MOLAR VOLUME OF A GAS

Transcription

1 1 MOLAR VOLUME OF A GAS INTRODUCTION Any substance can exist in any phase, solid, liquid or gas, depending upon the conditions surrounding the substance. We are accustomed to certain substances existing in one particular state since we normally observe matter in a narrow temperature and narrow pressure range. Temperatures of our everyday system, the earth, usually range from 0 o C to l00 o C, sometimes lower, sometimes higher. Normally barometric pressure is about 760 mm Hg (or 1 atm). Therefore, when we handle a piece of aluminum metal, it is in the solid state. However, aluminum melts to become liquid and boils to become gaseous just like everything else. Most of us have not seen liquid aluminum, since it melts at 660 o C, a temperature we do not experience often. Aluminum boils at a temperature over 2400 o C. On the other hand, when we think of oxygen, we think of a gas. At the normal conditions of our planet, oxygen is a gas. However, it can be liquefied (condensed) and even frozen. The condensation point of oxygen is -183 o C; the freezing point is -2l8 o C. The phase of a particular sample of matter depends on temperature and pressure. A solid is said to have a definite volume and a definite shape. To understand what this means, imagine taking a small cube of wood, a solid, having dimensions 5.1 cm (2.0 in) on a side. If we put this solid block into a beaker, its volume does not change to fill up the beaker, nor does its shape change to fit the inside of the beaker. The solid has a definite, unchanging shape and volume. Examination of the particles that make up a solid shows that they are very closely packed. There are significant forces of attraction that bind these particles together. A liquid, too, has a definite volume. When we put 10 ml of water into a 250 ml flask, the volume does not expand to fill the flask. A liquid's volume is fixed. However, the liquid does take on the shape of its container. Its shape is indefinite. Forces holding the particles together in the liquid phase are not as strong as they are for the solid phase. Liquid particles are a bit freer to move about. Compare, for instance, solid and liquid H 2 0. Water that comes from the sky during a rainfall will flow down a street quite readily once it hits the earth. However, should that water freeze, either before or after it hits the earth, it does not readily flow. In fact, it has to be moved. Otherwise, roads are impassable and school has to be cancelled. Gases are the least definite state of matter. A gas always fills its container. Chlorine gas, for example, released in the back of the room will spread out to fill it up. And, like liquids, the shape of the gas is the shape of its container. Both the volume and the shape of a gas sample are indefinite.

2 2 Particles in the gas phase have very weak, almost negligible, forces of attraction for one another. As a consequence, each individual gas particle is essentially on its own. Gas particles are in constant motion. Their movement is best described as random. In the gas phase, all matter exhibits remarkably similar physical behavior. What can be said of oxygen gas, for example, applies to nitrogen gas, as well as carbon dioxide gas, as well as helium gas, etc. One such physical trait is the relationship between the pressure and volume of a gas. As the volume of a gas is decreased, its pressure increases. (Such a relationship is called an inverse proportionality.) Another common characteristic of gases is that one mole of any gas occupies the same volume as one mole of any other gas, if both gases are at the same temperature and pressure. When that temperature happens to be 0 o C and the pressure happens to be 1 atm, then the volume occupied by one mole of a gas is 22.4 liters. Zero degrees Celsius (or 273 K) is defined as standard temperature, and one atmosphere (or 760 mm Hg) is defined as standard pressure. The volume occupied by one mole of a gas is called molar volume. Therefore, the molar volume of a gas at standard temperature and pressure (STP) is 22.4 L. The physical behavior of gases is summed up in the Ideal Gas Law, PV = nrt (Eq. 1) where P = pressure, V = volume, n = number of moles, and T = temperature. Any correct units may be used for P and V. T must always be in Kelvins; n must be in moles. R is a proportionality constant. If P is expressed in atmospheres, and V in liters, then the value of R is L atm mol -1 K -1 (or L atm/mol K). The numerical value of R is different when different units are used for P and V. The Ideal Gas Law is obeyed by gases at temperatures and pressures close to the normal conditions for earth. When conditions differ significantly from normal, most gases cease to behave "ideally." Gas behavior deviates from the Ideal Gas Law at high pressures and/or at low temperatures. Under these conditions, there are significant attractive forces between the particles. Also, under normal conditions, the size of each individual gas particle is insignificant since the molecules are so far apart (constant, random motion). At high pressures and/or low temperatures, the particles are closer together. Not only do attractive forces now matter, but the volume of the particles matters as well. To compensate for these factors, several adjustments are made to the Ideal Gas Law. Factors a and b are introduced. The resulting equation governs gas behavior under all conditions. 2 an P+ 2 ( V-nb ) =nrt V (Eq. 2) Note that the right side of the equation looks exactly like the Ideal Gas Law. The left side has P and V with their "correction factors." This equation is called the van der Waals gas law.

