# Using the Ideal Gas Law

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1 Lab 9 Using the Ideal Gas Law

2

3 Using the Ideal Gas Law Learning Objectives Determine the relationship between pressure and temperature Understand how to use Charles s Law Understand how to use the Ideal Gas Law Introduction Earth, fire, water, and air (Figure 1) made up the known elements in the ancient world that philosophers such as Aristotle and Plato observed. Aristotle believed that different combinations of these elements filled all of space, and that air, being a light substance, moved outwards away from the universe s center. Today, scientists know that Earth s gravity attracts particles and gases in the air towards the planet, making the air denser as it approaches the surface. Figure 1. Air consists primarily of nitrogen (78%) and oxygen (21%). Properties of Gases Isaac Beeckman (17th century) was one of the first people to realize that air had real substance. He speculated that air had weight, pressed down on objects on Earth, and was expandable. In this way, gases have several unique properties. For example, a gas expands spontaneously to fill its container, and the volume of a gas equals the volume of the container in which it is held. Gas is also highly compressible. When pressure is applied to a gas, its volume readily decreases. To further understand the properties of gases, it is important to appreciate temperature, pressure, and volume.

4 Using the Ideal Gas Law Temperature Temperature (T) is the property of matter which reflects the kinetic energy of the particles. There are several standardized scales used to measure this value (e.g., Kelvin, Celsius, and Fahrenheit). An increase in temperature means an increase in the motion of atoms in a material (Figure 2). Gas particles move past one another with little restriction, this is why gases occupy an entire container or space, while liquids and solids have a confined volume and surface area. Pressure Pressure (P) is defined as the amount of force gas molecules exert on the area of space they fill. If you have ever had low tire pressure due to cold weather, it was because the gas molecules that fill, were moving slower. Therefore, they did not exert as much force on the inside of the tire as they normally would (Figure 2). Changing a container s volume can also change pressure. Figure 2. When temperature decreases, molecules move slower. This decrease in velocity reduces the force applied to the tire causing a less inflated tire. Atmosphere Atmosphere refers to the gases surrounding a star or planet held in place by gravity as seen in Figure 1. Atmosphere is also a unit of pressure. One atmosphere is defined as the pressure caused by the weight of air above a given point. Normal atmospheric pressure at sea level is 14.7 pounds per square inch (lb/in2). In chemistry and in various industries, the standard pressure that is used is one atmosphere (1 atm). Volume Volume (V) is simply the amount of space a gas occupies. Pressure decreases when volume increases because the molecules have more space in which they can travel. Pressure increases when volume decreases, because the molecules have less space in which they can travel

5 (Figure 3). Figure 3. When the volume decrease, the pressure increases. Conversely, when the volume increases, the pressure decreases. This is what is known as an inverse relationship and is demonstrated in Boyle s Law (Figure 5). Gas Laws There are three fundamental gas laws that describe the relationship between pressure, temperature, volume, and amount of gas. Boyle's Law tells us that the volume of gas increases as the pressure decreases. Charles's Law tells us that the volume of gas increases as the temperature increases. Finally, Avogadro's Law tell us that the volume of gas increases as the amount of gas increases. The ideal gas law is the combination of the three simple gas laws. Charles s Law Charles s Law was developed in the 19 th century by Jacques Charles, a French chemist. Charles investigated the variation of volume with temperature for a fixed mass of gas at constant pressure. He found that as temperature decreases, the volume of a gas also decreases (Figure 4). Further, as temperature increases, the volume of a gas also increases. The two variables are directly proportional. The mathematical expression of this is:

6 Using the Ideal Gas Law Figure 4. Point A on the graph represents the initial volume (V1) while Point B represents the final volume (V2). Notice that as the temperature increases the gas expands, thus increasing its volume. Kelvin Charles is also credited with discovering that all gas law equations must be calculated in Kelvin. Kelvin is a temperature scale designed so that zero degrees K (written without the degree symbol) is defined as absolute zero. Absolute zero is a temperature in which all molecular movement stops. To convert from Celsius to Kelvin simply add 273. Note that you do not use the degree symbol when temperature is expressed in Kelvin. Example using Charles s Law: The volume of a gas sample is 746 ml at 20 C. What is its volume at body temperature (37 C)? Assume the pressure remains constant. Step 1: Use Charles s Law formula and write down all of the known values of the variables. Initial Volume = V1 = 746 ml Initial Temperature = T1 = 20 C

7 Using the Ideal Gas Law Final Temperature = T2 = 37 C Final Volume = V2 = unknown variable to solve for Step 2: Unit conversion. Step 3: Convert the formula to solve for the desired variable, plug in the known quantities, and calculate the unknown variable. Step 4: Check the logic of the answer. Is the answer reasonable? The final volume is larger than the initial volume. Since the temperature increased from 293 K to 310 K, it is reasonable that the volume of the gas increased. Boyle Boyle s Law is the gas law that relates pressure and volume. Boyle's Law states that when temperature and amount of chemical are held constant, pressure and volume are inversely proportional. In other words, as the pressure increases, the volume decreases (Figure 5). This is mathematically expressed as: Boyle s Law further states that the product of pressure and volume is a constant. This constant is referred to as k.

