The Relationship Between Temperature and Gas Volume

Categories: Science

Essay, Pages 6 (1411 words)

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Introduction

Charles's Law, attributed to the pioneering work of J. A. C. Charles and J. L. Gay-Lussac, provides a fundamental insight into the behavior of gases. It posits that, under constant pressure conditions, the volume occupied by a given amount of gas exhibits a direct proportionality to its absolute temperature measured in Kelvin units (Silberberg, 2013). This law serves as a cornerstone in the study of thermodynamics, offering a concise mathematical expression:

$V ^{1} T ^{1} = V ^{2/} T ^{2}$

The essence of Charles's Law lies in its assertion that as the temperature of a gas increases, its volume expands proportionally, and conversely, as temperature decreases, the volume contracts.

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This relationship underscores the intrinsic connection between temperature and volume, shedding light on the dynamic interplay within gaseous systems.

In the context of this experiment, our aim is to delve deeper into the implications of temperature fluctuations on gas volume. Through meticulous observation and analysis, we seek to unravel the intricacies of Charles's Law and discern its practical significance in real-world scenarios.

By systematically varying the temperature of the gas while holding the pressure constant, we endeavor to elucidate how changes in temperature manifest in alterations to the volume of the gas.

Through this exploration, we endeavor to enhance our comprehension of the underlying principles governing gas behavior. Moreover, we aspire to glean insights that transcend the confines of the laboratory, offering valuable implications for diverse fields ranging from chemistry and physics to engineering and environmental science. Thus, this experiment serves as a gateway to a deeper understanding of the fundamental laws that govern the behavior of matter, paving the way for further inquiry and discovery.

Method

Apparatus

Stopwatch
Erlenmeyer flask equipped with rubber stopper
Rubber tube with clip
500 mL beaker
Hot plate
Thermometer
Retort stand

Materials

Tap water

Procedure

Weighing the Erlenmeyer Flask: The first step entails accurately determining the mass of the Erlenmeyer flask, complete with the rubber stopper and clip. This initial measurement serves as a baseline reference for subsequent calculations and allows us to account for the mass of the apparatus in our analysis.
Immersion in Beaker of Water: Following the initial weighing, the Erlenmeyer flask is placed within a beaker containing water. This setup is crucial for subjecting the flask to controlled temperature conditions, as the water will serve as the medium through which heat is transferred to the gas inside the flask.
Boiling the Water: With the flask positioned in the beaker, the water is then brought to a vigorous boil for a duration of 10 minutes. This extended boiling period ensures that the water reaches a uniform temperature throughout, thereby establishing a stable thermal environment for the subsequent stages of the experiment.
Preparation of the Sink: Concurrently, a sink is filled with water to facilitate the rapid cooling of the gas inside the flask. This step is essential for swiftly transitioning the gas from a high-temperature state to a lower temperature, enabling us to capture precise data points across a range of temperatures.
Marking and Clipping the Rubber Tube: Prior to immersing the flask in the sink, the position of the rubber tube is marked, and a clip is affixed to secure the tube in place. This marking ensures consistency in the experimental setup and allows for accurate tracking of water flow into the flask during the subsequent phase.
Immersion in the Sink: Once the boiling process is complete, the Erlenmeyer flask is carefully removed from the beaker and submerged in the sink filled with water. This immersion serves to rapidly reduce the temperature of the gas inside the flask, bringing it into equilibrium with the surrounding water temperature.
Opening the Clip to Allow Water Inflow: With the flask positioned in the sink, the clip on the rubber tube is opened to permit the inflow of water into the flask. This influx of water displaces the air inside the flask, allowing us to measure the volume of the gas at the designated temperature.
Clipping the Tube and Removal from the Sink: Once the temperature inside the flask equilibrates with the surrounding water temperature, the rubber tube is clipped at the marked position, and the flask is removed from the sink. This marks the completion of the temperature adjustment phase, preparing the apparatus for volume measurement.
Measurement of Apparatus Volume: Subsequently, the volume of the entire apparatus setup, including the gas-filled flask, is meticulously measured. This measurement provides crucial data for plotting a graph of volume versus temperature, allowing us to visualize the relationship between these variables.
Plotting a Graph: Finally, the data collected from the experiment is used to construct a graph illustrating the relationship between volume and temperature. This graphical representation serves as a visual aid in analyzing the impact of temperature variations on gas volume, providing valuable insights into the behavior of gases under different thermal conditions.

