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Experiment_620_Calculation of the Ideal Gas Constant_1_1_3

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    Student Name 

     

    Laboratory Date: 

    Date Report Submitted: 

    ___________________________ 

     

    Student ID 

     

    Experiment Number and Title 

    Experiment 620:  Calculation of the Ideal Gas Constant 

     

     

     

    Experiment 620:  Calculation of the Ideal Gas Constant 

     

    Section 1:  Purpose and Summary 

     

    Determine the value of the ideal gas constant, R, by measuring the volume, temperature, and pressure of a known amount of gas. 

     

     

    Under ordinary conditions, the pressure (P) of any sample of an ideal gas is inversely proportional to its volume (V) and directly proportional to its absolute temperature (T) and to the number of moles (n) of the gas present in the sample. This proportionality may be written: 

     

    \(\mathrm{P} \alpha \frac{\mathrm{nT}}{\mathrm{V}}\)

     

    where α is read "is proportional to." It is more convenient to put this relationship in the form of an equation: 

     

    \(P=\frac{n R T}{V}\)

     

    where R, the “proportionality constant” is usually called the “ideal gas constant.” This equation is more familiar in the rearranged form PV = nRT, and this equation is called the “ideal gas equation” or the “ideal gas law.”  

     

    The purpose of this experiment is to verify this equation for a sample of hydrogen gas, H2 (g). To do this, we must measure P, V, T, and n. The value of R can then be calculated and compared with the accepted value of R. In this experiment, P, V, and T will be measured directly, while n will be calculated from the amount of magnesium used to produce the hydrogen gas from reacting with hydrochloric acid according to the equation: 

    Mg(s) +  2 HCl (aq)    → MgCl2 (aq)   + H2 (g

     

    Section 2:  Safety Precautions and Waste Disposal 

     

    Safety Precautions: 

     

    Wear your safety goggles. 

    Use caution when handling 6 M HCl. It is corrosive and can burn your skin. If any HCl comes into contact with your skin, rinse it off immediately and thoroughly with lots of water. 

    Confirm that access to an eyewash station is available and know where it is.  6 M HCl is an eye hazard.   

     

    Waste Disposal: 

     

    At the end of the experiment, the HCl solution will be much more dilute. The water, diluted HCl and MgCl2 mixture may be rinsed down the sink with plenty of water. 

     

    Section 3: Procedure 

     

    1. Obtain a piece of magnesium ribbon approximately 5 cm long. Clean the ribbon with fine steel wool and weigh it accurately (to the nearest 0.0001 g). Make sure that it weighs less than 0.04 grams. (If it weighs more, cut off a small piece and re-weigh.). Record the mass of the magnesium strip. 

    Mass of the magnesium strip:  

     

    (a) Trial 1: ___________ grams 

     

         Trial 2: ___________ grams 

     

    2. Roll the ribbon loosely and then wrap it in a little ball of fine copper wire (see the display in the laboratory), leaving a "handle" of copper wire. The wrapping is designed to prevent small pieces of magnesium from breaking off and escaping during the experiment. Make sure that the ball is not too large to fit into the gas measuring tube. 

     

    3.  Set up a ring stand with a burette clamp in position to hold a 50-mL gas-measuring tube (eudiometer). Fill a 400-mL beaker about 2/3 full of tap water and place it near the ring stand. 

     

    4. Tilt the gas-measuring tube slightly and pour in about 10 mL of 6 M HCl. (Estimate volume using the marks on the tube, and don't worry about getting exactly 10 mL) Then, with the tube still in the same tilted position, gently add some water from a wash bottle, being careful not to mix the water too much with the acid. Then, gently fill the tube to the top with water (pour from a beaker or wash bottle). While pouring, rinse down any acid that may have wet the sides of the tube. The object is to have acid at the bottom of the tube and water at the top. Try to avoid stirring up the acid layer at the bottom of the tube. Air bubbles that may cling to the insides of the tube can be dislodged by gentle tapping of the tube.  

     

    5. Holding the copper coil by the handle, insert the cage about 3 cm down into the tube. Hook the wire over the edge of the tube where it will be pinched by the rubber stopper and held in place. When you insert the stopper, don't put your finger over the hole in the stopper. Let the water overflow as you insert the stopper so that there are absolutely no air bubbles trapped in the tube. 

     

    6. Add some more water to the hole in the stopper so that it is completely filled with water. Cover the hole in the stopper with your finger and invert the tube in the beaker of water, so that the stoppered end is under water. Once the hole is under water, you can remove your finger; the water cannot now run out. Clamp the tube in place. The acid, being denser than the water, will diffuse down through the water and soon reach the metal sample. When the reaction begins, you will see bubbles of hydrogen gas form. 

     

    7. After the bubbles stop forming, you know that the reaction is completed, but you should wait for a few minutes for the tube to come to room temperature and for bubbles that may be clinging to the sides of the tube to be dislodged. (Tap, if necessary.) 

     

    8. Read and record the volume of the hydrogen gas in the eudiometer to the nearest 0.01 mL. 

    Volume of the hydrogen gas in the eudiometer: 

     

    (b) Trial 1: ____________ mL 

     

          Trial 2: ____________ mL 

     

    9. Without changing the position of the eudiometer, hold a ruler at the top surface of the water level inside the beaker, and measure the distance from the water level in the beaker to the water level inside the eudiometer. Record this height (in millimeters). This will be the "height of the liquid column" referred to in the calculations. 

