Introduction:
The Ideal Gas Law can be used to find any missing variable when all of the others are present. The Ideal Gas Law is stated in the equation, PV=nRT, where P is the gas pressure in atmospheres, V is volume that the gas occupies in liters, n is the number of moles of gas, R is the “gas constant," often expressed as 0.0821 L atm/ K mol, and T is temperature of the gas measured in Kelvins. The equation provides a useful, general description of the physical behavior of ideal gases.
The purpose of the overall experiment was to find the molecular weight of air by using the Ideal Gas Law. The objective of part one was to find the apparent mass of a helium sample by using a Mylar balloon. The experiment consisted of massing both an air-filled balloon and a helium-filled balloon, and finding the difference in apparent mass by substituting corresponding values into the equation, ∆m=[n*molecular weight of air]-[n*atomic weight of He]. In order to substitute a value in for n, the group had to complete part two of the lab. The objective of part two was to find the pressure, volume, and temperature of the balloon with a Vernier sensor, and then to find n by substituting the values into the manipulated Ideal Gas Law equation, n=PV/RT.
Experimental:
The procedure of the Molecular Weight of Air lab was obtained from the student’s course website
Results:
Part 1:
Table 1: Masses of Air-Filled and Helium-Filled Balloons
Trial 1 | Trial 2 | Trial 3 | Average | |
m_{air-filled balloon} | 2.88 g | 2.88 g | 2.88 g | |
m_{He-filled balloon} | (Balloon B) 1.99 g | (Balloon E) 1.72 g | (Balloon C) 1.64 g | |
∆m | .890 g | 1.16 g | 1.24 g | 1.10 g |
Part 2:
Table 2: P, V, and T of the Helium Sample
Trial 1 | Trial 2 | Trial 3 | |
Pressure | 0.970 atm | 0.970 atm | 0.970 atm |
Volume | .940 L | 1.39 L | 1.50 L |
Temperature | 298 K | 298 K | 298 K |
Table 3: Calculated Number of Moles of He
Trial 1 | Trial 2 | Trial 3 | Average | |
n= | 0.037 mol He | 0.055 mol He | 0.060 mol He | 0.050 mol He |
Sample Calculations:
Calculation of moles
0.970 atm | .940 L | K * mol | = 0.037 mol | ||
0.082057 L * atm | 298 K |
∆m= m_{air-filled balloon }– m_{helium-filled balloon}
2.88 g –1.99 g = .890g
Discussion
In order to determine the molecular weight of air, the experiment was conducted into two parts: the first to determine the apparent mass of both an empty Mylar balloon and a helium-filled Mylar balloon to calculate the change in mass. The masses were recorded into a table. To calculate ∆m, the groups used the difference in mass of the two balloons. There was nothing unusual about the change in mass. The group expected to see a change in mass between air and helium, from prior knowledge that a helium-filled balloon is “lighter" than an air-filled balloon, which causes it to rise. In part two, the lab group used a Vernier sensor and LoggerPro to determine and record the volume and temperature of the air, which was the same as the helium. After finding the ∆m of the two balloons, the molecular weight of helium, and solving for moles using the Ideal Gas Law equation, the groups were able to solve the unknown—the molar mass of air by again using the equation, PV=nRT.
The primary components of air are 78% N_{2} and about 21% O_{2}. The accepted value for air at 28.97 g/mol makes sense because .78 of the mol is Nitrogen and .21 of the mol is Oxygen. 21% of the molar mass of O_{2} is about 6.7 g, and 78% of the molar mass of N_{2 }is about 21.8 g. When adding those two values together, you get 28.5 g, which is extremely close to the accepted value of the molecular weight of air, 28.97 g. The obtained value of the molecular weight of air was slightly less, 26.0 g, than the accepted value of 28.97. The goal of determining the molecular weight of air in the lab was met.
The ideal gas law assumes that the gas molecules involved are ones that do not interact and are perfect spherical shapes that simply bounce off of each other.
A likely source of error came from measuring the volume of the air-filled balloon. It was difficult to hold the air-filled balloon steadily in the water-filled tank and measure the volume of the balloon without the group member’s hand affecting it. Also, holding the balloon unsteadily in the water tank caused waves and the water to spill over, which affected the volume, which in turn affected the values substituted into the ideal gas equation causing an askew result. Another source of error was the general idea of the ideal gas law, which assumes that the molecules of a substance do not interact with others. That assumption is wrong since air molecules are constantly experiencing dispersion forces. The percent error was calculated in the sample calculations, and found to be only 10.3%.
Conclusion:
Overall, the experimental goal to determine the molecular weight of air was successful. The fundamental experiment approach was conducted by calculating the difference in mass of both an air-filled balloon and a helium-filled balloon. The next step was to find the pressure and room temperature with a Vernier sensor, and the volume of the balloon through water displacement. Those four values were put into the ideal gas equation, n=PV/RT, to find the number of moles of air. The molecular weight of air was calculated by dividing the sum of the change in mass and the molar mass of helium by the moles of air found, as shown in the sample calculations. The molecular weight of air was found to be 26.0 g.
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