Determining the Relationships Between Pressure, Temperature and Volume - Lab Report Example

Gas Laws: Determining the relationships between pressure, temperature and volume This experiment investigated the three Gas Laws (Boyle’s; (pressure, volume), Gay-Lussac’s (pressure, temperature) and Charles’ (volume, temperature)) by subjecting a fixed amount of gas to different conditions of temperature, pressure and volume and then measuring how the dependent parameter changed. The three Gas Laws have dependent and independent variables, and altering the independent variable would result in the dependent’s variable to change. It was found that changing the pressure of a gas caused an inverse change in the pressure it exerted (Boyle’s Law), changing the temperature caused a change in the pressure (Gay-Lussac’s Law) and changing the temperature of a gas caused the volume to change (Charles’ law) Introduction The term ideal gas is used to describe a theoretical gas that is made up of arbitrarily moving particles. It is assumed that these particles are not subjected to any forces between them, and they do not occupy any space, indicating that their atomic volume can be ignored. The behavior of an ideal gas is governed by the relationships between these four interdependent variables: temperature (T), pressure (P), number of moles (n) and volume (V). The ideal gas law is written as PV=nRT; where R = gas constant. For an ideal gas, solving the equation gives an answer of 1. It can be rewritten as ((PV/nRT) = 1) (1). The ideal gas law is a combination of three individual laws: Boyle’s Law, Gay-Lussac’s Law and Charles’ Law. Boyle’s Law describes how the change in pressure causes the inverse change in the volume of a fixed amount of gas at a constant temperature. It is stated as P ∝ 1/V and can be written as (2): Gay-Lussac’s Law describes how the temperature and pressure of a fixed amount of gas are directly related when the volume is kept constant. It is stated as P∝T and can be written as (2): Charles’ Law describes how the temperature and volume of a fixed amount of gas are directly related when the pressure is kept constant. It is stated as V∝T and can be written as (2): This experiment aims to determine how the variables in each of the three laws are related. The hypotheses are: i. For Boyle’s Law: If the pressure of a fixed amount of gas at constant temperature is related to its volume, then changing the volume of the gas will lead to changes in the pressure. To test this hypothesis, the pressure of the gas in an enclosed space will be measured following decremental changes in the volume of the gas. ii. For Gay-Lussac’s Law: If the pressure of a fixed amount of gas at constant volume is related to its temperature, then changing the temperature of the gas will lead to changes in the pressure. To test this hypothesis, the pressure of a fixed amount of gas will be measured following incremental changes in the temperature of the gas. iii. For Charles’ Law: If the volume of a fixed amount of gas at constant pressure is related to its temperature, then changing the temperature of the gas will lead to changes in the volume. To test this hypothesis, the volume of a fixed amount of gas will be measured following incremental changes in the temperature of the gas. Methods Experiment 1: Boyle’s Law The apparatus was set up as shown in Figure 11-1 on the manual. The plunger in the setup was adjusted so that the volume of air trapped in the barrel of the syringe was 55 mL. The LabQuest instrument was connected to the pressure sensor and its units changed to atmospheres (atm). The syringe was then attached to the valve of the gas pressure sensor. Using the clamp handle to adjust the volume of the gas in the syringe, the volume was reduced by approximately 5 mL. The values of the new volume and pressure were recorded down. The step of volume reduction was repeated until 7 measurements of volume and pressure had been obtained. The volume values obtained were then converted to L. The pressure sensor was then disconnected. A plot of pressure (dependent variable) against volume (independent variable) was drawn and then used to determine the relationship between the two variables. Experiment 2: Gay-Lussac’s Law. The apparatus was set up as shown in Figure 11-2 on the manual. The LabQuest instrument was turned on and set up to measure the pressure (atm) and temperature (Kelvin). A 25-mL Erlenmeyer flask was obtained and tightly sealed with a one-holed rubber stopper. Caution was observed to ensure that the stopper and the neck of the flask were dry. The sealed flask was