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Molar Volume and Density of Gases Additional Review Material Relevant sections in the text (Chemistry for Engineering Students, 4th Ed., Brown, Holme): 5.3-5.5 Background Some of the earliest and most significant quantitative experiments reveal that four variables are usually sufficient to define the state, or condition, of a gas: temperature (T); pressure (P); volume (V); and the quantity of matter, usually expressed as the number of moles (n). These four variables are interdependent, i.e. any one of them can be determined by measuring the other three. The key relationships between the variables are Boyle's, Charles's, and Avogadro's gas laws. Each of these laws expresses the effect of one variable on another when the remaining two are held constant. A convenient combination of these simple gas laws is the ideal gas law which describes the relationship between the properties P, V, n, and T for any gas behaving as an ideal gas (Equation 1): PV = nRT (1) Where R is the universal gas constant (R = 0.082058 atm-L-mol ¹-K¹) and has the same value for all gases. The ideal gas law is useful when applied to a single set of conditions. It is often required, however, to compare two separate conditions. In this case, the ideal gas equation can be applied to both the initial and final conditions. The ideal gas equation can then be re-written as a general gas equation (Equation 2): P₁V₁ P₂V₂ = n₁ T₁ n₂T₂ (2) One application of the ideal gas law is to investigate the molar volume of a gas. Molar volume is defines as 'the volume occupied by one mole of a gas at STP'. Avogadro postulated that 'at the same temperature and pressure, equal volumes of all gases contain the same number of molecules. This statement is known as Avogadro's Law. Thus, the number of moles of molecules of a gas in a sample of a given volume, at a given temperature and pressure, does not depend on the identity of the gas. In the lab, if we determine the volume of a known quantity of gas at a known temperature and pressure, it is then possible to determine the volume at STP of one mole of this gas. This molar volume at STP, as stated by Avogadro's Law, should be the same for all gases. In this experiment we will determine the molar volume of both hydrogen and oxygen gas separately in order to verify Avogadro's Law. Hydrogen gas is produced by the reaction of magnesium metal with an excess of aqueous hydrochloric acid, whereas oxygen gas is produced through the decomposition reaction of hydrogen peroxide in an aqueous solution. Although the decomposition of H₂O₂ to O₂ and H₂O is a spontaneous process, it occurs slowly. We can speed up the reaction rate considerably by the addition of a catalyst, called enzyme catalase, found in yeast. The pressure change
between the initial and final conditions is used to calculate the volume occupied by one mole of gas at standard temperature (273.15 K) and pressure (1 atm). For an ideal gas, this volume is 22.414 L at STP. Dalton's Law of Partial Pressures states that the pressure of a mixture of gases is the sum of the partial pressure of the component gases. Although it may seem that either hydrogen or oxygen is the only gas present at one time it is important to note that the reactions take place 'over water' or in aqueous medium. The reaction vessel therefore also contains pressure contributed by water vapour. To assure a proper reading of gas pressure for the dry gas component, the partial pressure due to the water vapour component must be accounted for according to Dalton's Law: Ptotal = PH20 + Pgas (3) Another application of the ideal gas law is to measure the density of a gas. If we know the molar volume of an ideal gas at STP we can determine the density of the gas under these conditions. The density of a gas at STP is given by the following relationship: density= (4) Notice that density is directly proportional to molar mass. We would therefore expect an increase in density with increasing molar mass when comparing the standard density of hydrogen and oxygen gases. Glassware & Equipment • Balance (0.001 g) ● Beakers: 600 mL • • • Graduated cylinder: 50 mL • Syringe (3 mL & 10 mL), valve, and tubing Black rubber stopper (#5) Erlenmeyer flask: 125 mL Chemicals & Reagents . 