science

Charles' Law Jacques Alexandre Charles, a French physicist, performed an experiment using a balloon, hot water, and cold water. Based on his observations, he discovered the relationship between the volume and the temperature of gases at constant pressure. He found out that various gases expanded by the same amount when heated through the same temperature interval. Through his observations, he proposed the Charles' Law which states that the Kelvin temperature and the volume of a gas are directly related when there is no change in pressure. InLearning Competencies/ Objectives: At the end of this module, you should be able to: 1. Discuss Gay-Lussac's law, Combined gas law and Avogadro's law 2. Solve problems involving Gay-Lussac's law, Combined gas law and Avogadro's law Sources: Chemistry by Estrella E. Mendoza, Science learner's Material 10, and Chemistry by S. Baguio and R. Butaran Pretest Instructions: Choose the letter of the correct answer and write your answer on the answer sheet. 1. Which gas law states that the pressure of an ideal gas varies directly with the absolute temperature when the volume of the sample is held constant? a. Boyle's law b. Gay- Lussac's law c. Charles' law d. Combined gas law 2. Which gas law is a combination of all gas laws? a. Boyle's law b. Gay- Lussac's law c. Charles' law d. Combined gas law 3. Which of the following properties does not describe a gas? a. Pressure b. volume c. malleability d. temperature 4. The pressure of a gas is directly proportional to the Kelvin temperature. a. If the volume is small c. if the volume is kept constant b. If the mole is larger than d. if the temperature is expressed in degree Celsius 5. If the pressure and temperature of a gas remain constant, the volume will increase if a. the molecular mass of the gas increases b. the number of moles of the gas increases c. the partial pressure of the gas increases d. all of the aboveLesson Boyle's Law The relationship between the volume and pressure of gases at constant temperature was first stated by Robert Boyle during the 16" century, He performed an experiment wherein he trapped a fixed amount of air in the J-tube, he changed the pressure and controlled the temperature and then, he observed its effect to the volume of the air inside the J-tube. He found out that as the pressure is increased, the volume decreases. He finally concluded that the volume of a Robert Boyle (1627-1691) fixed amount of gas is inversely proportional to its pressure at constant temperature. 2Gay-Lussac's Law A temperature-pressure relationship, also known as Gay-Lussac's Law, states that the pressure of a gas is directly related to its Kelvin temperature. This means that an increase in temperature increases the pressure of a gas, and a decreases in temperature decreases the pressure of the gas as long as the volume and the number of moles of the gas remain constant. The ratio of pressure P to temperature T is the same under all conditions as long as the volume V and an amount of gas n, do not change. P1 = Pz T 1 T 2 Where: P, = initial pressure Ti= initial temperature P.= final pressure To= final temperature One example of the practical application of Gay-Lussac's law is the gas contained in a spray of the type commonly used for deodorants, spray nets, insecticides, and paints. Gay- Lussac's says that the pressure of the gas will increase if it is heated. This is why such cans contains warnings against storage above 120" F or 49 F, against incinerateon when empty , or against placing in hot water or near radiators or stoves . These cans built to withstand a certain internal pressure. Beyond that pressure, the can will burst or explode. Sample Problem Acrosol cans can be dangerous when they are heated because they can explode. Suppose a can of insecticide with a pressure of 4.0 atm at room temperature ( 28 .C ) is thrown into a fire. If the temperature of the gas inside the can reaches 400 "C, what will be its pressure ? Would you expect the can to explode if the maximum safe pressure is 8.0 atm? Given: P1= 4.0 atm Ti= 28 C +273 =301 K Ta= 400 "C +273 = 673 K Find : Pa 2this lesson you must take note that among the units of temperature, we always express it in Kelvin (K) temperature. Thus, you need to convert Celsius value to Kelvin, which was named after Lord Kelvin, a Scottish physicist who has identified the lowest attainable temperature known as absolute zero with a value -273.15 "C. To convert Celsius to Kelvin you have to use the equation K-C + 273.15. Charles" Law is mathematically expressed as VoT or V/T - K, where K is proportional constant. For a given sample of gas under two different conditions at a constant pressure, the equation can be written as: V1 Va T 1 T2 Where: Vi = initial volume