05 Determining The Molar Volume Of A Gas 6f25

Determination of the Molar Volume of a Gas Avogadro’s law states that equal volumes of gases contain an equal number of molecules under the same conditions of temperature and pressure. It follows, therefore, that all gas samples containing the same number of molecules will occupy the same volume if the temperature and pressure are kept constant. The volume occupied by one mole of a gas is called the molar volume. In this experiment, you will determine the molar volume of the gas produced by the chemical reaction shown below. Mg(s) + 2 HCl(aq) → MgCl2(aq) + H2(g) You will react a known mass of solid magnesium with an excess of hydrochloric acid, in a sealed vessel, and use the pressure change to calculate molar volume at STP.

OBJECTIVES In this experiment, you will  

Measure the gas production of a chemical reaction by a pressure change. Determine the molar volume of the gas produced in the reaction.  Calculate the molar volume of a gas at STP.

Figure 1

MATERIALS Data Collection Mechanism

3.0 M hydrochloric acid, HCl, solution (5 mL per trial)

sand paper or steel wool for polishing Mg ribbon Gas Pressure Sensor Temperature Probe 600 mL or one liter beaker 10 mL graduated cylinder magnesium ribbon, pre-cut (one approx. 15 mm piece per trial)

small beaker for HCl solution ruler (if analytical balance is not available) 125 mL Erlenmeyer flask 20 mL gas syringe plastic tubing with two Luer-lock connectors rubber stopper assembly with two-way valve

Adapted from Advanced Chemistry with Vernier & Laboratory Experiments for Advanced Placement Chemistry by Sally Ann Vonderbrink, Ph. D.

The Determination of the Molar Volume of a Gas

PROCEDURE 1. Obtain and wear goggles. Obtain the 125 mL Erlenmeyer flask that you will use for the experiment. Determine and record the available volume of the flask that the hydrogen gas will occupy as it is produced from the reaction of the solid magnesium and the hydrochloric acid solution. for the following items when you determine the volume of your flask:  A 125 mL flask does not have a volume of precisely 125 mL.  During the experiment, you will seal the flask with a rubber stopper and the stopper will occupy some of the volume of the flask.  You will add 5 mL of solution (3.0 M HCl solution) to the flask. 2. Obtain a piece of magnesium ribbon. Use a piece of sandpaper or steel wool to polish it until it is silver and shiny. Measure its mass on the analytical balance. If one is unavailable, then measure and record its length to the nearest mm. Ask your instructor for the mass of one meter of polished magnesium ribbon, and record this information. Use a simple proportion to calculate the mass of your sample of Mg ribbon and record its value. Place the piece of magnesium ribbon in a clean and dry 125 mL Erlenmeyer flask. 3. Prepare a room temperature water bath in a large beaker. The bath should be deep enough to completely cover the gas level in the Erlenmeyer flask. 4. Set up the data collection system. a. Connect a Gas Pressure Sensor and a Temperature Probe to the interface. b. Start the data collection program. c. Set up data collection for 2 seconds per sample and 150 samples. 5. Use the clear tubing to connect the white rubber stopper to the Gas Pressure Sensor. (About one-half turn of the fittings will secure the tubing tightly.) Twist the white stopper snugly into the neck of the Erlenmeyer flask to avoid losing any of the hydrogen gas that will be produced in the reaction (see Figure 1). Important: Close the valve on the white stopper by turning the white handle so it is perpendicular with the valve stem. 6. Obtain a small amount of 3.0 M hydrochloric acid. CAUTION: Handle the hydrochloric acid with care. It can cause painful burns if it comes in with the skin. Draw 5 mL of HCl solution into the 20 mL syringe. Thread the syringe onto the two-way valve on the white stopper (see Figure 1). Submerge the Erlenmeyer flask into the water bath. Position the Temperature Probe in the water bath so that the tip of the probe is not touching the beaker. 7. With the flask still submerged in the water bath, begin data collection. After about 20 seconds, open the two-way valve directly below the syringe, press the plunger to add all of the 5 mL of HCl solution to the flask, and close the two-way valve. 8. Gently swirl the flask, while keeping it immersed in the water bath, as the reaction proceeds. Data collection will stop after 5 minutes. 9. Carefully remove the white stopper from the flask to relieve the pressure in the flask. Important: Do not open the two-way valve to release the pressure in the flask. 10. Examine the pressure data to determine the change in pressure, ∆P, during the reaction. In addition, determine the mean temperature of the water bath during the reaction. Record these values in your data table. Adapted from Advanced Chemistry with Vernier & Laboratory Experiments for Advanced Placement Chemistry by Sally Ann Vonderbrink, Ph. D.

The Determination of the Molar Volume of a Gas 11. Store or record your data. 12. Rinse, clean, and dry the flask. 13. Conduct two more trials. 14. Use your text, or another appropriate reference, to find and record the water vapor pressure at the temperature of each trial.