1.0 M Hydrochloric acid, HCI (aq) • Magnesium turnings, Mg(s) molar mass molar volume • Two-hole white rubber stopper • Vernier gas pressure sensor Vernier LabQuest interface • • Vernier temperature probe Weighing funnel • 3.0 % w/w Hydrogen peroxide, H₂O₂ (aq) Active dry yeast . CAUTION: HCI is corrosive; handle with care. Procedure Part A- Production of H₂(g) 1. Power-on the LabQuest unit (top left power button). The LabQuest App launches automatically. Connect a temperature probe to the CH 1 port and a gas pressure sensor to CH 2. The LabQuest App will auto-ID the connected sensors and a live reading will appear in the Meter screen. The default setting should be in the Time Based Mode with a sample Rate of 1 sample/second for a Duration of 900 seconds. 2 of 9
CHEM 1103 Summer 2022 2. 3. 4. 5. 6. 7. 8. Experiment 4 if the pressure unit is kPa, change it to atm by clicking on the pressure live reading and from the dropdown menu select Change units and then atm. Determine the available volume in a 125 mL Erlenmeyer flask which the gases will occupy: a. Fill the entire volume of the flask with water and insert the black stopper to displace some of the water. b. Measure out the volume of water remaining in the flask using a 50 mL graduated cylinder. c. Empty the contents of the flask and completely dry the inside with a paper towel. Use the weighing funnel to weigh out 0.01-0.02 g of Mg and record the exact mass. Place the Mg in the dry 125 mL Erlenmeyer flask. Prepare a room temperature water bath in a 600 mL beaker. The bath should be just deep enough to completely cover the gas level in the Erlenmeyer flask but not the rubber stopper as shown in Figure 4.1. Twist the white stopper snugly into the neck of the Erlenmeyer flask. Close the valve on the white stopper by turning the handle so it is perpendicular to the valve stem. Figure 4.1. Equipment set-up with the Vernier gas pressure sensor and temperature probe. Obtain 20 mL 1.0 M HCl in a 50 mL beaker. Draw 5.0 mL into the 10 ml syringe and very carefully thread the syringe onto the two-way valve on the white stopper. Place the flask and temperature probe in the water bath. This step requires two people; one to handle the syringe and the other to firmly hold down the rubber stopper so that it does not pop out of the flask when the pressure increases. If any gas escapes, the experiment must be repeated. a. Tap Collect to start the data collection. After about 20 seconds, open the two-way valve directly below the syringe and slowly press the plunger to add HCI to the flask. Quickly close the two-way valve. 3 of 9
9. 10. 11. b. Gently swirl the flask as the reaction proceeds while holding down the stopper. C. Press Stop to end data collection once the pressure begins to drop. At this point all of the Mg should be dissolved. 15. Slowly remove the white stopper from the flask to relieve pressure in the flask. Do not open the two-way valve to release the pressure. 16. 17. 18. 19. Examine the pressure data to determine the change in pressure: Select Analyze/Statistics followed by both Temperature and Pressure. Record Ptotal (max. minus min. pressure) and the mean temperature during the reaction. 12. Perform two more trials. When you are ready to start a new run, tap Collect Discard to delete the previous run. Discard the contents of the flask in the waste container provided. Rinse and dry the inside of the flask with paper towel. Part B - Production of O₂(g) 13. 14. Place a small scoop of yeast in the dry 125 mL Erlenmeyer flask. Obtain about 12 mL 3.0 % w/w H₂O₂ (d = 1.01 g/mL) in a 50 mL beaker. Draw 3.0 mL of the H₂O₂ into the 3 mL syringe. Secure the stopper in the neck of the flask and the syringe into the valve. Repeat the necessary steps as outlined in Part A to determine the pressure change due to O₂(g). and select CAUTION: High pressure is generated; secure the stopper tightly during this reaction and be very careful when releasing the pressure. The content of the flask (yeast and H₂O₂) may be washed down the sink. Perform a total of three trials. Unplug both the temperature and the pressure probes. Rinse both syringes with water and return them to the front.
