Experiment 10 - Ideal Gases
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Experiment 10 – Gas Laws Name __________________ Lab Section __________________ Experiment 11 – Gas Laws Introduction An ideal gas is one that behaves ideally. That is to say that one can predict its behavior under a certain set of circumstances. For instance, intuition tells us that if you heat up a balloon, it will become larger. The balloon behaves as predicted because the gas inside it is acting as an ideal gas. The conditions for a gas to behave ideally are that it must be at relatively high temperatures and low pressures. If the temperature is too low for that particular gas, or the pressure too high, then it will deviate from predictable behavior. Thankfully, though, most of the gases that we deal with on a regular basis are ideal, and we can predict how they will behave. Ideal gases are governed by the Ideal Gas Equation: PV=nRT Where P is the pressure in atmospheres, V is the volume in liters, n is the number of moles of πΏ·ππ‘π gas, T is the temperature in Kelvin, and R is the gas constant, 0.08206 πππ·πΎ. If you know any three variables in this equation (because R is always given) you can determine the fourth. For instance, if you knew the pressure, volume and temperature of a gas, you could determine the amount, in moles, of that gas. This is precisely one of the things you will determine in this experiment. An interesting consequence of the equation above is that if the amount of gas remains unchanged, that is to say that the number of moles of the gas remains constant, but the conditions change, you can predict just what that change would be. Rearranging the ideal gas equation to put all constants on one side, we see: ππ = ππ = ππππ π‘πππ‘ π What this means is that any conditions of pressure, volume, and temperature will equal this same constant, nR, as long as the amount of gas remains unchanged. As a result, this equation can be rewritten such that two different sets of conditions, each equaling the constant, are now equal to one another. The subscripts denote the two conditions: conditions 1 and conditions 2. π1 π1 π2 π2 = π1 π2 Using this equation, you can predict how the gas will behave if you change one or more variables. For instance, if you knew the volume of a gas at a certain pressure and temperature, Experiment 10 – Gas Laws Name __________________ Lab Section __________________ and then changed both the pressure and temperature on that gas, you could predict the new volume that the gas would occupy. Measuring the volume of a gas poses and interesting problem, however. If you are doing a reaction that produces a gas, and you want to measure how much gas is produced, how do you capture the gas so you can determine its volume? The answer is: you collect it in a vessel over water. You take a container, fill it with water, invert it into a larger container with water, and bubble the gas into the container. The gas will begin to fill the container, pushing the water out from the container. The amount of gas that is pushed out of the container is the amount of gas produced. There is, however, an issue that must be addressed in order for this method to work properly: vapor pressure. Vapor pressure is the pressure of a gas over its liquid. In layman’s terms, any liquid wants to have a certain amount hovering above it in the gaseous phase. Once the gas begins to push out the water from the cylinder, water molecules now see an open, gaseous space above them, and some of the water will now go into gas phase to establish a new equilibrium with its vapor. Thankfully, there is a well understood correlation between temperature and the vapor pressure of water. This is given in Table 16.1 in the lab manual. At any given temperature, there will be a certain amount of water present above its liquid. This amount is expressed in terms of the pressure it would exert. By subtracting out the amount of water vapor pressure, the pressure due to the dry gas can be determined. The result of this subtraction means that when doing this experiment, you will know the pressure, temperature, and