Ti = initial temperature Va - final volume To= final temperature Sample Problem 1: A sample of carbon dioxide in a pump has volume of 20.5 mL and it is at 40."C. When the amount of gas and pressure remain constant, find the new volume of carbon dioxide in the pump if temperature is increased to 65 C. Initial Case Final Cure 7 2Formula : P1= P2 T 1 T 2 P2 = PITz T1 Solution: P2 = 4.0 atm (673 K) 301 K P2 =8.9 atm Answer: P. - 8.9 atm Since the calculated pressure exceeds 8.0 atm, you can expect the insecticide can explode. Practice Problem A 2.00-L flask contains helium gas at a pressure of 685 torr and a temperature 0 "C. What would be the pressure in the flask if the temperature is if the temperature is increased to 150 .C? Another practical example of Gay-Lussac's law is the pressure cooker. It is cooking vessel made of aluminum or steel with an airtight lid. The accumulated steam increases the pressure and the boiling point of water. The pressure cooker utilizes high pressure to cook food in one-third the time required by conventional methods. The pressure cooker saves fuel by about 50 %. When you heat any sealed metal container with constant volume and a constant amount of gas, the pressure increases. When the pressure increases, the boiling point also increases. Based on this principle, Denis Papin, a French physicist, invented the pressure cooker in 1679. Most of the steam is trapped, and water boils at a higher temperature. If the pressure inside is double the atmospheric pressure, the temperature the cooker can reach is about 120 "C . Pressure cooking is highly recommended for preventing botulism. Pressure cookers of all types must be fitted with safety valves to prevent explosion of the container. 3Boyle's Law states that under a constant temperature when the pressure on a gas increases its volume decreases. In other words, according to Boyle's law volume is inversely proportional to pressure when the temperature and the amount of gas are constant. Va - at constant T and n Where: V-volume, P-pressure, T- temperature and n =amount of gas How will you read the above sited equation? It is read as: The volume of a gas is inversely proportional to its pressure, if temperature and amount of a gas are held constant. It can also be read as: At constant temperature, the volume occupied by a fixed amount of gas is directly proportional to the reciprocal of pressure (I/P). Let's take a look at the equation again and try to change the proportionality sign (o ) with the equal sign ( =). Va at constant (k) P K V = Thus, k = VP P The latter equation is simply read as: The product of pressure and volume is constant. What is the value of V x P in Table 1? Table 1. Data on Volume- Pressure Relationship Trial Volume (L) Pressure (atm) VXP 1 2.0 10.0 12 4.0 5.00 8.0 2.50 16.0 1.25 3Given: V1 = 20.5 mL T, = 40.0C + 273 = 313 K T2 = 65. 0'C+273=338 K Required: V2 Formula: V1 - V1 T1 V, = VITZ T1 Solution: V.= (20.5 mL) (338 K() 313 K V, 6 929 ml 313 V2 = 22. 14 ml. Sample Problem 2: A sample of a gas has a volume of 78.5 mL at 45"C. What volume will the sample occupy at 0'C when the pressure is held constant? Given: V1= 78.5 mL Ti= 45.C + 273 =318 K Ta= 0'C +273 =273 K Required: Vz Formula: V1 V 2 T1 T 2 V2=- VIT 2 T 1 Solution: V2= 78.5 ml (273 K) 318 K 21,430.5 ml 318 = 67.39 mL Answer: Va-67.39 mL 3Activity 1 Solve the problem. A gas was contained in a rigid steel tank having a volume of 7.5 L. At 25 .C , the gas exerted a pressure of 5.173 atm. What pressure will be the gas exert if it is heated to a temperature of 89.6 "C? Given: Find: Formula: Solution: Answer: Combined Gas Law Experiments conducted in the laboratory do not always follow normal conditions. The customary reference point for gases is OC and I atm pressure. These conditions are known as the standard temperature and pressure (STP). To correct the volumes of gases, we multiply the original volume by two factors: the temperature and the pressure. In gas calculation involving more than one change, you must consider each change separately. For example, to determine the new volume when both the temperature and pressure are changed, you have to consider how the volume will change as temperature changes when pressure is held constant. The consider how the volume will change as the pressure changes, assuming temperature is constant, The gas laws may be combined to give P1V1 - P2V2 T 1 T 2 The combined gas law enables you to directly solve for the changes in pressure, volume, or temperature.Were you able to verify the meaning of proportionality constant ? Let us apply the equation you learned about Boyle's Law. Since volume and pressure of the gas can be varied, let P. and V, be the initial pressure and volume respectively and P, and Va be