EXPT 6. Boyle's Law and Graham's Law

Transcription

1 EXPT 6. Boyle's Law and Graham's Law [Key Contents] pressure-volume relation in gases, atomic model, ideal gas law kinetic theory of gases, effusion rate, diffusion rate, molecular weight [References] Principles of Modern Chemistry, 6th Ed. (Oxtoby et al.) Ch 9. The Gaseous State Chemistry for Life, Chemistry for Better Life (Kim et al.) Ch. 3. Atoms and Molecules Ch 7. States and Properties of Matter [Goal] - to verify Boyle's law using air and carbon dioxide - to verify dependence of diffusion rate on molecular weight [Background] The earth's atmosphere is mostly nitrogen (~78%) and oxygen (~21%) with small amounts of argon (~1%), and carbon dioxide (~0.038%). It has been known for a long time (at least since Archimedes) that the atmosphere exerts pressure, but it was in 1643 that Toricelli first showed that the atmospheric pressure is equivalent to 760 mm of mercury (density 13.6 g/cc). The distance between nitrogen molecules at 100 o C, 1 atm is about 37 A, which is about 20 times the size of the nitrogen molecule. The nitrogen and oxygen molecules are moving with a speed of about 500 m/s maintaining an average separation of about 40 A. Since the gas molecules are separated so much, they can be considered to move independently. Therefore, bulk properties of gases are easier to interprete than those of liquids. It is not surprising that gases played a key role in the development of the

2 molecular hypothesis. In 1662, Boyle determined the volume of gas at constant temperature yet at different pressures. He showed that the gas pressure is inversely proportional to the pressure. Boyle's law is commonly expressed as pv = constant. For a mole of gas at 0 o C, the constant is L atm. Boyle's law was combined with Charle's law and Avogadro's principle to the ideal gas law. The inverse relation between pressure and volume suggested that gases are not continuum but consist of discrete particles. Thus Boyle's law laid foundation of modern atomic theory. pv = constant Robert Boyle ( ) Thomas Graham ( ) Kinetic theory of gases enables one to calculate the effusion rate. The effusion rate depends on the temperature and the nature of the gas. In mid-19th century, Graham showed that the effusion rate is inversely proportional to the square root of the molecular weight.

3 effusion rate of A/effusion rate of B = (MW of B/MW of A) 1/2 This relationship was used in the 19th century to estimate the molecular weight of gases molecules. [Apparatus and Chemicals] Expt 1. Boyle's Law : pressure sensor dry ice Expt 2. Graham's Law : glass tube, rubber stopper, scotch tape, ruler ph paper concentrated HCl, concentrated ammonia solution [Procedure] Expt 1. Boyle's Law 1) Practice using the pressure sensor. 2) Adjust the end of the plunger to an appropriate volume mark of the syringe, connect the syringe to the pressure sensor, and set zero. 3) Move the plunger to change the gas volume in the syringe and record volume and pressure. Get data points varying the initail volume. 4) Repeat using CO 2 gas instead of air. Consider your own way of filling the syringe with CO 2 gas at 1 atm and room temperature using dry ice. Expt 2. Graham's Law (demonstration by TA)

4 1) Cut ph paper slightly longer than the length of the glass tube. Insert inside the tube and attach to the outer wall of the tube with scotch tape. 2) Place a cotton ball soaked in the HCl solution and another in the ammonia solution at the two ends of the tube at the same time. 3) Observe color change of the ph paper as the gases diffuse toward the center of the tube. 4) Make a note of the position on the tube where the first observable white ring is formed inside the tube. Measure the distance from both ends to the ring. [Caution] 1) Keep the bottle of HCl and ammonia covered. 2) Wear polyglove when handling HCl and ammonia. 3) Put used cotton ball in water after use to avoid smell. [Data Analysis] Expt 1. Boyle's Law 1) Add atmospheric pressure to the reading to get the actual

5 pressure. 2) Plot gas volume againt pressure using all the data points you obtained. 3) See if the same inverse relationship applies to both air and carbon dioxide. typical data for carbon dioxide atm volume (ml) Expt 2. Graham's Law 1) Assume that hydrogen chloride is an unknown compound. From the distance that both compounds traveled, calculate MW of hydrogen chloride. 2) Assume that ammonia is an unknown compound. From the distance that both compounds traveled, calculate MW of ammonia. [Additional Material] Daniel Bernoulli and Boyle's Law Search how in 1783 Bernoulli derived Boyle's law from Newton's law

6 of motion.