DATA TABLE Trial 1

Trial 2

Trial 3

*Mass of Mg (g) Volume of flask (mL) Maximum pressure (atm) Initial pressure (atm) Pressure change, ∆P (atm) Temperature (K) Vapor pressure of water (atm)

PRE-LAB QUESTION A reaction of 0.028 g of magnesium with excess hydrochloric acid generated 31.0 mL of gas. The gas was collected by water displacement in a 22 °C water bath. The barometric pressure that day was 746 mm Hg. (a) Use Dalton’s law and the vapor pressure of water at 22 °C (the table value is 19.8 mm Hg) to calculate the partial pressure of hydrogen gas collected. (b) Use the combined law to calculate the “corrected” volume of hydrogen gas collected at STP. (c) What is the theoretical number of moles of hydrogen that can be produced from 0.028 g of Mg? (d) Divide the corrected volume of hydrogen by the theoretical number of moles of hydrogen to calculate the molar volume (L/mol) of hydrogen at STP.

Adapted from Advanced Chemistry with Vernier & Laboratory Experiments for Advanced Placement Chemistry by Sally Ann Vonderbrink, Ph. D.

The Determination of the Molar Volume of a Gas

POST-LAB QUESTIONS AND DATA ANALYSIS 1. *Calculate the mass of each piece of magnesium that you used if an analytical balance was unavailable. 2. Calculate the number of moles of each piece of magnesium that you used. 3. Calculate the theoretical number of moles of hydrogen gas produced in each trial. 4. Use your results to calculate the molar amount of hydrogen gas that was produced in your reactions. 5. Compare your calculated molar volume, at STP, with the accepted molar volume of an ideal gas at STP, 22.4 L/mol. Calculate the % error for each trial. 6. A student fails to polish each sample of Mg ribbon before massing them. What effect does this error have on the calculated molar volume of hydrogen gas? Mathematically justify your answer. 7. A different student fails to insert the stopper into the flask while determining the available volume of the 125 mL flask. What effect does this error have on the calculated molar volume? Mathematically justify your answer.

Adapted from Advanced Chemistry with Vernier & Laboratory Experiments for Advanced Placement Chemistry by Sally Ann Vonderbrink, Ph. D.

The Determination of the Molar Volume of a Gas

TEACHER INFORMATION 1. This experiment conforms to the guidelines for the fifth laboratory experiment listed in the College Board AP Chemistry guide (the Acorn book). It requires the use of Vernier temperature and gas pressure sensors. A thermometer (preferably digital) may be substituted for the temperature probe. It is suitable for Pre-AP students and is best performed in first-year chemistry. 2. Step 1 of the procedure asks students to determine the volume of the 125 mL flask they will be using. The best technique for establishing the entire reaction volume is for students to insert the rubber stopper-syringe mechanism securely and use a water-proof marker to mark the bottom of the stopper on the outside of the flask. They then remove the stopper and fill the flask to that mark with tap water, reinsert the stopper and make any adjustments (such as using a plastic pipette to add or subtract a few drops of water). They would then insert the stopper to the same depth with each trial. 3. It is best to use an analytical balance with at least 0.001 g accuracy for this lab. If one is not available then polish and cut  15 mm (slightly more than 0.5 inch) sections of magnesium ribbon, which will have a mass of 0.010 g to 0.0150 g. The reaction will produce enough hydrogen gas for a good pressure change in the flask without popping the stopper. 4. The 3 M HCl need not be quantitatively prepared. 3.0 M HCl can be prepared by diluting 249 mL of 12 M HCl to a total volume of 1.0 liter. 5. The magnesium ribbon is the limiting reactant, thus the 5 mL of HCl does not have to be measured precisely. 6. For this experiment, you can use the syringe that is shipped with the Vernier Gas Pressure Sensor. When students are finished using the syringe, they should thoroughly clean it. Students will have to decide which pressure unit to use. They may benefit from a quick review regarding unit conversions. 7. Students will need access to a table of water vapor pressure at different temperatures.

HAZARD ALERTS Hydrochloric Acid: Highly toxic by ingestion or inhalation; severely corrosive to skin and eyes. Hazard Code: A—Extremely hazardous. Magnesium, ribbon: Flammable solid; burns with an intense flame: Hazard Code: C—Somewhat hazardous. The hazard information reference is: Flinn Scientific, Inc., Chemical and Biological Catalog Reference Manual, P.O. Box 219, Batavia, IL 60510, (800) 452-1261, www.flinnsci.com

Adapted from Advanced Chemistry with Vernier & Laboratory Experiments for Advanced Placement Chemistry by Sally Ann Vonderbrink, Ph. D.