the final pressure and volume respectively . According to Boyle's Law , PV = k therefore: P Vik then P, V1=P2Vz Where: P, = initial pressure Vi = initial volume P. = final pressure Va = final volume Sample Problems: 1. A 17.50mL sample of gas is at 4.500 atm. What will be the volume if the pressure becomes 1.500 atm. with a fixed amount of gas and temperature? Initial Case Final Case At the time temperature Figure 2 http://deped.in/wyRdHOjCharles' Law gives the relationship between volume and temperature if the pressure (P) and the amount of gas (n) are held constant: 1). If the Kelvin temperature of a gas is increased, the volume of the gas increases. (P and n are Constant) 2). If the Kelvin temperature of a gas is decreased, the volume of the gas decreases. (P and n are Constant) This means that the volume of a gas is directly proportional to its Kelvin temperature. Think of it this way, if you increase the volume of a gas and must keep the pressure constant the only way to achieve this is for the temperature of the gas to increase as well. Observe the illustrations in figure I below. Volume (V1) Volume (V2) Temperature (T1) Temperature (T2) Figure 1 Charles Law Experiment The concept of Charles' Law is evident in an inflated balloon that shrinks when placed inside the refrigerator. It is also applied during cold weather, bicycle tires become flat because the air inside the bicycle tires shrink. Shrinking of an inflated balloon and a bicycle tire in a very low temperature show the decrease of volume which explains that the relationship of volume and temperature is directly related at constant pressure.Sample Problem A 30.0 mL bubble is released from a diver's air tank at a pressure of 4.5 atm and a temperature of 15 "C. What is the volume of the bubble when it reaches the ocean surface, where the pressure is 1.0 atm and the temperature is 20 C? Given: P1= 4.5 atm P1= 1,0 atm V1= 30.0 mL TI = 15 . C+273=288 K T:= 20" C + 273 = 293 K Find: Va Formula : P1V1 = PzV2 T1 T2 _PiViTz V2 = P271 V, 4.5 atm(30.0 ml) (293 K) 1.0 atm(288K) V2 = 137.34 mL Answer: V2 = 137.34 mL The combined effect of the decrease in pressure and increase in temperature is an increase in volume. LnGiven: P, = 4.500 atm V1 = 17.50 mL P2 = 1.5 atm Required: V2 Formula: P, V1 = P2V 2 V2 = Pill P 2 Solution: Va _C4.500 atm) (17.50 ml) 1.500 atm V z _78.75 ml 1.500 V2 = 52. 5 mL 2. If 100 mL of H2 gas was collected at 760 mm Hg, what is the new volume of gas when the barometer reads 745 mm Hg at this same temperature? Given: P. = 760 mm Hg VI = 100 mL P:- 745 mm Hg Required: V2 Formula: P, V1 = P2 Vz V2 = PIV, P 2 Solution: V. (760 mmHg)(100 ml) 745 mmHg _76 000 mLL 745 V2 = 102 mL LnActivity 2 Solve the problem. Helium gas has a volume Of 250 mL. at 0'C at 1.0 atm. What will be the final pressure if the volume is reduced to 100 mL at 45 .C? Given: Find: Formula: Solution: Answer. Avogadro's Law In this section, you will consider how the properties of gas change when there is a change in the number of moles or grams. For instance, when you blow up a balloon, its volume increases because of the addition of more air molecules. If a ball is punctured and some of the air leaks out, its volume decreases. Amedco Avogadro in 1811 stated that the volume of a gas is directly related to the number of moles of a gas when temperature and pressure are not changed. This statement of direct relations is called Avogadro's law. If the moles of a gas are doubled, then the volume will double as long as the pressure and temperature remain the same. To illustrate these two conditions, you may write: V1 _ Vz n1 nz Where: V is the volume of gas n is the amount of gas in moles 6Sample Problem A balloon containing 2.00 moles of helium has a volume 880 mL. What is the new volume after 4 more moles of helium are added to the balloon at the same temperature and pressure? Given : VI = 880 mL 1= 2.00 moles na = 6.00 moles Find : Va Formula : V1 - V2 Vinz 880 ml(6.00 moles) 2.00 moles V= = 2, 640 mL Answer: V= = 2, 640 mLActivity 3 Solve the problem A 7.25 L sample of nitrogen gas (Na) is identified to contain 0.75 mole of nitrogen. How many moles of nitrogen gas would there be in a 20.0 L sample provided the temperature and pressure remains the same? Given: Find: Formula: Solution: Answer: Posttest Complete the table below. Summary of Gas Laws Law Statement Equation Constant Boyle's Charles" Gay-Lussac'sPT Activity 3 Avogadro's law Given: Find Formula: Solution: Answer. WW Posttest Complete the table below. Summary of Gas Laws Law Statement Equation Constant Boyle's Charles' Gay-Lussac's 10WW Pretest 1. 2. 3. 4. 5. PT Activity 1 Gay-Lussac's law Given: Find: Formula: Solution: Answer: PT Activity 2 Combined Gas law Given: Find: Formula: Solution: Answer. 9