## Abstract

The experiment aimed at explaining the interaction of the molecules at different pressure, temperature and volumes. At low temperatures, the volume of the gas was low while at high temperatures, the volume of gas increased. The experiment successfully determined the value of absolute temperature using the Charles’s Law as 202.75OC which was lower than the theoretical value. The experiment also successfully verified the Boyle’s Law. The interaction of temperature and the volume of the fluid can be concluded to be directly proportional with an increase in temperature leading to increase in volume. On the other hand, the interaction of gas pressure and volume is inversely proportional where increase in pressure reduces the volume of the gas.

## Introduction

Advances in gas studies were witnessed in 19th century when Charles and Gay-Lussac, made detailed investigations on how temperature affected the volume of a gas. Charles's law, which is also referred to as law of volumes, is gas law experiment that describes how there is the tendency of gas to expand when it is heated and contract when cooled. The modern Charles’s law statement states that, for an ideal gas with a given mass, the volume increases proportionally as the temperature value increases on absolute temperature scale. This means that the value of volume divided by temperature is a constant. This can be shown using the equation:

VT=k

In an experiment where gas in a container is kept at constant pressure, the initial parameters can be related with the final ones using the equation:

VinitialTinitial=VfinalTfinal

It is thus expected that increase in the volume of the gas occurs as the temperature is increased. Similarly decreasing the temperature would be caused by a decrease in the volume of the gas. Since there cannot be negative volume, the lowest volume is zero and the lowest temperature at which zero volume is achieved is referred to as absolute zero[1]. The application of Charles’s Law is observed when an inflated ball is taken outside where the temperature is low during winter seems deflated as the volume of the gas inside reduces.

The study of the Boyle’s law was conducted first by Robert Boyle in 1662. In the study, Boyle used J-shaped glass tubing, which was closed on one end and air trapped in the sealed end. Varying mercury amount was added put into the glass tubing in order to vary the pressure in the system and the volume of the gas in the tubing measured. The measurements were done at a constant temperature and using a fixed gas amount. The relationship deducted from the experiment between the pressure and gas volume was

PV = k

The experiment thus enabled the examination of the relation between pressure and the volume of gas while maintaining the amount and the temperatures constant. The height of the column is usually used to represent the volume of gas since the volume of the tube is directly proportional to its height[2]. The gas that follows these gas laws as they are is known as an ideal gas. A good application for the Boyle’s law is seem when the syringe is used to draw blood. The pulling back of the plunger causes an increase in the volume of the syringe container and decreases the pressure. This causes blood to flow in to balance the pressure in the syringe with the one outside[3].

This experiment aimed to observe the Boyle’s Law and Charles’ Law of a gas mixture (air), become familiar with the extrapolation method for the determination of the absolute zero, and in the development of scientific writing skills.

## Materials and Method

Part A: Charles’ Law

The experiment was started with a demonstration of the Charles’s Law using a blood serum tube with a glycerin red plug. The volume change (V) was measured at four different temperatures (T), starting with 4.7, 20.9, 33.7 and 98.3OC. The tube was placed into a constant-temperature bath for 1 minute, and the height, h, read within 2-3 seconds and the values recorded. The tube was taken out from the boiling water bath after a few seconds to avoid melting.

## Part B: Boyle’s Law

The setup in Figure 2 below was used to prepare the equipments for the experiment to observe the Boyle’s Law. An inverted Erlenmeyer flask was utilized as a reservoir. The height of the flask was varied, and the volume change in the burette observed. The stopcock was opened, and the apparatus filled with water making sure that the burette is approximately half full when the reservoir is near the midpoint of the burette. The top of the burette was stopped to tarp the air sample at atmospheric pressure.

Figure 1: Equipment setup for the Boyle’s Law experiment

The reservoir was moved to several positions above and below the starting point, covering a range as large as possible. For each reservoir position, measure and record HB, HR, and Hgas (in mm) were measured and recorded.

