The Ideal Gas Law in a Practical Experiment Report

Introduction

The purpose of this laboratory work was to evaluate the ideal gas law for the case of gas in a syringe when the pressure was increased. Lowering the piston caused a pressure build-up in the container, which the data showed increased pressure and temperature. Ideal gas ratios are used to check for collected data, and any patterns and errors are explained. This work showed a low error rate, indicating that the experiment was successful.

Data

For this lab work, thermodynamic parameters (Pressure, Temperature, Volume) were measured for the two states depending on whether the piston was lowered or not. Table 1 below shows the results of these direct measurements. It can be well seen that when the piston was lowered, the volume of free space inside the syringe decreased by 42.5%; it is natural that there was an increase in pressure when the volume was lowered. In particular, the pressure increased sharply by about 50.7% to 111.0 kPa at the end point with the lowered piston. The temperature also increased as a result of compressing the piston, and the increase was 4.7% or 14.4 Kelvin.

Table 1. Measurement results.

Results

The change in pressure with a decrease in volume does not seem surprising: the law of the ideal gas shows an inversely proportional relationship between P and V. Thus, a decrease in pressure led to an increase in volume. From the point of view of thermodynamic configuration, in a closed container with gas there was no exchange of energy and matter with the environment, so it is assumed that there is no escape of matter outside the syringe. It is also worth specifying that when space is compressed in such a closed container, gas molecules cannot propagate, which leads to the only possible variant of their configuration, namely compaction. As a result, the probability of particles colliding with each other as a result of chaotic motion increases, which in turn increases the temperature.

The ideal gas equation shows that the ratio V₁ / V₂=P₂ / P₁ turns out to be true at constant temperature. This is easily verified for the data obtained, viz:

40 mL /23 mL = 111.0 kPa/ 65.5 kPA

1.74 ≠ 1.69

Obviously, this condition was not fulfilled for real gas, because the container with the gas was not in ideal conditions, that is, the practical application of this law differs from the theoretical concept. The difference between practice and theory can be solved by introducing an additional parameter, namely the volume of air inside the syringe, V₀. Then the equation takes the form of:

V₁ + V₀/ V₂+ V₀ = P₂ / P₁

40 + V₀ = 1.69(23 + V₀)

40 + V₀ = 38.87 + 1.69 V₀

V₀ =40 – 38.87 / 0.69 = 1.64

Therefore, there was another 1.64 mL of air in the syringe. In addition, it can be calculated PV/T ratios for the ideal gas for the two boundary states based on the available data. In particular:

P₁ V₁ / T₁ = P₂ V₂ / T₂

(65.5 kPa)(40 mL + 1.64 mL) / 302.4 K = (111.0 kPa)(23 mL+ 1.64 mL) / 316.7 K

9.02 Kpa mL K^-1 = 8.64 kPa mL K^-1

The values were not identical, which means that there was a measurement error caused by measurement errors and/or uncertainties. The percentage error in this case was:

PD = 9.02 – 8.64 / 9.02 = 4.21 %

1. The pressure increase with volume reduction is really not identical in this experiment as one would expect (LibreTexts, 2022). The difference is due to the presence of air in the container, which means that the real gas was far from the ideal state.
2. The decrease in temperature is due to heat transfer through the walls of the container, which means that the closed system tends to compensate for thermal equilibrium. In contrast to temperature, pressure does not return to the initial pressure, because under the conditions of hermeticity, escape of the substance outside the container is excluded, that is, pressure is not pressurized and is not removed from the system. Since it is known that pressure is inversely proportional to volume, and an additional volume of air was present in the syringe, a return of pressure to its original state is impossible.
3. When the piston is lowered, that is, the pressure is applied, the temperature naturally increases by 14.4 Kelvin. This follows from the law of ideal gas, which postulates a direct proportionality between pressure and temperature: an increase of one lead to an increase of the other.

Conclusion

The present laboratory work evaluated the law of the ideal gas in a practical experiment. It was shown that the real gas in the syringe differs slightly from the characteristics of the ideal gas, also due to the presence of air in the container, namely 1.64 mL. The percentage error was 4.21 between the ideal gas ratios at the starting point and the end point, indicating the overall success of the experiment.

Reference

LibreTexts. (2022). The ideal gas equation. LibreTexts Chemistry. Web.