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Experiment 8 Ideal gas Objective: 1. Advance core knowledge of ideal gas law; 2. Construct the generator to produce gases; 3. Collect the gas under ambient temperature. Introduction: An ideal gas is defined as the entity composed of a set of randomly-moving, noninteracting point particles. These particles are considered having mass only, but its volume can be negligible due to its small size. According to the Kinetic-Molecular Theory, there are three key postulations in terms of the ideal gas and its behavior. Postulate 1: Particle Volume The volume of an individual gas molecule can be negligible due to its significantly small size compared to the volume of its container. Therefore, the gas molecules are considered to have only mass, but zero volume. In another word, the gas molecule has a negligible volume compared with its containing vessel. Postulate 2: Particle Motion Gas particles move in a constant and random motion, which is in a straight-line unless the collision between gas molecules or gas molecules with the container walls occurs. The gas molecules change their motion randomly and erratically. Postulate 3: Particle Collisions Collisions are elastic, therefore the total kinetic energy (E k ) of the particles is constant. This means the gas molecules will not lose kinetic energy after collide. All gases display distinctive properties compared with liquid or solid. Among them, five properties are the most important and listed below: Gas volume (V) changes greatly when its pressure (P) changes. Gas volume (V) changes greatly when its temperature (T) changes. Gases have relatively low viscosity, due to the significant weak intermolecular forces. Most gases have relatively low densities (d, in the unit of g/l) under normal conditions. Gases are miscible. Commonly, gas properties are measured by four main parameters. They are listed below: the pressure (P, in Pa (SI unit), or atm (commonly used unit)), the volume (V, in L), the number of moles of gas particles (n, in mol); and 118
Pressure of gas (torr) Reciprocol of pressure (1/torr) the temperature (T, in K). The properties of gases follow the rules of (1) Boyle s law, (2) Charles s law, (3) Avogadro s Law, and (4) Gay-Lussac's Law. Ideal gas law (described as PV = nrt) summarizes the behavior of ideal gases and this law is the most useful law to study the behavior of gas molecule. It is also logic to point out that gas moelcules are mixed homogeneously (means in one phase) in any proportions and each gas in a mixture behaves as if it were the only gas present. 1. Boyle, s Law: this law indicates that the volume (V, L) of gas molecules is inversely proportional to its pressure (P, atm). This property is expressed in the equation 1 and shown in Figure 1: P 1/V or that P 1 V 1 = P 2 V 2 = constant (at constant n and T) equation 1 3500 3000 Pressure Reciprocol of pressure 0.0014 0.0012 2500 0.001 2000 0.0008 1500 0.0006 1000 0.0004 500 0.0002 0 0 10 20 30 0 Volume of gas in ml Figure 1: The relationship between gas volume and its pressure. 2. Charles's Law: This law indicates that volume (V, L) of gas molecules is directly proportional to its temperature (T, K). The formal expression is in equation 2: V T or V 1 /V 2 =T 1 /T 2 = constant (at constant n and P) equation 2 119
If graph is plotted as volume (V) versus temperature (T in Kelvin), a straight line is obtained. If we extrapolate to zero volume, absolute temperature (negative 273.15 C) is obtained. The plot is shown in figure 2. Figure 2: The relationship between volume and temperature of gases. 3. Avogadro's Law: Avogadro s law states that equal volumes of gas molecules contain the same number of moles of gas molecules at the same temperature and pressure or the volume of gas molecule is directly proportional to its moles. The expression for Avogadro s law is shown in equation 3: V n, or V 1 /V 2 = n 1 /n 2 (at constant P and T) equation 3 From the equation 3, it can be seen that the volume of gas molecules is directly proportional to its moles. When a graph is plotted using volume as a function of moles, a straight-line is obtained (shown in figure 3). 120
Volume of gas (L) 250 200 p = 2atm, T = 298 K P = 1.5 atm, T = 273 K 150 100 50 0 0 1 2 3 4 5 6 Moles of gas (mol) Figure 3: The relationship between volume and moles of gases. 4. Gay-Lussac's Law this law states that the pressure (P, atm) of gas molecules is directly proportional to its absolute temperature (T, K). The relationship between P and T can be expressed as equation 4: P T, or that P 1 /P 2 =T 1 /T 2 =constant (at constant n and V) equation 4 When a graph of P as a function of T is plotted, a straight line is obtained. The plot of pressure as a function of temperature is shown in figure 4. 121