## Results

Part A: Charles’ Law

The heights measured at the four different temperatures were recorded in the Table 1 below. The height increase as the temperature of water increased where at 4.7OC, the height was 2.7 cm, 20.9OC had 2.9cm, 33.7OC, and at 98.3OC had a height of 3.9cm. The different temperatures were converted from degrees Celsius to Kelvin as illustrated below using the 4.7OC.

Degrees in Kelvin=℃+273

=4.7+273

=277.7 K

The value of constant k was calculated using the formula VT=k

## For instance the value of k in the ice system was

2.7277.7=0.0097

## A graph of the measured length (in cm) as a function of temperature (in OC) was plotted as in Figure 1.

Figure 2: A graph of the measured length (in cm) as a function of temperature (in OC). The length increased as water temperature increased.

The value for the absolute zero, which is the temperature at zero volume, can be calculated from the equation of the line using the follows equation. Where y is the length and x, is the temperature.

y = 0.0129x + 2.6156

At y=o,

x=-2.61560.0129= -202.75℃

## The value can also be determined by extrapolating the curve as follows

Figure 3: An extrapolated graph of length against temperature

## In OF the absolute zero temperature cam be presented as follows

℉=95℃+32

℉=95-202.75+32

-332.96℉

## Part B: Boyle’s Law

The HB, HR, and Hgas (in mm) that were measured were recorded in Table 2 below. The Pgas (in torr) and Vgas (in mm3) for each of the points were calculated using the following equation.

Pgas=Patm-HB-HRρWaterρMercury

Where ρWater=1.00, ρMercury=13.55g/cm3and Patm=754.6 mmHg

## For instance at the highest reservoir position, 478mm was done as follows

Pgas=754.6-868-4781.013.55

=754.6—390.00.0738

=754.6—-28.78

=783.38

## Using the Pgas calculated and the 1/V, a graph of Pgas against 1/Vgas was plotted as shown in Figure 3 below.

Figure 4: A graph of Pgas against 1/Vgas. The pressure of gas is shown to have an inverse relationship with the volume of the gas.

## Discussion

This experiment aimed to show the relationship that exists between the volume of gas and its temperature. At low temperatures, the volume of the gas was low while at high temperatures, the volume of gas increased. The graph of length which is directly proportional to the volume against the temperature gave a straight line. This is a confirmation of the law of gas called Charles’s law, which indicated that the volume increases as temperature increases. The length reading was at 4.7 cm when the tube was placed in ice which increased to 20.9 cm in the water at room temperature. The increase in height resulted from the increased temperature. In warm water, there was a further increase in height and when the tube was placed in hot water bath the height shoot to 98.3 cm. This increase in height is contributed to the linear relationship between temperature and the volume of the fluid.

The Using the graph the temperature at absolute zero mark was calculated to be -202.75OC. The theoretical value for absolute zero is -273.2OC which is higher than the calculated value [4]. This may have been due to errors in the measurement of the height or from loss of energy in the course of heating the tube. The theoretical value also refers to an ideal system which was not the case in the experiment and thus the difference in absolute temperature values.

In the Boyle’s Law, the graph of the pressure of the gas calculated against the inverse of the gas volume resulted into a straight line as described by Boyle. The linearity of the graph is verification of the Boyle’s Law. As the volume of the gas was being an increase, the pressure of the gas reduced. This is an illustration of the inverse relationship that exists between the pressure and the volume of gas. Some of the points making the graph were far from the line of best fit and may have played a part in lowering the fitness of the curve as indicated by the R2 value which was 0.9453. The R2 value of 1 is usually an indication of a perfect relation.

## Conclusion

The experiment successfully determined the value of absolute temperature using the Charles’s Law as 202.75OC which was lower than the theoretical value. It may thus be necessary to create the conditions of the experiment in order to achieve a figure that is closer to the theoretical figure. The experiment also successfully verified the Boyle’s Law.

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