then connected to the pressure sensor using the tubing provided. An ice-water bath on approximately 273K was created in a 400-mL beaker. This was stirred to ensure uniform temperature. The flask and the temperature probe were placed in the ice-water bath. The other end of the connected tubing was hooked up to the pressure sensor after the pressure sensor had been immersed in the ice-water bath for 2 minutes. The water bath was periodically stirred while the pressure stabilized. After stabilization, the pressure and temperature were recorded down. The temperature of the water bath was varied using hot and cold water, as well as ice. After a variation of approximately 10K, the pressure and temperature readings were recorded down. This variation was repeated, starting from the coldest bath and then working up as the temperature rose, until 4 more measurements had been recorded. After each measurement was taken, the bath was stirred until the pressure stabilized. The apparatus was then disassembled. A plot of pressure (dependent variable) against temperature (dependent variable) was drawn and then used to determine the relationships between the two variables. Experiment III: Charles’ Law. The apparatus was set up as shown in Figure 11-3 on the manual. The LabQuest instrument was then set up to measure pressure (atm) and temperature (Kelvin). The tubing was connected to the bottle. An ice-water bath was prepared and the mixed well to ensure that a uniform temperature is achieved. The utility clamp was adjusted to that the syringe and bottle were just above the top of the cooler and the bottle and most of the cooler were immersed in the water. The temperature probe was inserted through the middle of the clamp. The other end of the tubing was connected to the pressure sensor after the bottle had been immersed in the ice-water bath for 2 minutes. The bath was stirred to allow the pressure to stabilize. After stabilization, the initial pressure was recorded. The temperature of the water bath was varied using ice, and hot and cold water. After a variation of approximately 10K, the pressure and temperature readings were recorded down. This variation was repeated, starting from the coldest bath and then working up as the temperature rose, until 4 more measurements had been recorded. The bath was adjusted with the hot or cold water to maintain the desired temperatures. The apparatus was immersed in each of the water baths prepared, allowing the pressure to stabilize while stirring. Using the plunger, the pressure was adjusted until the pressure returned to the pressure initially recorded. This was repeated until all five volume-temperature measurements had been made. To obtain V bottle (for use in V total­ = V bottle + V syringe + V tubing), the bottle was filled with water and stoppered. The stopper was removed and the contents poured into a 100-mL graduated cylinder. The volume obtained was recorded. Using V tubing = 4.0 mL, the recorded volume data obtained in the previous steps were adjusted to calculate V total. All volumes were converted to L from mL. A plot of volume against temperature was then drawn. Results Experiment I: Boyle’s Law Initial volume (V1) = 0.055 L (1/V = 18.18) Initial pressure (P1) = 0.9801 atm Vol (L) (1/V) V2 = 0.050 (20.00) V3 = 0.045 (22.22) V4 =0.040 (25.00) V5 = 0.035 (28.57) V6 = 0.030 (33.33) V7 = 0.025 (40.00) Pressure (atm) P2 = 1.0653 P3 = 1.1845 P4 = 1.3238 P5 = 1.5003 P6 = 1.7267 P7 = 2.0600 Figure 1 : Graph of pressure against 1/Volume From the curve, the equation is y=mx+b. Since the y-intercept = 0, it becomes: P = m(1/V) + 0 Therefore PV=m K1 =0.0539 K2 = 0.0533 K3 = 0.0533 K4 = 0.053 K5 = 0.0525 K6 = 0.0518 K7 = 0.0515 Kaverage = 0.0527 This differs from the m value obtained in the curve (0.266). Variance = 6.486x10-7 Standard deviation = 6.486x10-7 = ± 8.0533x10-4 Experiment II Initial temperature (T1) = 273.3K Initial pressure (P1) = 0.9375 atm Temperature (K) T2 = 283.5 T3 = 293.1 T4 = 303.6 T5 = 313.3 Pressure (atm) P2 = 0.9684 P3 =0.9961 P4 = 1.0284 P5 =1.0585 Figure 2: Graph of pressure against temperature Using n = 1, and m = 0.003, then using Gay-Lussac’s Law, the equation below is derived: P = m(T)1 From the graph, m = 0.0030. This can be proven by using the formula K=P/(T)n. n can be ignored since a value of 1 is used. Using the initial temperature and pressure yields a value of K of (0.9375/273) = 0.0034. The other values of K are: K2 = 0.0034 K3 = 0.00339 K4 = 0.00339 K5 =0.00337 Kaverage = (0.01695/5) = 0.00339 Variance = (1.0x10-5)2+(1.00x10-5)2+(-2.00x10-5)2+ 0 + ) = 6.0x10-10/5 = 1.20x10-10 Standard