By meticulously following these procedures, we aim to conduct a systematic and rigorous investigation into the relationship between temperature and gas volume, shedding light on the principles underlying Charles's Law and its practical implications.

Result & Calculation

Weight of empty equipped flask = 155.05g

Weight of equipped flask and sucked water = 190.52g

Weight of equipped flask and full with water = 354.52g

Weight of water in full flask = 199.47g

Weight of sucked water = 35.47g

Density of water at standard room and temperature = 1g/mL

Volume of sucked water = 35.47mL

Volume of air at 100°C = 199.47mL

Volume of air in room temperature = 164.00mL

Temperature obtained from the graph is -312°C. The theoretical temperature of water is -273°C when the volume of air is 0. The difference between the theoretical and experimental values may be attributed to heat loss from the flask during transportation to the sink.

Using Charles's Law and the volume of gas at 100°C from the experiment, the volume at the water temperature in the sink can be determined:

$ V_2 = \frac{{V_1 \times T_1}}{{T_2}} $

Substituting the values, $ V_2 = \frac{{199.47mL \times 373K}}{{297K}} = 158.83mL $

A graph illustrating the theoretical volume of water in the sink was plotted. The graph crosses the temperature axis at -260°C, which deviates from the theoretical value of -273°C. The percent error in the lab was calculated to be 4.76%. Possible errors in the experiment include heat loss from the flask during cooling and inaccuracies in timing.

Discussion

The temperature of the air in the flask when boiling was recorded as 100°C (T1). Converting this to Kelvin yields 373K. The value of $ \frac{{V_1}}{{T_1}} $ was calculated as 0.53. The volume of air in the flask at the second temperature was measured as 164.00 mL (V2). The temperature of the air in the cooled flask was recorded as 24°C (T2), which converts to 297K. The value of $ \frac{{V_2}}{{T_2}} $ was calculated as 0.55. The close proximity of these values can be attributed to Charles's Law, which states that as temperature increases, so does the volume of a gas sample when pressure is held constant.

The percent error in the lab was 4.76%, indicating potential sources of error such as heat loss and timing inaccuracies. Despite these challenges, the results align closely with theoretical expectations, validating the application of Charles's Law in predicting gas behavior.

Conclusion

In summary, this experiment embarked on a comprehensive exploration of the intricate relationship between temperature and gas volume, as elucidated by Charles's Law. Through meticulous experimentation and detailed analysis, we have uncovered compelling evidence that corroborates the fundamental principles outlined by this law. The alignment between theoretical expectations and empirical findings underscores the robustness and reliability of Charles's Law in describing the behavior of gases under controlled conditions.

However, it is important to acknowledge the presence of minor discrepancies between theoretical predictions and experimental results. While these variations may stem from inherent limitations in experimental procedures or unavoidable sources of error, they provide valuable opportunities for further inquiry and refinement. By critically examining these discrepancies, future research endeavors can uncover new insights and refine existing methodologies, ultimately advancing our understanding of gas behavior and the underlying principles governing it.

Looking ahead, future experiments in this area should prioritize efforts to minimize sources of error and enhance experimental accuracy and reliability. This may involve refining experimental techniques, optimizing equipment design, and implementing stringent quality control measures. Additionally, exploring the influence of external factors, such as pressure and composition, on the relationship between temperature and gas volume could yield valuable insights and broaden the scope of our understanding.