    Height of the liquid column: 

     

    (c) Trial 1: ____________ mm 

     

         Trial 2: ____________ mm 

    10. Measure and record the temperature of the gas (to the nearest 0.1°C) by holding a thermometer against the eudiometer where it contains gas. 

    Temperature of the hydrogen gas: 

     

    (d) Trial 1: ____________ oC  

     

          Trial 2: ____________ o

     

    11. Record the atmospheric pressure (to the nearest 0.1 mmHg) (the instructor will read the barometer and write today's atmospheric pressure on the board). 

    Atmospheric pressure: 

     

    (e) Trial 1: __________ mm Hg 

     

         Trial 2: __________ mm Hg 

     

    12. Disassemble the apparatus and pour the solutions from the beaker and eudiometer down the drain.  Rinse the eudiometer well with laboratory water. 

     

    13. Repeat the entire procedure with a second sample of magnesium. 

     

     

     

    Section 4 Calculations 

     

    For each sample of H2 gas you collected in Part 1, you collected enough data to determine its pressure, volume, number of moles, and temperature.  When you substitute your values of P, V, n, and T into the ideal gas law, PV = nRT, you will be able to determine your own value of R, the ideal gas constant. 

     

     

    Trial 1 

    Trial 2 

    1. Number of Moles (n)From the mass of magnesium used and the balanced equation, calculate the number of moles of hydrogen gas expected for each trial. 

     

    Show your equation here: 

     

     

     

     

     

    (f) 

    n = _________ mol H2 

     

     

    (f) 

    n = _________ mol H

    2. Pressure (P):  To calculate the partial pressure of hydrogen in the tube, there are two corrections to take into account. 

    The first correction has to do with the fact that the hydrogen gas was collected over water.  The gas in the eudiometer is really a mixture of hydrogen gas and water vapor.  The contribution of water to the total pressure is called the vapor pressure of water.  It depends on temperature and can be looked up in a chemistry handbook.  To find the vapor pressure of water in your experiment, look up “water, vapor pressure” in the CRC Handbook of Chemistry and Physics.  There will be a table that shows the vapor pressure of water (in mmHg) for any given temperature (in °C). 

     

    The second correction has to do with the difference in water levels in the eudiometer and in the beaker.  If the levels were equal, then the pressure inside and outside would be equal. When the levels are unequal, it means that the atmosphere and the gas inside the eudiometer are not pushing down equally on the surface of the water.  The difference in water levels that you measured corresponds to the pressure difference in units of mmH2O. This can be converted to mmHg, using the relation 13.6 mmH2O = 1 mmHg: 

     

     Pcorr = (c) x \(\frac{1 \mathrm{~mm} \mathrm{Hg}}{13.6 \mathrm{~mm} \mathrm{H}_{2} \mathrm{O}}\)

     

     

    Taking both corrections into account: 

    P(H2) = (e) – (g) – (h) 

     

    Convert the pressure of H2 to atm. 

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    (g) 

    PH2O = _______ mmHg 

     

     

     

     

     

     

     

     

     

    (h) 

    Pcorr = _______ mmHg 

     

     

     

     

     

     

     

    (i) 

    P(H2) = ________ atm 

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    (g) 

    PH2O = _______ mmHg 

     

     

     

     

     

     

     

     

     

    (h) 

    Pcorr = _______ mmHg 

     

     

     

     

     

     

     

    (i) 

    P(H2) = ________ atm 

    3. Volume (V): For each trial, convert the volume of gas (b) from mL to L. 

     

     

     

    (j) 

    V(H2) = ________ mL 

     

    (j) 

    V(H2) = ________ mL 

    4. Temperature (T): For each trial, convert the temperature (d), from °C to K. 

     

    (k) 

    T(H2) = ________ K 

    (k) 

    T(H2) = ________ K 

    5. Using the Ideal Gas Law, PV = nRT, calculate an experimental value for R for each trial. 

    R = \(\frac{P V}{n T}=\frac{(i) \mathrm{x}(j)}{(f) \mathrm{x}(k)}\)

     

    Rexptl = _____________  

     

     

    Rexptl = _____________   

     

    6. Report the value of R obtained for each trial and the average value.  

    \(R_{\text {average }}=\frac{R_{\text {trial } 1}+R_{\text {trial } 2}}{2}\)

     

     

     

     

     

     

    Raverage = _____________________________ 

    7. Calculate the percent error using the theoretical value of R (0.08206 L•atm/K•mol) and your average experimental value of R. 

    error \(\%=\frac{\left|R_{\text {theoretical }}-R_{\text {average }}\right|}{R_{\text {theoretical }}} \times 100\)

     

     

     

    % error = _____________________________ 

     

    Show ALL work here: 

     

     

     

     

     

     

    Post Lab Questions: 

     

    1. Why don’t you need to measure the exact volume of acid used? 

     

     

     

     

     

     

     

     

     

    2. In a similar experiment, a piece of aluminum was reacted with HCl. The hydrogen gas produced was collected in a eudiometer in the same way. 

     

    a) Write and balance the equation for this reaction. (Hint: what is the formula of aluminum chloride, the other product?) 

     

     

     

     

     

     

     

     

    b) If 39.5 mL of H2 are produced at 21°C when the atmospheric pressure is 762.8 mmHg, and if the height of the liquid column in the eudiometer is 11.2 cm, what mass of aluminum was used? 

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     


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