3 3 PURPOSE The purpose of this lab exercise is to determine the molar volume of a gas at STP, and to compare it with the accepted value. We will not adjust the conditions of the lab to be STP; most people find 0 o C a bit uncomfortable for lab work. Instead, we will perform the experiment at the conditions of the lab, whatever they are. Then we will use the Ideal Gas Law to convert our results to what we would have found, had we done the experiment at standard conditions. To accomplish our goal, we must know the number of moles of gas in a certain volume. The gas we will use is hydrogen, H 2. First, we will make the hydrogen in a reaction between hydrochloric acid and magnesium. By a stoichiometry calculation, the number of moles of hydrogen produced can be determined from the mass of magnesium ribbon that reacts. The volume of this hydrogen will be measured directly, using an instrument called a eudiometer. In addition, temperature and pressure must be measured as well. Since the volume of hydrogen is being measured over water, there will actually be two gases in the eudiometer; H 2 (from the reaction) and H 2 O (evaporated from the liquid water in which the reaction is done). While the water vapor does not affect the volume of the hydrogen gas, it does have an effect on pressure. When we measure the pressure of the gas, we will actually be measuring the total pressure of the hydrogen gas/water vapor mixture. Dalton's Law governs the pressure of a gas mixture. P total = P A + P B + P C + etc. (Eq.3) Since our mixture contains only two gases, the form of Dalton's Law we must use is: P total = P hydrogen gas + P water vapor (Eq. 4) Water vapor pressure is related to temperature. Consult a table of temperature and water vapor pressure values to use Equation 4. Once we have a list of temperature (T 1 ), pressure (P 1 ), and volume (V 1 ) for our number of moles of hydrogen (n 1 ), we can find the volume (V 2 ) that one mole (n 2 ) would occupy at STP (T 2 and P 2 ) using this form of the Ideal Gas Law, also known as the Combined Gas Law, or General Gas Law: PV 1 1 PV 2 2 = (Eq. 5) nt nt

4 4 PROCEDURE 1. Record the atmospheric pressure in the lab as measured by the lab barometer. 2. Fill a 400-mL beaker with about 350 ml of tap water. Add 4 or 5 drops of blue food coloring. Place a clamp on a ring stand. Set the beaker and ring stand aside. 3. Obtain a piece of magnesium ribbon, about 3-5 cm in length. Weigh the magnesium ribbon on an analytical balance to the nearest g. 4. Roll the magnesium, or fold it over so that it will easily fit into the gas eudiometer to be used in the experiment. Tie a piece of thread to the magnesium. NOTE: A eudiometer (or "gas buret") is used to measure the volume of a gas as it is formed in a reaction. The closed end is the top. We will fill the eudiometer with water. As the gas is formed, it goes to the top, where it is trapped, and displaces the water. The volume of the gas (in ml) call be read from the scale on the eudiometer. 5. Measure out 10 ml of 3.0 M hydrochloric acid in a graduated cylinder. Pour it into the eudiometer. Hydrochloric acid is the excess reactant in this reaction, so it is not crucial to record the exact amount used. 6. Now fill the rest of the eudiometer with water from your beaker. Hold the eudiometer on a slant (45 o angle) while you do this. Add the water slowly so as minimize the mixing of acid and water. Also avoid allowing air bubbles into the tube. The water should overflow so that the entire eudiometer is filled with liquid. 7. Place the folded magnesium into the eudiometer, about 3-4 cm from the open end. The thread should hang out. Place a one-holed rubber stopper into the eudiometer. Fill the hole with water. 8. THIS STEP MUST BE DONE CAREFULLY. AVOID AIR BUBBLES. Place a finger over the hole in the stopper and turn the eudiometer over. Quickly place it into the water in the 400 ml beaker. Do not release your finger until the bottom of the eudiometer is fully submerged in the water. Support the eudiometer with the clamp on the ring stand (see Figure 1). 9. Now watch. You may be able to see the Figure 1