Figure 4: The relationship between volume and temperature of gases. 5. The Ideal Gas Law All the above equations from various laws, including Boyle, s Law, Charles's Law, Avogadro's Law, and Gay-Lussac's Law can be combined to derive one equation. This equation is called the ideal gas law shown as below: PV = nrt Where R is the ideal or universial gas constant, (R= 8.314J K -1 mol -1 or R= 0.08206 L atm mol -1 K -1 ) ; P is the pressure of ideal gas (atm); V is the volume of gas (L); n is the moles of gas (mol); T is the temperature (K, note: the temperature is usually given by C and make sure convert Celsius to Kelvin (K = 273.15 + C). The Ideal Gas Law is the most useful equation for calculations of gases variables. If the pressure and concentrations of real gas is low, the real gases behave like an ideal gas. Otherwise, correction on volume and pressure of the real gas is needed. It is also useful to define a standard molar volume of gas molecules, denoted as V m. This standard molar volume expresses the gas volume for one mole in standard pressure and temperature (STP) regardless of the type of gas molecules. In other words, the molar volume is independent on the nature of the gas molecules. 122
V m can be calculated using the ideal gas law, PV = 1 RT at different temperatures and pressures. Table 1 displays the standard molar volume of three ideal gases. Again, please be aware that the V m at SPT is independent on the nature of the gases. Table 1: standard molar volume of ideal gases (He, O 2 and N 2 ) 123
Chemicals needed: CaCO 3 powder HCl (6.0 M aqueous solution) Iced water and hot water Equipment needed: Glass syringe (with volume of 50 ml) Test tube Rubber stopper Rubber tube (with thin wall) A metal clip An electronic scale Weighing papers Benson Burner Matches or lighters Digital thermometer Stands Tube holders 124
Procedures of the experiment: A: CO 2 generation (two trials are required for comparison) 1. Weight about 2.000 grams of CaCO 3 accurately. 2. Transfer the power into the test tube carefully and tap with figure softly. 3. Connect the rubber tube to one end of the syringe (see figure 5, first stand on your right). 4. Secure the position of syringe piston and there is no gas leakage. (Student may use the snoopy to test whether the syringe is leaking or not). 5. Attach the stopper to the test tube (figure 5, the second stand from your right hand side). 6. Connect the rubber tube to the hole of the stopper. 7. Carefully heat the bottom of the test tube using less intense flame (the blue flame instead of roaring blue), until the reaction is completed. 8. Remove the Bunsen burner and observe the syringe piston movement until it fully stopped. (note: after reaction completes, you may observe that the syringe piston continues moving forward slightly.) Figure 5: The experimental setup of the CO 2 generation 125
B: Temperature affect on the volume (two trials are required for comparison) B-1 Decrease temperature 1. Carefully and solidly clap the rubber tube with a clip. 2. Remove the syringe from the stand (shown in figure 5, the first stand on your right). 3. Place it into a bath (such as 1L) containing ice water (600-800 ml) and a thermometer. 4. This water bath will allow water cooling to zero Celsius (0 C) and will allow gas to contrast. 5. Measure the temperature of the water bath using the digital thermometer. This temperature represents the temperature of gas CO 2. 6. When the syringe piston is fully stabilized, record the volume of the gas CO 2 (in ml). 7. Write down the volume on your data sheet provided in your lab report. B-2 Increase temperature 1. Place the syringe in a bath (such as 1L) containing large amount of water (600-800 ml) and a thermometer. 2. Increase temperature and until water boils; this will allow gas to expand. 3. Measure the temperature of the bath. This temperature represents the gas temperature. 4. When the syringe piston is fully stabilized, record the volume of the gas CO 2 (in ml). 5. Write down the volume on your data sheet provided in your lab report. C: Ideal Gas Law 1. Allow the syringe cool down to room temperature (about 25 C); 2. Weigh the mass of the syringe containing CO 2 gas (note: with three digits, such as 0.123 g); 3. Release CO 2 into the NaOH waste bottle; the reaction will occur: CO 2 (g) + NaOH (aq) NaCO 3 (aq) + H 2 O (l) 4. Measure the mass of empty syringe (note: with three digits, such as 0.123 g); 5. Calculate the net mass of CO 2 (tabulated in table 1) by this equation: Mass of CO2 = Mass of syringe containing CO2 - Mass of syringe 6. Use ideal gas law (PV = nrt) to calculate the moles of CO 2 (n =PV / RT). 7. Calculate the molar mass of CO 2 (molar mass = mass of CO2 / moles of CO2 ). 8. Compare this measured molar mass with the theoretical value (44.01 g/mol). (note: the difference between mass of syringe + CO 2 and the mass of syringe equals the net mass of CO 2 ) 126