The Determination of the Molar Volume of a Gas

SAMPLE DATA TABLE *Mass of Mg (g)

0.012 g

Volume of flask (mL)

146.0 mL

Maximum pressure (atm)

1.07 atm

Initial pressure (atm)

0.991 atm

Pressure change, ∆P (atm)

0.079 atm

Temperature (K) Vapor pressure of water (atm)

296 K 22.1 mm Hg = 0.02777 atm

Answer to PRE-LAB QUESTION A reaction of 0.028 g of magnesium with excess hydrochloric acid generated 31.0 mL of gas. The gas was collected by water displacement in a 22 °C water bath. The barometric pressure that day was 746 mm Hg. (a) Use Dalton’s law and the vapor pressure of water at 22 °C (the table value is 19.8 mm Hg) to calculate the partial pressure of hydrogen gas collected. Ptotal  746 mm = PH2  19.8 mm Hg  PH2   746  19.8  mm Hg = 726 mm Hg (b) Use the combined law to calculate the “corrected” volume of hydrogen gas collected at STP. PV 1 1T2  PV 2 2T1 V2 

 726 mm Hg   31.0 mL   273 K  PV 1 1T2  P2T1  760 mm Hg   295 K 

 27.4 mL or 0.0274 L (c) What is the theoretical number of moles of hydrogen that can be produced from 0.028 g of Mg? From the balanced equation given: Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g) 1 mol Mg  0.0012 mol Mg = 0.0012 mol H 2 mol Mg = mol H2, therefore 0.028 g  24.3 g (d) Divide the corrected volume of hydrogen by the theoretical number of moles of hydrogen to calculate the molar volume (L/mol) of hydrogen at STP. Molar Volume =

0.0274 L  23 L/mol 0.0012 mol

Adapted from Advanced Chemistry with Vernier & Laboratory Experiments for Advanced Placement Chemistry by Sally Ann Vonderbrink, Ph. D.

The Determination of the Molar Volume of a Gas

Answers to POST-LAB QUESTIONS AND DATA ANALYSIS 1. *Calculate the mass of each piece of magnesium that you used if an analytical balance was unavailable. Answers will vary depending on the thickness of your Mg ribbon and how much oxidation you removed during polishing. For example, if a student’s sample measured 17 mm, and your 1.00 m strip had a mass 1.00 m 0.015 m   x  0.0147 g x of 0.980 g, then 0.980 g 2. Calculate the number of moles of each piece of magnesium that you used. 1 mol Mg  4.94  104 mol Mg Answers will vary. For the sample data 0.012 g  24.3 g 3. Calculate the theoretical number of moles of hydrogen gas produced in each trial. Since there is a 1:1 mol:mol ratio, the number of moles Mg calculated for each trial should be equal to the number of moles of H2 gas produced for each trial. 4. Use your results to calculate the molar amount of hydrogen gas that was produced in your reactions. Answers will vary. The change in the pressure ΔP is attributed to the production of H2(g). According to the sample data: P  0.079 atm  PH2 

 0.079 atm   146.0 mL   273 K  PV 1 1T2   10.64 mL= 0.01064 L P2T1  1 atm   296 K 

 Molar Volume =

L 0.01064 L L   21.53 4 mol 4.94 10 mol H 2 mol

5. Compare your calculated molar volume, at STP, with the accepted molar volume of an ideal gas at STP, 22.4 L/mol. Calculate the % error for each trial. 22.40  21.53 % error = 100%  3.9% 22.40 Answers will vary. According to the sample data: 6. A student fails to polish each sample of Mg ribbon before massing them. What effect does this error have on the calculated molar volume of hydrogen gas? Mathematically justify your answer. The oxidation of Mg converts Mg to MgO (or Mg2N3 or MgS) which still reacts with HCl, but does not produce H2(g). Therefore, less hydrogen gas is produced and both the calculated volume of hydrogen gas (liters of gas in the numerator) at STP and the molar volume reported would be too low as a result.

Adapted from Advanced Chemistry with Vernier & Laboratory Experiments for Advanced Placement Chemistry by Sally Ann Vonderbrink, Ph. D.

The Determination of the Molar Volume of a Gas 7. A different student fails to insert the stopper into the flask while determining the available volume of the 125 mL flask. What effect does this error have on the calculated molar volume? Mathematically justify your answer. The initial volume of the flask, would be reported as too large. This term is in the numerator of the expression below, thus the reported volume of the hydrogen gas at STP is reported as too large as is the molar volume. P  0.079 atm  PH2 

 0.079 atm   146.0 mL   273 K   10.64 mL= 0.01064 L PV 1 1T2  P2T1  1 atm   296 K 

 Molar Volume =

L 0.01064 L L   21.53 4 mol 4.94 10 mol H 2 mol

Adapted from Advanced Chemistry with Vernier & Laboratory Experiments for Advanced Placement Chemistry by Sally Ann Vonderbrink, Ph. D.