5 5 acid moving down the eudiometer. The blue food color turns yellow in the presence of acid. Within several minutes, acid will reach the magnesium metal. When it does, the reaction will begin. As hydrogen gas is formed, it bubbles up and displaces water, which flows out of the hole in the stopper and into the beaker. Allow the reaction to proceed until the magnesium is consumed and the bubbling ceases. Position yourself so your eye is at the same level as the bottom of the beaker. What do you see in the bottom of the beaker? Why does this occur? 10. Place the thermometer in the beaker and measure the temperature of the water. Since the hydrogen gas bubbled through the water, we will assume that the temperature of the hydrogen gas (the value we need to know for our gas law calculation) is equal to the temperature of the water. 11. THIS STEP MUST BE DONE CAREFULLY. AVOID AIR BUBBLES. Place a finger over the hole in the stopper and transfer the eudiometer to a 1000 ml cylinder filled with water. Do not release your finger until your finger and the stopper are well into the water in the cylinder. 12. Move the eudiometer up and down in the cylinder until the level of the water in the cylinder is exactly the same as the level of the water inside of the eudiometer (see Figure 2). You might notice that the volume of the hydrogen gas in the eudiometer changes as you move the tube up and down in the cylinder. When the water levels are the same, the pressure of the gas in the eudiometer equals the pressure of the gas (air) in the lab. Record the volume of the gas in the eudiometer. Remember, the eudiometer actually contains two gases now, hydrogen from the reaction and water vapor. gas (H 2 + H0 2 vapor) P gas < P P > P air gas air P gas = Pair Figure Remove the eudiometer from the cylinder.

6 6 CALCULATIONS 1. The temperature of the hydrogen gas may be assumed to be the same as the water temperature. 2. This is just the mass of magnesium ribbon that you weighed in step 3 of the procedure. 3. Calculate moles of magnesium from the mass of magnesium. 4. Calculate moles of hydrogen stoichiometrically from the moles of magnesium used (calculation 3) and the balanced equation for the reaction. 5. Assume that the total pressure of the gas mixture (H 2 and water vapor) in the eudiometer is the same as the atmospheric (barometric) pressure, in mm Hg. Don t forget to apply Dalton s Law to find the partial pressure of just the hydrogen gas mm Hg = kpa. 6. Volume of hydrogen gas collected, in L. (HINT: Look at Data line 4 and the units.) 7. Use the combined gas law (Eq. 5) to calculate the volume in liters of 1 mole of hydrogen gas at STP. 8. Use Eq. 6 to calculate the percentage error in your determination. 9. Use your experimental data to calculate a value for R, the ideal gas constant, including correct units.

7 Name MOLAR VOLUME OF A GAS Lab Report Partner 7 DATA 1. Temperature of H 2, o C 2. Barometric pressure of the lab, mm Hg 3. Mass of magnesium ribbon, g 4. Volume of H 2 gas collected, ml 5. Vapor pressure of H 2 O, at recorded temp., in mm Hg (760.0 mm Hg = kpa) CALCULATIONS Show your work clearly for these calculations on another sheet of paper which should be turned in with your report. 1. Temperature of H 2, K 2. Mass of magnesium used, g 3. Moles of magnesium used, mol 4. Moles of H 2 produced, mol 5. Pressure of H 2 gas collected, mm Hg 6. Volume of H 2 gas collected, L 7. Now that you have determined P, V, n and T for the sample of hydrogen you produced in the lab at lab conditions, determine the volume that one mole of a gas would occupy at STP. Molar volume of H 2 at STP, L 8. Percentage error The percentage error tells us how close a measured value is to an accepted value, and is calculated by this equation: experimental value - accepted value percent error = x 100 (Eq. 6) accepted value 9. Experimental value for R

8 8 MOLAR VOLUME OF A GAS Pre-Lab Assignment Name Section 1. To generate H 2 gas in this experiment, magnesium metal will be reacted with hydrochloric acid. A. Write the balanced equation for this reaction. B. Classify the reaction as combination, decomposition, single displacement or double displacement. 2. A student performed this experiment, using 25.0 ml of 4.5 M hydrochloric acid and g of magnesium. The barometric pressure of the lab was mm Hg and the temperature of the hydrogen was 22.0 o C. The volume of hydrogen collected was ml when the eudiometer was placed in a tall cylinder, as in Figure 2. (NOTE: Water vapor pressure at 22.0 o C is mm Hg.) A. What was the limiting reagent in this reaction? B. Based on your answer to part A, perform a stoichiometry calculation to find how many moles of hydrogen gas were produced. C. Using this student's work, find the volume of one mole of H 2 at STP. (HINT: Make a list of everything you know before you decide which gas law to use.) Last revised 10/5/2015 DN D. What is the student's percentage error?