid (accepted)

22.13 g/mol

Percent error 24 %

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General Chemistry Online. http://antoine.frostburg.edu/chem/senese/101/solutions/faq/thermo-explanation-offreezingpoint-depression.shtml National Institute of Standards and Technology. http://portal.acs.org/portal/acs/corg/content?_nfpb=true&_pageLabel=PP_ARTICLEMAI N&node_id=924&content_id=WPCP_007610&use_sec=true&sec_url_var=region1&__u uid= SAT Subject Test: Chemistry Preparation. “Colligative Properties of Solutions”. Pages 198-199. Joseph A. Mascetta. 2009. CRC Handbook of Chemistry and Physics. David R. Lide. 2006-2007. Barron’s AP Chemistry. “Freezing-Point-Depression and Boiling-Point-Elevation”. Pages 352-353. Neil D. Jespersen, Ph.D. 2008. “Freezing Point Depression” Handout Packet. Vernier Software.