Table 1 Mass of CO 2 determination Mass of syringe and CO 2 m 1 Mass of syringe m 2 Mass of CO 2 m = m 1 - m 2 127
Texas A&M University-Kingsville Experiment 8 Name: Date: General Chemistry laboratory report Ideal Gas Law K number: Locations: Objectives: Objectives 1 Objectives 2 Objectives 3 Introduction: Procedure Procedure A: CO 2 generation Your summary B: Temperature affect on the volume C: Avogadro's Law 128
Data and observation A: Ideal gas generation (two trails are required) Table 1: CO 2 preparation by decomposition of CaCO 3 Compounds Student A Student B CaCO 3 When you heat the test tube, CO2 is produced. What is your observation on the piston movement? After you stopped heating the test tube, what is your observation? Calculate the volume of CO 2 in the syringe After you stopped heating the test tube, the syringe keeps moving slightly. Explain why. B: Temperature effect on volume of ideal gas Temperature decrease: Table 2: Volume decreases when temperature decrease Chemicals Student A Student B Ambient temperature (K) Initial volume of CO 2 contained in syringe (ml) Temperature of iced water (K) Final volume of CO 2 contained in syringe after place it in iced water (ml) 129
Volume change from fringe reading (ml) Calculated final volume after place syringe in iced water (ml) Explain why measured final volume is different from calculated volume of CO 2 Temperature increase: Chemicals Student A Student B Ambient temperature (K) Initial volume of CO 2 (ml) Temperature of boiling water (K) Final volume of CO 2 after place it in iced water (ml) Volume change from fringe reading (ml) Calculated final volume after place syringe in boiling water (ml) Explain why measured V final is different from calculated volume of CO 2 C: Ideal gas law Table 3: determination of CO 2 moles using ideal gas law. Chemicals Student A Student B Mass of syringe containing CO 2 (mg) m 1 Mass of syringe without CO 2 (mg) m 2 Mass of CO 2 (mg) m 1 - m 2 Ambient temperature (K) 130
Pressure (atm) Ideal gas constant, R 0.0821 atm L/mol K 0.0821 atm L/mol K Moles of CO 2 using ideal gas law Moles calculated from the CaCO 3 decomposition Comparison of the theoretical and the measured amounts of CO 2 (g). The theoretical and the measured amounts of CO 2 (g) are different from each other. Explain why. Conclusions: Acknowledgements: 131
References Requirements: 1. Students need to know how to construct gas generator properly. 2. Students need to collect gas efficiently. 3. Students need to understand the ideal gas law. 132
Pre-test: 1. What is the ideal gas law (specify each variable, the meaning and its unit)? 2. Noble gas, helium (He) is injected into a balloon. Its volume is determined to be 4500 cm 3 at 33 C. If the balloon is cooled to -18 C, calculate the new volume of this balloon? (Note: temperature must be in Kelvin, using Charles s Law : V 1 /T 1 = V 2 /T 2 ) 3. If 1.75 g CO 2 gas has been collected using an evacuated 1.50 L flask at 30 C, what is the pressure inside this flask? (R = 0.08206 L atm/mol K, using PV = nrt) 4. The CO 2 is produced after HCl is added into CaCO 3. If 4.40 g CO 2 gas has been collected using an evacuated 2.50 L flask at 25 C, calculate the mass of CaCO 3 required to produce 4.40 g CO 2? (R = 0.08206 L atm/mol K) 133
5. Postulate the Kinetic-Molecular Theory of Gas. 6. Indicate the meaning and unit of difference parameters in the ideal gas law, PV=nRT. Variables Meaning Unit V P n T R 134
Post-Test 1. What is the ideal gas law? 2. Noble gas, helium (He) is injected into a balloon. Its volume is determeind to be 3849 cm 3 at 25 C. If the balloon is cooled to -42 C, calculate the new volume of this balloon? (Note: temperature must be in Kelvin, using Charles s Law : V 1 /T 1 = V 2 /T 2 ) 3. If 3.98 g CO 2 gas has been collected using an evacuated 2.50 L flask at 33 C, what is the pressure inside this flask? (R = 0.08206 L atm/mol K, using PV = nrt) 4. The CO 2 is produced after HCl is added into CaCO 3. If 2.20 g CO 2 gas has been collected using an evacuated 1.50 L flask at 25 C, calculate the mass of CaCO 3 required to produce this amount of CO 2? (R = 0.08206 L atm/mol K) 135
5. Postulate the Kinetic-Molecular Theory of Gas. 6. Indicate the meaning and unit of difference parameters in the ideal gas law, PV=nRT. Variables Meaning Unit V P n T R 136
Marking Scheme (100 pts in total) Content Points for each question Total Points Pre-test 3.5 20 Lab report Objectives: 4 60 Introduction 6 Procedure 5 Data and 30 observation Conclusion 5 Acknowledgement 5 References 5 Post test 3.5 20 137