8 Figure 5. The relationship between the pressure and volume of an ideal gas. With a constant temperature and number of moles, pressure will decrease as volume increases. For example, suppose an experiment begins with a pressure of 1 atmosphere (atm) and a volume of 10 L. In this case, k is equal to 1 atm x 10 L = 10 atm x 1 L. As the experiment proceeds, the pressure increases to 2 atm and the volume decreases to 5 L. As this happens, k will remain the same because 2 atm x 5 L is still equal to 10 atm x 1 L. Therefore, P 1 V 1 = P 2 V 2 is just another way of expressing k = k. Avogadro Avogadro s Law describes the relationship between volume (V) and the amount of gas (n) (measured in moles) when pressure and temperature are held constant (Figure 6). For example, 1L of carbon dioxide will have just as many molecules in it as a liter of nitrogen. The mathematical expression of this is:

9 Figure 6. There is a direct relationship between volume and amount of a gas. As the volume increases, so will the number of moles of the gas. Ideal Gas Law The Ideal Gas Law is a combination of all the simple gas laws (Figure 7). The Ideal Gas Law describes the behavior of real gases as long as the pressure and temperature are not too extreme. The Ideal Gas Law is very valuable when dealing with gases since it establishes a relationship between temperature, pressure, volume, and amount of a gas. Figure 7. An ideal gas is an idealized model of a real gas. The behavior of an ideal gas, that is, the relationship of pressure (P), volume (V), and temperature (T) can be mathematically expressed as:

10 Where: P = the gas pressure in atmospheres (atm) V = the volume of the gas in liters (L) n = the number of moles of the gas R = the constant value of L x (atm/mol x K) T = for the temperature of the gas in Kelvin Example using the Ideal Gas Law: 5.0 g of neon is at 256 mm Hg and at a temperature of 35 C. What is the volume? Step 1: Use the Ideal Gas Law formula and write down all of the known values of the variables. Step 2: Unit conversion (round up).

11 Step 3: Convert the formula to solve for the desired variable, plug in the known quantities, and calculate the unknown variable (round up). Step 4: Check the logic of the answer. Imagine 9.5 two liter bottles of a soft drink all stacked on top of each other. That is the volume (19 L) that was calculated. Hydrogen Peroxide Now that we know how to use the Ideal Gas Law, let us take a look at a couple of real world reagents that can be used in the application of the Ideal Gas Law. Hydrogen peroxide (H 2 O 2 ) is a chemical used in industry and research for its oxidative properties and in medicine as an antiseptic. You may have a bottle of 3% hydrogen peroxide in your medicine cabinet. At room temperature, a water solution of hydrogen peroxide (H 2 O 2 ) will undergo an extremely slow decomposition reaction to form molecular oxygen gas (O 2 ) and liquid water (H 2 O). Since hydrogen peroxide forms oxygen gas when it decomposes, we can use the Ideal Gas Law to observe this decomposition reaction. However, since the reaction will decompose very slowly (weeks) we will use a catalyst. Catalase A catalyst is a substance that speeds up a reaction, without being part of the reaction. Yeast cells contain a catalyst called catalase. Catalase speeds up the decomposition of hydrogen peroxide to water and oxygen (Figure 8). Catalase is very effective at decomposing hydrogen peroxide. In fact, one molecule of the enzyme can catalyze the conversion of over 6,000,000 hydrogen peroxide molecules into water and oxygen every second.

12 Figure 8. Catalase catalyzes the decomposition of hydrogen peroxide to water and oxygen.

13 Pre-Lab Questions Using the Ideal Gas Law 1. Write the balanced equation for the decomposition of hydrogen peroxide. 2. According to Charles s law, what is the relationship between temperature and pressure? 3. Atmospheric pressure depends on the altitude (or height) of your location. How should the air pressure change if you were in Denver, Colorado, which is 1.5 kilometers (1 mile) above sea level? 4. Considering that catalysts are not consumed in a reaction, how do you think increasing the amount of catalyst would affect the reaction rate for the decomposition of hydrogen peroxide.

14 Using the Ideal Gas Law Experiment 1: Charles In this experiment, you will explore the relationship between temperature and volume, and connect this to Charles s Law. Materials 1 Graph Paper Sheet 10 ml Sealable Syringe with Cap (1) 8 oz. Styrofoam Cup Thermometer *Ice *Pencil *Stopwatch/Clock *Tap Water *You Must Provide Procedure 1. Fill the syringe halfway with air, and seal the syringe by screwing the cap on. Record the volume (ml) of gas in the cylinder in Table Use the stopwatch and hold the top of the thermometer up in the air for 30 seconds. Record the temperature of the room in Table Fill one Styrofoam cup with hot water from the sink. Place the thermometer in the cup. LAB SAFETY: Avoid using extremely hot water. Handle hot water carefully. 4. Fully submerge and hold the air-filled syringe in the hot water for thirty seconds. Use the stopwatch to monitor time. 5. Gently push the piston down until the plunger cannot move any farther. Observe the new volume inside of the syringe. Record this volume and the water temperature in Table Prepare a cup full of water mixed with ice. Repeat Step 4-5 for the cold water bath.

