The Ideal Gas Law

Introduction

The purpose of this lab was to investigate relationships between the properties of gas, including pressure, volume, moles, and temperature, and then use the Ideal Gas Law (eq 1) to explain observations made. The lab consisted of a pressure-volume experiment and a pressure-temperature experiment.

Equation 1 is the The Ideal Gas Law, where P is pressure, V is volume, n is moles, R is the ideal gas constant, and T is temperature. 

PV=nRT (1)

In equation 2, Boyle’s Law, pressure multiplied by volume equal a constant.

PV=Constant (2)

In equation 3, Charles Law, pressure divided by temperature equal a constant.

P/T=Constant (3)

Procedure

Detailed procedures may be found in reference 1.

Results 

Figure 1 shows the pressure compared with the volume from part one. 

Figure 1. The pressure of air measured by controlling the volume.

The average volume was 0.014 L ± 0.004 and the average pressure was 1.4 atm ± 0.4. The curve of Figure 1 means the pressure was inversely related to volume. 

Figure 2 shows the pressure compared with 1/volume of the air from the same data. 

Figure 2. The pressure of air versus the inverse volume.

The data in Figure 1 was used to solve Equation 1 for the number of moles of air in the syringe, which was calculated to be 7.71 x 10^-4 moles. The pressure was multiplied by the volume for each data point according to Boyle’s Law (eq 2). The results from each data pair were constant, confirming Boyle’s Law.  The value of R, calculated using equation 1 and the slope of the trendline in Figure 2, was 0.0757 L atm/mol K.

Figures 3 and 4 show the relationship of temperature versus pressure of the data obtained from the pressure-temperature experiment. Figure 3 is atmospheres versus degrees Celsius, Figure 4 is atmospheres versus degrees Kevin.

Figure 3. The relationship of pressure (Atmospheres) versus temperature (Celsius) of air.

Figure 4. The relationship of pressure (Atmospheres) versus temperature (Kelvin) of air.

It is known that pressure and temperature are normally directly related ¹ (eq 3), which was tested using the data from Figure 4. Pressure was divided by temperature for each data point to determine if they equal one constant value. The calculated values remained relatively constant, they got smaller as the temperature and pressure increased, which agrees with equation 3.

By setting the pressure (y value) equal to zero and solving for the volume (x value) in the trendline of figure 4, the pressure was calculated to be 12.1 atm. Then trendline was solved for the pressure when the temperature equaled 200 and 400 degrees K. It was found that when the temperature was doubled that the pressure also doubled. 

Discussion

The Ideal Gas Law was tested by observing a pressure-volume relationship and a temperature-pressure relationship. The R value was calculated with the data in Figure 1 to be 0.0757 L atm/mol K. This value is smaller than the accepted R value of 0.08206 L atm/mol K.¹ Error in this value may be due to composition of the air in the room that the lab was done deviated from where the accepted value was determined. 

Temperature would double if pressure was doubled. When temperature increases the amount of kinetic energy in molecules, in the form of heat, increases with with pressure. With the increase of kinetic energy the molecules increase in velocity and collide more frequently.

References

1. General Chemistry Experiments: A Manual for Chemistry 204, 205, and 206,Department of Chemistry, Southern Oregon University: Ashland, OR, 2010