The Ideal Gas Law

Introduction

The purpose of this lab was to investigate several properties of gases and use the ideal gas law (eq 3) to explain the observations made. The lab consisted of a pressure-volume experiment which relates to eq. 1, and a pressure-temperature experiment which relates to eq. 2.

Equation 1, Boyle’s Law, shows the relationship of pressure and the inverse of volume.

P α 1/V   (1)

Equation 2, Charle’s Law, gives the relationship of pressure and temperature.

P α T (2)

Equation 3, The Ideal Gas Law, is a combination of eq 1 and eq 2, where P is pressure, V is volume, n is the amount of moles, and T is temperature.

PV=nRT (3)

Procedure

  In part one of the experiment the relationship between the pressure and volume of air was determined. Air was confined in a syringe which was connected to a pressure sensor. Data from the pressure sensor was saved on the computer. This data was analyzed and a graph created of pressure vs volume and of pressure vs 1/volume. The data was converted to the appropriate units and the number of moles of air in the syringe calculated using the Ideal Gas Law (eq 3).

In part two of the lab the temperature-pressure relationship was explored using a vernier testing apparatus, which consisted of a sealed flask with a pressure sensor and a temperature sensor connected, suspended in a beaker of water. Data was collected in 5°C intervals and saved on the computer. The data was analyzed and put into a graph comparing pressure and temperature.

Detailed procedures may be found in reference 1.

Results 

In this lab the Ideal Gas Law was tested by measuring the pressure of gas in comparison to volume and temperature. 

Figure 1 shows the data collected of Pressure level compared with the volume of the air. 

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

The average volume was 0.014 L ± 0.0039 and the average pressure was 1.4 atm ± 0.38.

As eq. 1 states, pressure is inversely related to volume.

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

Figure 2. The pressure of air as a function of inverse volume.

The data in figures 1 and 2 were used to solve eq. 3 for the number of mols of air in the syringe, which was calculated to be 0.00076 mols. The value of R, calculated using the slope of the trendline in figure 2 was 0.072 L-atm/mol-K.

Figure 3 shows the relationship of temperature vs. pressure using the data obtained from the second part of the experiment.

Figure 3. The relationship of pressure vs. temperature of air.

The relationship of pressure and temperature is direct, as seen in eq. 2 and proved by the fact that the data made a linear graph. As temperature increases so does pressure, this is because when temperature increases the molecules increase in velocity and collide more frequently. The average temperature was 325 K ± 18.9 and the average pressure was 1.0 atm ± 0.055.

Discussion

In this lab the Ideal Gas Law was tested by observing a pressure-volume relationship and a temperature-pressure relationship. The R value of the data in Figure 1 was calculated to be 0.072 L-atm/mol-K, which has a 13% relative error when compared to the accepted value. This may be due to the fact that it was near impossible to precisely control how much the the syringe would tighten. It is also possible that the composition of the air in the room that the lab was done deviated slightly from where the accepted value was determined. The average pressure constant for part one was 115 ± 68.5.

From the data used to make figure 1, the average volume was 0.014 L ± 0.0039 and the average pressure was 1.4 atm ± 0.38. From the data used to make figure 3, the average temperature was 325 K ± 18.9 and the average pressure was 1.0 atm ± 0.055. These standard deviations are not bad, and probably exist due to human error. If the temperature was doubled the pressure would also double. The average pressure constant for part two was 0.0179 ± .000512.

References

1. General Chemistry Experiments: A Manual for Chemistry 204, 205, and 206,Department of Chemistry, Southern Oregon University: Ashland, OR, 2009