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. When dealing with gases, the Ideal Gas Law equation is the most famous equation used to relate all the factors in dealing and solving the problem. The four factors or variables for gas are: pressure (P), volume (V), number of mole of gas (n), and temperature (T), and the constant in the equation is R, known as the gas constant.
The Ideal Gas law equation which is pV=nRT is obtained by combining the three Gas Laws: Boyle’s Law, Charles’s Law and Avogadro’s Law. Boyle’s Law describes the inverse proportional relationship between pressure and volume at a constant temperature and a fixed amount of gas. Charles’s Law describes the directly proportional relationship between the volume and temperature (in Kelvin) of a fixed amount of gas, when the pressure is held constant. Avogadro’s Law describes that volume of a gas is directly proportional to the amount of gas at a constant temperature and pressure. The Ideal Gas equation shows that the volume of a gas is dependent on both pressure and temperature. In comparing volumes of two gases, they must be in the same pressure and temperature known as the Standard Temperature and Pressure, or STP. The purpose of this experiment is to derive the universal gas constant for gases experimentally by collecting gases from the neutralization reaction and determining the volume and pressure of the gas and then the partial pressure of the gas formed. 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)
In preparing the metal, a two centimeter long Magnesium ribbon was polished to remove the oxide film that has deposited on its surface. It was cut into five equal pieces and weighed in an analytical balance and recorded its respective weights. The metal was tied with a copper wire with a 6-7 cm straight wire as handle. A 10 mL graduated cylinder with 3-4 mL concentrated HCl and filled with water was inverted in a 600 mL beaker filled with three-fourths full of water. The metal was immediately inserted inside the graduated cylinder and let the reaction happen as hydrogen bubbles started to displace the acid in the graduated cylinder.
After the reaction, to ensure that the pressure of hydrogen collected is equal to the atmospheric pressure, the graduated cylinder was raised or lowered to make the water levels inside the cylinder and beaker equal. If not equal, the difference of the two levels was measured in millimeters and converted the mmH2O to mmHg using the densities of water and Hg. After equalizing the water levels, the volume of hydrogen gas collected in the cylinder was measured, in mL. A thermometer was placed in the beaker of water and was allowed to equilibrate for a few minutes and recorded its temperature in the corresponding table.
The students were sent to the stockroom to have a demonstration on how to measure the barometric pressure using the barometer. The barometric pressure was then recorded. The experiment was repeated for a total of four trials. From the gathered temperature of wet hydrogen, the vapor pressure of wet hydrogen was recorded using the table of vapor pressure of water. The number of moles of metal used was then calculated from the stoichiometry and determined the gas constant, R. Data and Calculations
Table 1. List of Mass of Unknown Metal, Temperature and Volume H2 collected Trial No.12345
Mass of Mg ribbon, g0.00330.00310.00340.00310.0040
Volume of H2, mL188.8.131.52.3——
Barometric Pressure, mmHg761.50
Table 2. Summary of Pressure of Wet Hydrogen, Calculated Moles of H2 gas and Volume of H2 Trial No.12345
Pressure of Wet hydrogen, mmHg30303030——-
Moles of H21.4×1041.3×10-31.4×10-41.3×10-4——-
Volume of H2, m33.9×10-63.5×10-63.6×10-63.3×10-6——-
Table 3. Summary of Calculated Gas Constant value, R
Gas Constant, R , J/mol∙K8.99588.69428.30388.1973
Shown in table 1 were the tabulated data observed in the experiment. Five pieces of magnesium ribbon were weighed and recorded its weights. After preparing the set-up, the procedure was followed and observed the reaction. In the experiment, when the magnesium ribbon was inserted immediately in the graduated cylinder a reaction occurred. Colorless bubbles were observed. It was produced slowly and then almost instantaneously the rate at which the gas was being produced speeds up rapidly. After the reaction, the magnesium ribbon diminished. Hydrogen gas was produced by displacing with magnesium. The temperature of the hydrogen gas collected was also recorded after the reaction. Four trials were done. Table 2 showed the data of the pressure of wet hydrogen, the calculated moles of hydrogen gas collected and the volume.
The gas in the cylinder is mostly H2. However, there is also some water vapor. The amount of water vapor depends on the temperature in the cylinder so the pressure is a mixture of the pressure exerted by the hydrogen gas and the water vapor. The pressure of water vapor at 29 degrees Celsius was found to be 30 mmHg. This value was subtracted to the barometric pressure which was measured using a barometer. The calculated result was the corrected pressure exerted by the hydrogen gas. The volume was converted to cubic meters. From the known quantity of magnesium used and the stoichiometry of the following reaction the number of moles of hydrogen produced was calculated. After having the four variables needed, the gas constant was calculated using the equation pV=nRT. Shown in table 3 are the calculated values of R for the four trials.
The values in each trial differ after calculating. It is evident that errors were incorporated during the experiment. The nature of the errors incurred were mostly systematic error, specifically personal errors. During the experiment the students must practice first on how to properly perform the experiment in inverting the cylinder to the beaker properly that no bubbles will be included.