deviation = = ±1.0950x10-5 The values obtained by calculation are similar to the value of m (0.003) obtained by finding the slope of the plot of pressure against temperature. Experiment III Initial pressure (P1) = 1.0040 atm Initial temperature (T1) = 275.4 K Vsyringe (1) = 0.00 L Vbottle = 0.069 L Vbottle + Vtubing = 0.072 L. Using V total­ = V bottle + V syringe + V tubing Pressure (atm) P2 = 1.0087 P3 = 1.0066 P4 = 1.0044 P5 = 1.0049 Temperature (K) T2 = 285.9 T3 = 295.2 T4 = 305.4 T5 = 314.3 Vsyringe (L) 0.001 0.0011 0.0012 0.0015 Vtotal (1) = 0.072 Vtotal (2) = 0.073 Vtotal (3) = 0.0731 Vtotal (4) = 0.0732 Vtotal (5) = 0.0735 Plotting Vtotal against temperature: Figure 3: Graph of volume against temperature The equation is y=mx+b. b= 0 since y-intercept is 0. y = V, x = T. Therefore V = mT. Since the number of moles (n) is assumed to be constant at 1, the equation can be written as V=m(T)n. From the graph, m = 0.02. K can be calculated by: K = Vtotal/T. Using this, the value of K is: K1 = 0.000252 K2 = 0.000256 K3 = 0.000248 K4 = 0.00024 K5 = 0.0002333 Kaverage = 0.000246 Standard deviation = 8.717x10-6 Discussion The results obtained showed that for Boyle’s law, plotting a graph of pressure against volume resulted in a non-linear curve. This was overcome by using values of (1/Volume) instead of volume, resulting in a straight curve drawn above. This curve gave an m value of 0.266 that differs from the Kaverage value (0.0527). The results obtained proved that the pressure that was exerted by the fixed amount of gas used in the experiment at a constant temperature in inversely related to the volume it exerted (1). As the volume decreased, the pressure exerted rose. This proved that the hypothesis set out at the start of the experiment was correct. The relationship between pressure and volume is inverse, thus the equation is PV = m PV = 0.0527 For trial 2: 0.05x1.0653 = 0.0533 For trial 3: 0.045x1.1845 = 0.0533 The equation can be rewritten as P1V1 = P2V2 For Gay-Lussac’s Law, the results obtained showed that the pressure exerted by the fixed amount of gas at a constant volume is directly related to the temperature. For every rise in temperature there was also a rise in the pressure exerted by the gas (1). The plot drawn showed that the m value was 0.003, a value close to the one obtained by finding the average of the K values of the pairs of parameters in the experiment (Kaverage = 0.00339). The direct relationship between the pressure and temperature proved that the hypothesis set out to achieve at the start of the experiment was achieved. The relationship between pressure and temperature is direct, thus the equation is P/T = m P/T = 0.00339 For trial 3: 0.9961/293.1 = 0.00339 For trial 4: 1.0284/303.6 = 0.00339 The equation can be rewritten as: . For Charles’ Law, the results obtained showed that the volume of the fixed amount of gas at the constant pressure is directly related to the temperature it is exposed to. The plot revealed a straight curve with an m value of 0.02. This value differs from the Kaverage value of 0.000246. This difference can be attributed to experimental errors resulting from improper measurement reading. The hypothesis was successfully proven because the results obtained showed that the changes in the temperature brought about changes in the volume of the gas (2). The relationship between volume and temperature is direct, thus the equation is V/T = m V/T = 0.000246 For trial 3: 0.0731/295.2 = 0.000248 For trial 4: 0.0732/305.4 = 0.00024 The equation can be rewritten as: Conclusion The three experiments successfully proved all the hypotheses set out at the start. Experiment I proved that the pressure exerted by the gas is inversely proportional to the volume it occupied. This can apply to other gases as well, provided the temperature is maintained constant. The graph drawn was a best fit one, indicating that the results obtained contained errors. These errors may have arisen from the improper use of the instruments as well as errors brought upon by the environmental factors. For Experiment II, it was proven that the volume of the fixed amount of gas at the constant pressure is directly related to the temperature it is exposed to. This can apply to other gases as well. The relationship between the volume of a gas and the temperature was shown to be direct, as per the results from Experiment III. References x Moritmer, R. G. Behavior of Gases and Liquids. In Physical Chemistry, 3rd ed.; Academic Press, 2008; pp 4-5. Meyer, S. Gases and Their Properties, Illustrated ed.; The Rosen Publishing Group, 2011. x Read More