EXPERIMENT 9 Evaluation of the Universal Gas Constant, R

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1 Outcomes EXPERIMENT 9 Evaluation of the Universal Gas Constant, R After completing this experiment, the student should be able to: 1. Determine universal gas constant using reaction of an acid with a metal. 2. Demonstrate understanding of universal gas constant. 3. Show accuracy and precision of their results using average and standard deviation of their results. Introduction The ideal gas law gives the relation between the pressure (P), volume (V), temperature (T), and the number of moles of gas (n) in volume V: PV = nrt (1) R is called the universal gas constant. Eq. 1 is called the ideal gas law because it assumes that there are no attractive or repulsive forces between the gas molecules. For this reason, it can be applied to any gas or gas mixture, independent of the nature of the gas. Real gases will show deviations from the ideal gas law, but for most applications such deviations become important only at high pressures or low temperatures. At atmospheric pressure and room temperature deviations from the ideal gas law typically are only 1 to 2%. In this experiment we will assume that the ideal gas law can be applied to hydrogen gas (H 2 ), and we will determine the value of R by measuring the volume of H 2 gas evolved in the reaction of a known mass of Magnesium metal, Mg, with excess hydrochloric acid, HCl. In the L.atm system, pressure has the units of atmosphere (atm), volume is in L, n in moles and T in Kelvin (K). If we write these units in the gas law: P(atm).V(L) = n(mol).r.t(k) We see that the units for the gas constant R are L.atm/mol.K. In the SI system, pressure has the units of pascal (Pa), volume is in m 3, n in moles and T in Kelvin (K). The pressure unit Pa equals N.m 2 (force/area). R will then have the units J/mol.K. L.atm.system: R = L.atm/mol.K SI system: R = J/mol.K In the calculations for this experiment we will use the L.atm system. You will be able to calculate the value of R from your own experimentation, by measuring the values of P and V for a known number of moles of gas evolved, n, in three separate trials, then calculating the value of R as determined in each trial. Obviously, in your final calculation of R, it is important to use consistent units. The procedure uses the reaction between magnesium metal and hydrochloric acid, resulting in the formation of hydrogen gas: Mg(s) + 2HCl(aq) MgCl 2 (aq) + H 2 (g) 94

2 The hydrogen gas evolved will be collected over the dilute HCl solution in an inverted buret. This means that the gas collected will contain H 2 but also water vapours, which has a vapour pressure, P H2O. The pressure exerted by the H 2 will be the atmospheric pressure P atm minus the vapour pressure of water: P H2 = P atm P H2O (2) The vapour pressure of water, P H2O, is given in mm Hg (see the following table). Table 1. Vapour pressure of water, P H2O, at different temperatures. T ( o C) P H2O (mm Hg) T ( o C) P H2O (mm Hg) The atmospheric pressure may be assumed to be 1 atm (760 mm Hg) or can be read on a barometer. The temperature T will be the temperature in the laboratory. A further correction to P atm is needed to correct for the final liquid level in the buret after the reaction is complete. The correction for the difference in water level between inside the buret and the beaker must be measured in order to correct for the pressure difference. Since the density of mercury (Hg) is 13.6 g/ml, and for water it is 1.0 g/ml, we can directly convert the level difference in mm water to mm Hg: ΔP level correction (mm Hg) = mm level difference 13.6 (3) Of course this ΔP may be positive (when the level of water in the burette is above the level in the beaker) or negative (when the level in the buret is below the level in the beaker). The final result is: P H2 = P atm P H2O ΔP level correction (4) To convert mm Hg to atm or Pa, and o C to K you need the following conversions: 1 atm = 760 mm Hg K = o C

3 Measurement versus Numbers: There is an important conceptual distinction between measurements and numbers. It is important to note that measurements are not simply just numbers, rather measurements are obtained by comparing an object with a standard "unit." On the other hand, numbers are obtained by counting or by definition. Numbers are exact values of expression whereas measurements are intrinsically inexact. Finally, arithmetic is based on manipulating numbers, whereas the sciences such as chemistry, are based on measurements. Uncertainty: There is no such thing as a perfect measurement with no associated error. In fact, every measurement has an inherent degree of uncertainty which is referred to as associated uncertainty. This uncertainty comes from a combination of factors including the instrument, the experimental method, and the person making the measurement. In fact, each time a repetitive measurement is made, it is possible that a slightly different measured value can be recorded. Average Value: Since it is impossible to determine any measured value with absolute certainty, we are often confined to using mathematical expressions that define the accuracy and precision of the measurement(s). An average value calculated by using the numerical values for the measurements reflects the accuracy of a given set of measurements. An average,, is mathematically expressed as the sum of all the values divided by the total number of measurements (values) made. This can symbolically be written as, where x is the average of n different number of measured values. Standard Deviation: The precision of a set of measurements is reflected in the statistical expression called the standard deviation (σ). The standard deviation reflects the spread in the measured data points. It is symbolically written as, Note: Any scientific calculator has built in functions that determine the average and standard deviation of a series of values. When making a measurement, the right-most quoted digit provides the last degree of precision for that measurement. Figure 1.2 gives two examples of this statement. For the ruler, the measurement is only precise to the hundredths place. For the analytical balance, the measurement is only precise to the ten-thousandth place. It is important to realize that instruments that provide greater precision come at a higher cost and maintenance. A typical bathroom scale that has precision to the ones place costs approximately fifteen dollars. An analytical balance in the chemistry lab which has precision to the ten-thousandths place, costs several thousands of dollars. Example. You repetitively weigh a penny three times and find the masses to be, g g g The average mass: x The standard deviation for this set of n=3 measurements is,

