Chemistry 11 (Papazyan) Santa Monica College

The Molecular Weight (Molar Mass) of Carbon Dioxide

Objectives The purpose of this experiment is to determine the molecular weight (molar mass) of carbon dioxide based on measurements of the pressure, temperature, volume and mass of a sample of the gas. Once obtained, the experimental molecular weight (molar mass) will be compared to the theoretical molecular weight (molar mass) of carbon dioxide.

Background From the ideal gas law, PV=nRT , it is easy to show that the density of an ideal gas is:

(Eq. 1) = = where M is the “molecular weight” (molar mass) of the gas. This can be solved to obtain: (Eq. 2) = Thus, the molecular weight (molar mass) of a gas can be determined by measuring the temperature , pressure , volume, and the mass of a sample of the gas. In this experiment the molecular weight (molar mass) of carbon dioxide will be determined. The carbon dioxide gas is produced by the reaction of calcium carbonate with hydrochloric acid.

CaCO 3 (s) + 2 HCl (aq) → CO 2 (g) + CaCl 2 (aq) + H 2O (l) The carbon dioxide gas will be collected in an Erlenmeyer flask that is covered with aluminum foil. The foil and the fact that carbon dioxide gas is denser than air inhibit the rate at which the carbon dioxide mixes with the outside air. The temperature of the gas will be measured by briefly placing a thermometer underneath the foil. The temperature of the air will be measured outside of the flask by holding the thermometer near it. Since the flask is not sealed the pressure of the gas in the flask will be equal to the pressure in the laboratory. The laboratory pressure will be measured with a barometer. The volume of the gas is equal to the volume of the flask. The volume of the flask will be measured by filling it to the brim with deionized water. From the measured mass of the water and the known density of water we will determine the volume of the water (thus the volume of the flask.) Tables of densities of water and dry air at various temperatures as well as a detailed description of the calculations involved are given in the following two pages. While normally negligible, the buoyant force due to air displaced by the flask is central to obtain the correct mass of the CO 2 gas because its weight is comparable to the weight of the displaced air (calculated using flask volume and air density.)

Note: since the forces due to weight and air buoyancy are central in this experiment, we will use the term “weight” throughout, with the understanding that ultimately what we obtain will be the mass of CO2 collected. Also note that the force unit here is “gram force” (the gravitational force on 1 gram of mass), making it interchangeable with the mass unit “gram” for the purposes of this experiment.

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Calculations

The mass of collected CO 2 is given by the true weight of CO 2:

(Eq. 3) True weight of CO 2 = (True weight of flask+CO 2) – (True weight of the flask))

True weight of the flask actually equals the weight reading of flask filled with air, because the weight of air in the flask is exactly cancelled by the buoyant force equal to the weight of air displaced by the flask:

Weight reading of flask with air = (True weight of flask) + (Weight of Air) – (Weight of Air)

(Eq. 4) True weight of flask = Weight reading of flask with air

However, when the flask is filled with anything else, we need to correct for the buoyant force due to air, which is equal to the weight of air displaced by the volume of the flask:

Weight reading for flask+CO 2 = (True weight of flask+CO 2) – (Weight of displaced air)

(Eq. 5) True weight of flask+CO 2 = (Weight reading for flask+CO 2) + (Weight of displaced air)

To obtain the true weight of flask+CO 2, we need to calculate the buoyant force due to air first:

(Eq. 6) Buoyant force due to air = Weight of displaced air = (Volume of flask)(density of air)

To calculate the weight of air displaced, we need the volume of the flask, which is equal to the volume of water that would fill it completely:

(Eq. 7) Volume of flask = Volume of water

We obtain the volume water from the true weight of the water:

(Eq. 8) Volume of water = (Weight of water) / (density of water)

Weight of water is the difference between the weight of flask+water and the weight of the flask:

(Eq. 9) Weight of water = (Weight reading for flask+water) – (True weight of the flask)

We are using “Weight reading for flask+water” rather than the “True weight of flask+water” in Eq. 9. We cannot yet correct the weight of the flask+water for air buoyancy because we are trying to calculate the buoyant force itself at this stage. But the percent error introduced into the weight of water (therefore volume of water, volume of flask, and magnitude of buoyant force) is negligible. We now use Equations 9, 8, 7, and 6 to calculate the buoyant force. We can then use Eq. 5 and Eq. 3 to calculate the true weight of CO 2 in the flask. Remember that we should use the largest of the readings (C), (D), and (E) for “Weight reading for flask+CO 2” in Eq. 5.

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The molecular weight (molar mass) of CO 2 is then calculated using Equation 2. The percentage error in the experimental molar mass is given by: Percentage Error = | [(Experimental Value) – (True Value)] / (True Value) | × 100 where “True Value” is the usual “theoretical” molar mass calculated from the molar masses of its constituent elements.