volume of the dry gas that was produced from a reaction. Knowing these three factors, the amount of gas can be determined. Equipment Needed: 1 – 600 mL beaker (or larger) 1 – Eudiometer 1 – test tube clamp 1 – Rubber Stopper with hole 6M HCl (aq) Copper Wire Magnesium Unknown metal Experiment 10 – Gas Laws Name __________________ Lab Section __________________ Examples 1) A 1.316 g sample of zinc is reacted with excess hydrochloric acid, and the resulting volume of 496.50 mL of gas is collected over water at 24°C with an atmospheric pressure of 767 mmHg. How many moles of the gas were produced? What would be the calculated value for the gas constant, R? ππ (π ) + 2 π»πΆπ (ππ) → πππΆπ2 (ππ) + π»2 (π) First calculate the moles of hydrogen gas produced by the zinc using the above equation: 1.316 π ππ [ 1 πππ ππ 65.38 π ππ ][ 1 πππ π»2 1 πππ ππ ] = 0.02013 πππ π»2 Convert the pressure, volume, and temperature into the units of the gas constant, namely atmospheres, liters, and Kelvin. Subtract out the pressure due to the water vapor (see Table 11.1). In this case it is 24 mmHg, so our actual pressure due to the dry hydrogen gas is 743 mmHg. (24°C = 297K, 743 mmHg = 0.978 atm, 496.50 mL = 0.49650 L) Using PV=nRT and rearranging for R, we get ππ ππ =π (0.978 ππ‘π)(0.49650 πΏ) and plugging in the numbers (0.0213 πππ)(297πΎ) = π. ππππ π³·πππ πππ·π² 2) A 0.101 g sample of a metal was dropped into HCl. If 65.25 mL of H2 gas is collected over water at 21.0°C, and the pressure is 766 mmHg, what metal was dropped into the acid? 2 π (π ) + 6 π»πΆπ (ππ) → 2 ππΆπ3 (ππ) + 3 π»2 (π) First calculate the number of moles of gas using the ideal gas law. Remember to keep proper units and to subtract out the vapor pressure of water, as the gas is being collected over water. 757.2 mmHg = 0.996 atm ππ π = π π n= 21.0°C = 294 K (0.996 atm)(0.06525L) (0.08206 πΏ·ππ‘π )(294 πΎ) πππ·πΎ 65.25 mL = 0.06525 L = 0.002637731 πππ π»2 Use these moles to determine the number of moles of the unknown metal 2 πππ π 0.002637731 πππ π»2 [3 πππ π» ] = 0.0017958487 πππ π 2 Divide the mass of the metal by the moles to determine the molar mass of the metal. Look up the molar mass on the periodic table to determine what it is. 0.101 π π 0.0017958487 πππ π = ππ. ππ π πππ πΏ → X = Fe Experiment 10 – Gas Laws Name __________________ Lab Section __________________ Procedure Magnesium Ribbon Weigh out a sample of magnesium ribbon. Be sure it weighs between 0.035 g and 0.045 g. Record the mass of the magnesium. Put the copper wire through the rubber stopper hole and secure the magnesium ribbon to the copper wire on the narrow portion of the stopper. Make sure the magnesium is approximately 2 cm from the end of the stopper so that it protrudes far enough into the solution during the experiment. Bend the end of the copper wire on the larger end of the stopper to secure the wire and magnesium ribbon to it. Fill a 600 mL (or larger) beaker with tap water and ready a test tube clamp on the ring stand to support the eudiometer inside the beaker during the experiment. Pour approximately 7 mL of 6 M HCl into the eudiometer. Gently fill the eudiometer with water using a squirt bottle, taking care not to disturb the HCl on the bottom of the tube. Put the stopper into the eudiometer and invert the tube into the beaker of water. Secure it inside the beaker using the test tube clamp. When the magnesium has fully reacted, try to equalize the liquid heights between the eudiometer and the beaker by raising or lowering the tube within the beaker. This will minimize pressure differences between the atmosphere and the tube. Record the volume of the gas inside the tube. Save copper wire for second run (and future generations). Calculate the ideal gas constant and the molar mass of magnesium Unknown Solid Weigh out a chunk of the unknown solid. It should weigh between 0.030 and 0.050 g. Repeat the steps as before. Calculate the gas constant and the molar mass of the unknown metal. What is it? Post Experiment Instructions: All waste can go down the drain with plenty of water to wash it down. Remember to save the copper wires and