4 In this experiment, you will do three separate trials to find the value of R as determined in each trial. The SD can be expressed as absolute value or as a relative value (%): SD(%) = {SD(absolute)/R ave }x100% Sample calculations: a) P H2 = P atm P H2O ΔP with ΔP = mm level difference/13.6 (mm Hg) P atm = P H2O = (mm Hg) (mm Hg) ΔP = (mmhg) P H2 = (mm Hg) = atm V H2 = ml = L b) n = mass Mg (g)/atomic mass Mg = moles Mg = moles H 2 (n in gas equation) c) R = PV/nT R = L.atm/mol.K

5 Safety Precautions Handle concentrated HCl in the fumehood only, wear gloves and safety glasses (as always!). Rinse any spills immediately. Hydrogen is highly flammable, so don t keep any open flames or electrical sparks close to your experiment. The amount of gas evolved is relatively small and causes no danger once released in the laboratory. Materials and Equipment Balance, 500 ml beaker, 50 ml buret, 10 ml graduated cylinder, conc. HCl, Mg ribbon, funnel, ruler (mm scale). Procedure 1. Weigh approximately 25 mg ( mg) Mg ribbon to the nearest g on a top-loading balance. 2. Bend the piece of ribbon to make a ring so that it will fit tightly into neck (open end) of the buret (check with your instructor if you are not sure). 3. Obtain a 500 ml beaker and fill it with water to almost full. 4. Obtain a 50 ml buret. Make sure the stopcock is tightly closed. Measure the volume at the bottom of the buret between the stopcock and the 50 ml mark by adding water from a 10 ml graduated cylinder. Record this volume in your datasheet (it will be approximately 4-5 ml). Empty the buret. 5. In the fumehood, pour approximately 10 ml 6M. HCl (provided) into the buret. Wash down with water any acid drops that may stick to the buret wall. 6. Push the Mg ribbon into the open end of the buret, to approximately 5 cm from the top. Fill the buret to the top with water. 7. Close the buret with your figure and invert it in the 500 ml beaker, making sure the Mg stays in place. The open end of the buret should be close to the bottom of the beaker but should not be touching it. 8. The HCl in the buret will gradually sink and diffuse to reach the Mg and start to react. If the Mg breaks free make sure that all will still react. This may be a slow process but you will have to wait until all Mg is reacted. Once all Mg has reacted, make sure that the buret is in an accurately vertical position and record the solution level. Also record the level difference (in mm, not ml!) between the water level in buret and top of the water in the beaker. 9. Calculate the value of R using eq. 4, of course with correct units! 10. Repeat this complete procedure two times. 11. Calculate the average value and the standard deviation of R from your three experiments. Disposal The only reaction products are MgCl 2 and the remaining excess HCl. Dispose as instructed by your Instructor/Teaching Assistant. Rinse out the buret and beaker with distilled water.

6 Experimental General Chemistry 1 Experiment 9: Evaluation of the universal gas constant, R Laboratory Data Sheet Name: Section: 1. Experimental results and calculation of the gas law constant 1. Mass of Mg Trial 1 Trial 2 Trial 3 2. Moles Mg = mass/24.3 (g/mol) 3. Mol of Mg = mol of H 2 4. Buret volume above 50 ml mark 5. Final buret reading (ml) ml - #5 above 7. Volume of gas (ml) = (4) + (6) 8. Volume of gas (L) = (7)/ Barometric pressure (mm Hg) of lab 10. Level difference: (H 2 O level in buret H 2 O level in beaker) (mm) 11. ΔP use equation 3 (mm Hg) 12. Room temperature (K) 13. P H2O (mm Hg) see Table P H2 (eq. 4) (mm Hg) 760 (11) (13) 15. P H2 (atm) = (mmhg/760) 16. R (L.atm/mol.K: (8)*(15)/(3)*(12) Calculations: Average value of R Standard deviation (SD) of R for 3 trials Relative SD of R, % = (SD/R ave )x100% Difference with literature value for R (%) 09

7 Show calculations: R average SD for R RSD for R Difference (%) from literature value (R = L.atm/(mol.K) 00

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