Density of Liquid Water

Temperature, °C Density, g/mL To use the table directly, round the temperature to the nearest 15 0.9991 entry (e.g. 22.4 to 22) 16 0.9989 17 0.9988 Or you can use the actual temperature measurement in the following equation that describes the data: 18 0.9986 19 0.9984 d = 0.9999 + 6 ×10 -5 T – 8×10 -6 T2 + 4×10 -8 T3 20 0.9982 21 0.9980 22 0.9978 23 0.9975 24 0.9973 25 0.9970 26 0.9968 30 0.9957 Information from the CRC Handbook of Chemistry and Physics , 64th ed., 1983-4

Density of Dry Air

Density, g/L To use the table directly, round the temperature and pressure to the nearest entry (e.g. 22.4°C to 22°C, and

P = 750 torr P = 760 tor r P = 770 torr 758.3 torr to 760 torr) T (°C) 17 1.201 1.217 1.233 Or you can use the actual temperature and pressure 18 1.197 1.213 1.229 measurements in the following equation that describes 19 1.193 1.209 1.225 the data: 20 1.189 1.205 1.221

21 1.185 1.201 1.216 d = 0.0913 – 0.00406 T + 0.001572 P

22 1.181 1.197 1.212

23 1.177 1.193 1.208

24 1.173 1.189 1.204

25 1.169 1.185 1.200

Information from the CRC Handbook of Chemistry and Physics , 64th ed., 1983-4

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Procedure

Safety 6 M hydrochloric acid is capable of causing serious chemical burns and blindness and should be handled with care. If the acid comes in contact with your skin immediately rinse the affected area with water for several minutes. As always, you should be wearing your safety goggles.

Materials and Equipment The following items must be obtained from the stockroom.

• A straight piece of glass tubing connected to a piece of rubber tubing

• A two holed rubber stopper with a thistle tube inserted into one hole and a piece of bent glass tubing (connected to a piece of rubber tubing) inserted into the other hole

• A CaCl 2 drying tube

• A piece of aluminum foil that is approximately 15 cm by 15 cm and two 250-mL Erlenmeyer flasks are also needed. Make sure that the rubber stoppers will fit tightly into the mouth of each Erlenmeyer flask. 1. Obtain one of the 250 mL Erlenmeyer flasks. This will be designated as flask B. Make sure that the flask is both clean and dry. Record the mass of the flask and the foil to the nearest 0.001 g using the analytical balance. Note that it is mass (flask + foil + air) that is being measured here. 2. Place about 25 grams of calcium carbonate into the other 250 mL Erlenmeyer flask designated as flask A. Add about 10 mL of water, or enough to cover the chips completely. Insert the two-holed rubber stopper (with the thistle tube and the bent tube) into flask A, making sure that the thistle tube is adjusted so that it is beneath the water but not touching the bottom of flask. The stopper must fit tightly into the flask. Also obtain about 25 mL of dilute (6 M) hydrochloric acid, HCl, in a small, labeled beaker. 3. Assemble the apparatus shown in the figure on Page 4. Insert the straight glass tube (the one that is attached to the flexible tubing but not attached to the one-holed rubber stopper) into flask B by placing it between the foil and the flask and pressing the foil against it to hold it in place. Be careful to fold and shape the foil only as much as necessary since it is fragile and will easily tear. Attach the flexible end of the tubing to the drying tube. The small rubber stopper attached to the bent glass tubing should be inserted into the other end of the drying tube.

4. When all is ready pour 5 –10 mL of the hydrochloric acid into the top of the thistle tube and allow it to run through the tube and into flask A. The reaction should begin immediately as evidenced by gas evolution. Allow the reaction to continue for at least 20 minutes to displace all of the air in flask B with carbon dioxide gas. During this time pay attention to what is happening in flask A; if the gas evolution ceases, add additional HCl solution through the thistle tube. After the 20 minutes remove the tube from flask B (keep the foil in place) and immediately weigh the flask containing carbon dioxide on the analytical balance to the nearest 0.001 g.

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5. Reassemble the apparatus and allow gas evolution to continue and flow into flask B for an additional 15 minutes. Again, weigh flask B (with the foil). The two masses (before and after the 15 minutes) should agree closely (to within 0.005 g). If the mass has increased by more than 0.005 g reassemble the apparatus and continue to collect carbon dioxide gas for an additional 5 minutes then reweigh the flask. Continue this procedure until successive masses agree to within 0.005 g (or until a decrease in mass is observed). • Measure and record the temperature of the carbon dioxide in the flask. • Measure and record the temperature of the air outside, near the flask. • Use the barometer to read the atmospheric pressure. 6. Finally, in order to determine the volume of flask B, fill this flask with deionized water to the brim, wipe any water from the outside of the flask and weigh it, with the foil, to the nearest 0.01 g using the triple beam balance . Next, measure and record the temperature of the water. The volume of water in the flask can now be calculated from the mass and density of water in the flask at the temperature recorded.

Cleanup Neutralize the contents of flask A and any unused HCl by adding solid sodium bicarbonate until the solution no longer fizzes upon addition of additional bicarbonate. Remember that goggles should be worn at all times in the laboratory . This step is best performed in the sink as the flask tends to overflow. Decant off the liquid, leaving any solid marble chips behind. Rinse the chips with water and decant off the water. Pour the chips into the labeled recovery beaker.

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