Estimation of Avogadro’s Number - Principles of Chemistry Lab I - Notes | CHEM 1211L, Study notes of Chemistry

Download Estimation of Avogadro’s Number - Principles of Chemistry Lab I - Notes | CHEM 1211L and more Study notes Chemistry in PDF only on Docsity! 19 Estimation of Avagadro’s Number The objective of this experiment is to estimate Avogadro’s number using octadecanoic acid. Avogadro’s number is the number of objects (atoms or molecules) present in one mole of a substance. The number was named after an Italian physicist, Amedeo Avogadro, who determined the number of particles present in given volumes of substances. The unique structural properties of octadecanoic acid provide a convenient way of estimating the number of molecules present in one mole of the acid. The molar mass of octadecanoic acid, CH3(CH2)16COOH, is known to be 284.47 g/mol. This experiment involves the creation of a monolayer (thin film with a thickness of one molecule) of octadecanoic acid molecules of known mass and surface area. The number of moles of the octadecanoic acid in the monolayer can be determined using the known mass and the molar mass. The diameter of the monolayer can be measured and used to determine the surface area. The volume of the monolayer can also be calculated using the surface area and approximated size the acid molecules, which can then be used to estimate the number of the acid molecules in the monolayer. Avogadro’s number is the result of dividing the number of molecules by the number of moles of octadecanoic acid in the monolayer. Water molecules are polar (polar covalent bonds are present due to unequal sharing of electrons between an oxygen atom and a hydrogen atom). Generally, polar molecules are hydrophilic (water loving), which implies that they are soluble in water. On the other hand, nonpolar molecules are hydrophobic (water hating), indicating that they are insoluble in water. For instance, oxygen – hydrogen bonds are polar covalent and are hydrophilic, whereas carbon – hydrogen bonds and carbon – carbon bonds are nonpolar covalent and are hydrophobic. The octadecanoic acid molecule has both polar and nonpolar regions. The nonpolar region is a long hydrocarbon chain (CH3(CH2)16 –), which consists of carbon – carbon bonds and carbon – hydrogen bonds. This nonpolar region is hydrophobic and is not soluble in water. The polar region is a carboxylic acid end (– COOH) of the molecule. This polar region, which is hydrophilic and soluble in water, consists of carbon – oxygen bonds and oxygen – hydrogen bonds. The differences in structural properties within an octadecanoic acid can be exploited to create a monolayer, which has a thickness of the height of one molecule. When an octadecanoic acid comes in contact with water, the hydrophilic end of the molecule dissolves in the water, but the hydrophobic chain of the molecule does not dissolve in the water and is oriented away. When enough number of the octadecanoic acid molecules are present in a given surface area of water, the hydrophobic chain of the molecules are assumed to stick upright away from the water. This leads to the formation of a monolayer of one molecule thick, provided the amount of octadecanoic acid required is not exceeded. By approximating the shape of an octadecanoic acid molecule as a cylinder, the volume of each molecule (Vmolecule) can be estimated (see figures below). 20 ( )2moleculemolecule rπhV ⋅= where h and r are the height and radius of the cylinder, respectively. The height of the cylinder is the length of one octadecanoic acid molecule and is estimated to be 22.9 Angstroms (1 Angstrom = 1 x 10-10 meters). The radius of the cylinder is the average radius of one octadecanoic molecule and is estimated be to 1.75 Angstroms. Similarly, the volume of the monolayer (Vmonolayer) can be calculated using the equation below. ( )2monolayermonolayer rπhV ⋅= where h is the height of the monolayer (the length of one octadecanoic acid molecule) and r is the radius of the monolayer. In other words, the volume of the monolayer is the product of the surface area of the monolayer and the length of one molecule. The number of acid molecules in the monolayer (Nm) can be calculated from the volume of the molecule and the volume of the monolayer. moleculemmonolayer VNV ⋅= and ( )( ) 2 molecule monolayer 2 molecule 2 monolayer molecule monolayer m r r πrh πrh V V N       = ⋅ ⋅ == 23 Calibration of Pasteur Pipet Trial 1 Trial 2 Trial 3 Average Trial # Drops in 1.00 mL Determination of Avogadro’s Number Trial 1 Trial 2 Trial 3 Conc. of Octadecanoic Acid Solution Diameter of Monolayer # Drops to Create Monolayer Volume to Create Monolayer       = ncalibratio monolayersolution drops#average 1.00mLxdrops#V Sample Calculation: Mass of Acid in Monolayer      = solution mL acid gramxVMass solutionacid Sample Calculation: Moles of Acid in Monolayer       = acid gram MM acidmole1xMassMoles acidacid Sample Calculation: Number of Molecules of Acid =      = 2 molecule monolayer m r r N Sample Calculation: Avogadro’s Number == acidmoles# NN mA Sample Calculation: Average Avogadro’s Number 24 Questions 1. Report your average result as ___________ x 1023. 2. State three assumptions or approximations made in this experiment. 3. Assuming you added less octadecanoic acid solution than required to form a complete monolayer, would your estimated Avogadro’s number be lower or higher? Explain 4. Supposing you did not cover your actadecanoic acid solution with parafilm and some heptane evaporated, causing the concentration of octadecanoic acid to change from trial to trial. How would this affect your calculations? Would the estimated Avogadro’s number be artificially high or low? Explain. 5. A chemist conducts an experiment to estimate Avogadro’s number using octadecanoic acid solution. He uses 5.25 x 10-6 mol octadecanoic acid to create a complete monolayer and obtains an estimate of 6.02 x 1023. How many octadecanoic acid molecules are present in the monolayer he created? How many carbon atoms are present in the monolayer he created?