return them to their place of origin. Return stoppers to their place of origin. Rinse out eudiometers well and return them to the bin. Experiment 10 – Gas Laws Name __________________ Lab Section __________________ Figure 10: Magnesium on copper wire Figure 10: Inverted eudiometer Table 10.1: Vapor Pressure of Water Temperature (°C) 17 18 19 20 21 22 23 24 25 26 27 28 29 Pressure (mmHg) 14.5 15.5 16.5 17.5 18.7 19.8 21.1 22.4 23.8 25.2 26.7 28.3 30 Experiment 10 – Gas Laws Name __________________ Lab Section __________________ Prelaboratory Questions A 0.075 g sample of calcium is reacted with excess hydrochloric acid at 22.3°C with an atmospheric pressure of 756 mmHg. The resulting gas was collected over water and was measured to be 48.50 mL. How many moles of the gas were produced? What would be the calculated value for the gas constant, R? πΆπ (π ) + 2 π»πΆπ (ππ) → πΆππΆπ2 (ππ) + π»2 (π) 5) A 0.196 g sample of a metal was dropped into HCl. If 80.00 mL of H 2 gas is collected over water at 20°C, and the pressure is 777 mmHg, what metal was dropped into the acid? (vapor pressure of water at 20°C is 17.3 mmHg) π (π ) + 4 π»πΆπ (ππ) → ππΆπ4 (ππ) + 2 π»2 (π) Experiment 10 – Gas Laws Name __________________ Lab Section __________________ Data Tables – Mg with HCl Trial 1 Trial 2 Mass of magnesium ___________ ` ___________ Atmospheric pressure ___________ ___________ Partial pressure of water (see Table 1) ___________ ___________ Pressure of dry hydrogen gas ___________ ___________ Volume of wet hydrogen gas ___________ ___________ Temperature of hydrogen gas ___________ ___________ Calculate the number of moles of dry hydrogen gas for each trial ___________ ___________ Calculate the gas constant, R, for each trial πΏ·ππ‘π ___________ πππ·πΎ πΏ·ππ‘π __________ πππ·πΎ Experiment 10 – Gas Laws Name __________________ Lab Section __________________ Data Tables – Unknown Solid Trial 1 Trial 2 Mass of Unknown ___________ ___________ Atmospheric pressure ___________ ___________ Partial pressure of water (see Table 1) ___________ ___________ Pressure of dry hydrogen gas ___________ ___________ Volume of wet hydrogen gas ___________ ___________ Temperature of hydrogen gas ___________ ___________ Calculate the number of moles of dry hydrogen gas for each trial using the true gas constant ___________ ___________ Calculate the molar mass of Unknown for each trial ___________ ___________ What is the unknown metal? __________ Experiment 10 – Gas Laws Name __________________ Lab Section __________________ Postlaboratory Questions 1) What happens if: The number of moles is doubled, the volume ___________________ The number of moles is halved, the pressure ___________________ The temperature is tripled, the volume ___________________ The temperature is quadrupled, the pressure ___________________ The pressure is doubled, the volume ___________________ The pressure is cut by 1/3, the volume ___________________ 2) Please convert the following pressure units to atmospheres: 457 mmHg 499 torr 115 psi 29.9 inHg 3) If water is placed in a test tube, covered with a piece of stiff paper and inverted, the paper and water will not fall from the test tube. Why does it remain in the test tube? Experiment 10 – Gas Laws Name __________________ Lab Section __________________ 4) Hydrogen peroxide decomposes spontaneously, albeit slowly, to form water and oxygen gas according to the following chemical equation: π»2 π2 (π) → π»2 π (π) + π2 (π) If the H2O2 decomposition is catalyzed by MnO2, the oxygen gas collected over water is 72.5 mL at 756 mmHg and 23°C. Calculate the gas constant, R. What would the molar volume of O2 be at STP? What would the calculated molar mass of H2O2 if the volume of the H2O2 decomposed had been π 70.0 οL? (ο²π» π = 1.45 ππΏ) 2 2 Experiment 10 – Gas Laws Name __________________ Lab Section __________________ 5) A 0.196 g sample of a metal was dropped into HCl. If 80.00 mL of H2 gas is collected over water at 20°C, and the pressure is 777 mmHg, what metal was dropped into the acid? (vapor pressure of water at 20°C is 19 mmHg) π (π ) + 4 π»πΆπ (ππ) → ππΆπ4 (ππ) + 2 π»2 (π)
