Experimental Determination of the Gas Constant Objectives The objectives of this lab are to experimentally determine the value of the Gas Constant R and to practice using the Gas Laws to solve a variety of problems Background A gas is the state of matter that is characterized by having neither a fixed shape nor a fixed volume Gases exert pressure are compressible have low densities and diffuse rapidly when mixed with other gases On a microscopic level the molecules or atoms in a gas are separated by large distances and are in constant random motion Four measurable properties can be used to describe a gas quantitatively pressure P volume V temperature T and mole quantity n The relationships among these properties are summarized by the Gas Laws as shown in the table below Charles s Law V T P and n are held constant As gas temperature increases gas volume increases Boyle s Law V 1 P T and n are held constant As gas pressure increases gas volume decreases Avogadro s Law V n P and T are held constant As the number of moles of gas increase gas volume increases Combined Law V T P n is held constant Obtained by combining Boyle s Law and Charles s Law V1 V2 T1 T2 P1V1 P2V2 V1 V2 n1 n2 P1V1 P2V2 T1 T2 A closer look at the Combined Law reveals that the volume of a gas depends on both the pressure and temperature Thus if the volumes of two gases are to be compared they must be under the same P and T A commonly used set of P and T reference conditions is known as Standard Temperature and Pressure or STP Standard temperature is defined as exactly 0 C 273 K and standard pressure is defined as exactly1 atm 760 mm Hg The Ideal Gas Law is obtained by combining Boyle s Law Charles s Law and Avogadro s Law together PV nRT Here P represents as the gas pressure in atmospheres V is the gas volume in Liters n is the number of moles of gas in the sample T is the gas temperature in Kelvins R is a proportionality constant called the Gas Constant and has a theoretical value of 0 08206 L atm K mol Note that the units of R will allow the units of P V n and T in the Ideal Gas Law to cancel correctly Page 1 of 4 In this lab students will measure various properties of a sample of hydrogen gas in order to experimentally determine the value of the Gas Constant R The single displacement reaction between magnesium metal and hydrochloric acid will be used to generate the hydrogen gas Mg s 2 HCl aq MgCl2 aq H2 g The hydrogen gas will be collected in a eudiometer a tube closed at one end and marked in milliliter volume units The gas will be collected in the closed end of the tube over a water bath via the technique of water displacement see figures on page 4 Students will then obtain the following values for the collected sample of hydrogen gas 1 Volume 2 Temperature 3 Moles and 4 Pressure The hydrogen volume will be directly measured from the eudiometer scale The hydrogen temperature will also be directly measured using a thermometer However the mole quantity and pressure of the hydrogen gas must be determined indirectly The mole quantity of the collected hydrogen can be easily calculated from the measured mass of the magnesium reactant using stoichiometry But the hydrogen pressure is a little more difficult to obtain Since hydrogen is collected over a water bath a small amount of water vapor is mixed with the hydrogen in the eudiometer The combined pressure of the H2 and H2O gases will be equal after adjustments to the external atmospheric pressure Patm Phydrogen Pwater vapor Patm atmospheric pressure will be measured using a barometer Pwater vapor the partial pressure of water vapor depends on the temperature of the water bath and can be obtained from the table supplied below By substituting these values in the above equation the pressure of hydrogen Phydrogen will be determined Temperature C 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Pwater vapor mm Hg 13 5 14 5 15 5 16 5 17 5 18 7 19 3 21 1 22 4 23 8 25 2 26 7 28 3 30 0 Finally to determine the value of the Gas Constant R the quantities V T n and P obtained for the hydrogen gas must simply be substituted into the Ideal Gas Equation Students can then evaluate their accuracy in this experiment by comparing their experimental result to the true theoretical value of R and by calculating their percent error Page 2 of 4 Procedure Safety Concentrated HCl is dangerous Handle it with extreme care as demonstrated by your instructor If any spills occur inform your instructor immediately Wash under running water sink or shower and use the neutralizing sodium bicarbonate solution supplied at the sinks if necessary Also note that hydrogen gas is flammable so be sure to have no open flames nearby when you perform this experiment Materials and Equipment 4 0 cm ribbon of magnesium length of copper wire reusable 6M HCl aq 50 mL eudiometer eudiometer stopper with hole s burette stand large beaker thermometer small funnel small graduated cylinder barometer large tub of water electronic balance and sandpaper Experimental Procedure Magnesium Ribbon 1 Obtain a 4 0 cm ribbon of magnesium Mg a piece of sandpaper and a length of copper wire 2 Carefully sand the outside of the Mg ribbon to remove any oxide coating Do not sand on the bench top Place the Mg ribbon on a paper towel while sanding Weigh the cleaned Mg ribbon and record this mass on your report form Note that this mass should be less than 0 040 grams If it is heavier your Mg ribbon will have to be trimmed by your instructor 3 Wrap the Mg around the end of the copper wire Do this in a tight ball with only a small gap between layers Then wrap the copper wire to form a cage around the Mg ball The cage must be tight enough to keep the Mg inside but loose enough to allow water to easily flow around the wire Roughly 3 cm of copper wire should be left over as a handle see Figure 1 Eudiometer Set Up and Reaction 4 Obtain a eudiometer tube and stopper with holes from the stockroom Use the burette clamp to hold it in place open end up 5 Add 10 mL of 6M HCl aq to the eudiometer tube using a small funnel Then add tap water to the eudiometer carefully until it is filled to the brim see Figure 1 6 Hang the Mg ball inside the open end of the eudiometer 2 cm down from the top Then insert the stopper into this end and while holding it in place quickly invert the entire tube into your largest beaker filled with water Clamp the tube in the water in the …