REPORT SHEETS- EXPERIMENT 4 Molar Volume and Density of Gases Hypothesis [2.0] A hypothesis summarizes what outcomes you anticipate for the experimental procedure. Typically the outcomes will be presented in terms of the relationship between dependent and independent variables. Give the reason for your hypothesis based on what you know about the scientific concept of the lab and how that knowledge led you to the hypothesis. Data and Results [10.0] Volume of water occupying the flask (Vw):. Volume of produced gas (V₂) = Vw + volume of gas occupying tubing and sensor*- volume of added acid or H₂O₂: (0.25 Marks) Water bath mean temperature: Vapour pressure (atm) of water at water bath mean temp. from CRC hand book: kPa atm (0.25 Marks) 5 of 9
Part A-Molar Volume of H₂ Give the balanced reaction equation and determine the limiting reagent: (1.0 Marks) Table 4.1. Trial Mass of Mg Mol of H₂ (na) Pmax Pmin Ptotal (Pmax-Pmin.). PH, (P₁) Mean temp., K (T₁) Volume H₂ at STP, (V₂) 1 2 3 Average Calculations: Complete Table 4.1, using the correct units calculate the average molar volume of H₂ at STP, V₂. Where n₁ is the moles of gas produced based on the amount of limiting reactant and the reaction stoichiometry, and P₁ is the pressure of dry gas (see Eq. 3). Show all of your work. (3.0 Marks) 6 of 9
-Calculate the % error of the molar volume of H₂. (0.25 Marks) Part B-Molar Volume of O₂ Give the balanced reaction equation: (0.25 Marks) Table 4.2 Trial Vol. H₂O₂ Mol 0₂ (₁) Pmax Ptotal (Pmax max. - Phin Pminh Po, (P₁) Mean temp.,(T₁) Volume O₂ at STP, (V₂) 2 3 Average Note: If you notice an outlier in the results, you can exclude that from calculating the average volume of the gas at STP. 7 of 9
Question: Discuss why the value of one of the trials cannot be used in the calculation of the average volume of O₂ gas and give the possible reason for getting this out of the range value. (0.75 marks) Calculations: Complete Table 4.2 using the correct units, calculate the average molar volume of O₂ at STP, V₂. Where n₁ is the moles of gas produced based on the volume, concentration and density of H₂O₂ as well as the reaction stoichiometry. Show all of your work. (3.0 Marks) - Calculate the % error of the molar volume of O₂. (0.25 Marks)
- Calculate the density (in g/L) of both hydrogen and oxygen gas from average molar volumes at STP. (1.0 Marks) Discussion [3.0] Explain how the data supports, or does not support, your hypothesis. Discuss the accuracy (% error) between experimental and expected values in regards to molar volume and density. Identify at least one source of error. How does this error affect the data and how could it be improved?
Data and Results [10.0] Volume of water occupying the flask (Vw): 137ml Volume of produced gas (V₁) = Vw + volume of gas occupying tubing and sensor*- volume of added acid or H₂O₂: (0.25 Marks) Water bath mean temperature: 24.0°C Vapour pressure (atm) of water at water bath mean temp. from CRC hand book: kPa atm (0.25 Marks)
Table 4.1 Trial Mass of Mg 0.0179 Mol of H₂ (n1) 1 Pmax, Pmin. Ptotal (Pmax. - Pmin.) PH₂, (P1) Mean temp., K (T₁) 24.04 C Volume H₂ at STP, (V₂) Average 113.01 kpa 99.27 kepa 0.0179 2 113.13 kpa 99.31 kpa 24.02 0.0169 3 112.87 кра 99.13 kepa 24.04%
Table 4.2 Trial Vol. H₂O₂ Mol 0₂ (1) Pmax. Pmin.. 3ml Volume O₂ at STP, (V₂) 1 12.05 kepa 47.27 kepa Ptotal (Pmax.-Pmin.) Po₁, (P₁) Mean temp., (T₁) 24.4°C. 3ml 2 112.01 kepa 96.31 kpa 24.7 3 3ml. 12.4. а кра 98.13 kpa 24.31°C Average Note: If you notice an outlier in the results, you can exclude that from calculating the average volume of the gas at STP.