15 Record the volume and temperature in Table 3.

16 Table 1 Temperature vs. Volume of Gas Data Temperature Conditions Temperature (ºC) Volume (ml) Room Temperature Hot Water Ice Water Post-Lab Questions 1. Use a pencil and graph paper to create a graph of temperature and volume data. Place temperature on the x-axis (in Kelvin) and volume (ml) on the y-axis. Leave room on the left side of your chart for temperature values below zero. You can also use a graphing program to create your graph. 2. What happened to the volume of gas when the syringe was exposed to various temperature conditions? Using the concepts explored in the Introduction, describe why this occurred, keeping in mind the definition of temperature. 3. Using a ruler, draw a straight line of best fit through your data points, extrapolating the line until it intersects the (negative) x-axis. Why can you assume a linear relationship (a straight-lined slope)? 4. At what temperature does your line intersect the x-axis? What volume corresponds to this temperature?

17 Experiment 2: Using The Ideal Gas Law In this experiment you will use a catalyst to observe the Ideal Gas Law. Materials (1) 250 ml Beaker (1) 500 ml Beaker (1) 250 ml Erlenmeyer Flask 24 in. Flexible Tubing Glass Stir Rod (1) 10 ml Graduated Cylinder (1) 100 ml Graduated Cylinder 10 ml Hydrogen Peroxide, H 2 O 2 Paper Clip (2) Pipettes 3 in. Rigid Tubing Rubber Band Thermometer Stopper with 1-hole Yeast Packet *Clear Tape *Internet *Stopwatch or Clock *100 ml Warm Tap Water *500 ml Distilled Water *You must provide

18 Procedure 1. Prepare the materials for the apparatus as shown in Figure 9. Insert the smaller rigid tubing into one end of the larger, flexible tubing. Insert the free end of the rigid tubing securely into the rubber stopper hole. Caution: Be careful when working with rigid tubing. This tubing is made of glass and can break if excess force is applied. 2. Bend the free end of the flexible tubing into a U-shape, and use a rubber band to hold this shape in place. This will allow you to more easily insert the end of the flexible tubing into the inverted graduated cylinder. Make sure the tubing is not pinched and that gas can flow freely through it. 3. Fill the 100 ml graduated cylinder with distilled water to the 100 ml mark. 4. Fill the 500 ml beaker with 400 ml of distilled water. 5. Take the temperature of the water in the 500 ml beaker, and record it in Table 2. Also, use the internet to determine the barometric pressure in the room, and record it in Table 2. Hint: If necessary, use the regional pressure as a close substitute to the room pressure. This can easily be found online - if necessary, convert this value to atm. 6. Mix 100 ml of warm water (45 C) and one packet of baker s yeast in a 250 ml beaker. This will activate the yeast from the dormant (dry) state. Be sure to mix well with a glass stir rod until the yeast is completely dissolved. Hint: Water must be between C otherwise you will kill the yeast (e.g., no activation). 7. Use a 10 ml graduated cylinder and pipette to measure out 5 ml of hydrogen peroxide. Pour the hydrogen peroxide into the Erlenmeyer flask, and securely place the stopper with stopper tube into the top of the Erlenmeyer flask.

19 8. Clean the 10 ml graduated cylinder by rinsing it at least three times with tap water. Dispose of the rinse down the drain. 9. Cover the opening of the graduated cylinder with two or three fingers and quickly turn it upside down into the 500 ml beaker already containing 400 ml of water. DO NOT remove your fingers from the opening until the graduated cylinder is fully submerged under the water. If the amount of trapped air exceeds 10 ml, refill the cylinder and try again. 10. Insert the U-shaped flexible tubing into the beaker, and carefully snake it into the submerged opening of the graduated cylinder. You want as little air as possible to be in the graduated cylinder. 11. Secure the graduated cylinder to the beaker by bending a paper clip around the graduated cylinder and using a piece of tape to hold it in place. 12. With the cylinder vertical, record the volume of air inside (the line at which the water reaches in the cylinder) in Table 2.

21 Table 2 Temperature, Pressure and Volume Data Temperature of Distilled H 2O: Room (or regional) Pressure (atm): Initial Volume of Air (ml) Final Volume of Air (after reaction) (ml) Volume of O 2 Collected (Final Volume - Initial Volume) Table 3 Reaction Time Data Time Reaction Started Time Reaction Ended Total Reaction Time Post-Lab Questions 1. What would happen if you added more than five ml to the H 2 O 2? 2. What would happen if you added more than 5 ml H 2 O 2 to the 5 ml of yeast? 3. What was going on in the graduated cylinder as the H 2 O was pushed out?

22 4. How would the number of moles (n) of O 2 change if your atmosphere was doubled and all other variables stayed the same? 5. How would the number of moles (n) of O 2 change if your temperature was doubled and all other variables stayed the same? 6. In this experiment, the temperature of the gas evolved is equal to the temperature of the water in the beaker, which ideally should be the same as the air temperature. Explain how the volume of oxygen evolved would change if you used ice water instead of room temperature water. How would it change if you used boiling water?

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