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Condition of matter known as gaseous form is one in which the component has no defined shape or volume. It takes on the shape and dimensions of the container. Pressures, volume, temp, and mass of a gas are the essential macroscopic attributes of the gas. Kinetic theory can interpret these by looking at their chemical structure and mobility. Volume of gas grows as the pressure is reduced, according to Boyle's Law. According to Charles' Law, capacity of a gas increases with increasing temperature rises. According to Avogadro's Law, the volume of gas grows as the concentration of gas expands. The ideal gas theory is the result of combining the three basic gas laws.
Also read: Unit of Pressure
Key Terms: Volume, Air pressure, Temperature, Ideal gas, Boyle’s law
Boyle’s Law
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Boyle's law asserts that the pressure generated by a gas (of a certain mass and temp) is directly proportional to the capacity covered by it. As far as the temp and amount of gas remain constant, the tension and amount of gas are directly proportional.
The connection involving volume and pressure in a gas can be stated in an algebraic equation (at constant weight and temperature).
P ∝ (1/V)
The pressure applied by the gas is P, and the space occupied by it is V. By inserting a constant, k, to this ratio, it can be transformed into an expression.
PV = k*(1/V) P = k*(1/V)
Also Read: Boyle's Law Solved Questions
Variation in Volume with Pressure: Experiment
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Now, let’s move further to understand the Experiment:
Aim: Planning graphs between P and V, as well as P and 1 /V, to investigate the fluctuation in volume (V) with pressure (P) for a sampling of air at a comfortable rate.
Apparatus & Materials Needed: Boyle's law equipment, Fortin's barometer, Vernier Callipers, thermostat, set square, and pressure gauge are some of the tools used.
Description: Two glass tubing, each about 25 cm in length and 0.5 cm in diameter, make up the Boyle's law device. One end of the AB tube is sealed, while the other tip of the CD tunnel is accessible. At the opposite end, the two tubes are pulled into a small aperture (B and D). A thick-walled rubber piping connects the ends B and D.
Alongside the metre scale, the glass tube AB is fastened vertically. Also, with help of screw S, the other tube CD can be adjusted vertically across a vertical rod and connected to it at any height. Mercury is present in the CD, AB, and rubber ducting. The air is trapped in the sealed tube AB.
Since the air column has an equal cross section, the air volume is proportionate to its length. The device is supported by a vertical stand and is mounted on a horizontal base. The levelling studs are included with the item.
Boyle’s Law Experiment
Also Read: Boyle's Law Important Formula & Graphical Representation
Variation in Volume with Pressure: Procedure
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The Experiment process is Given below:
- Pressure Measurement: The disparity (h) in the mercury content (X and Y) in the twin tubes AB and CD is used to calculate the tension of the contained air in tube AB. Because the tension in linked tubes is the same across any horizontal position, P (Sealed air pressure) = H h, where H is the air pressure.
- Measurement of Trapped Air Volume: If the enclosed tube is not graded, the amount of trapped air can be measured. The air volume in the tube equals the quantity of air in the length PR minus the amount of air in the curved segment, PQ. Take r as the tube's radius, and The capacity of the curved part is equivalent to the amount of the hemispheric radius r.
- Measuring Air Volume at Given Temperature:
- Using a thermometer, record the room's temp.
- Applying Fortin's Barometer, record the air pressure.
- Applying the levelling studs and a spirit level, align the equipment vertically.
- Modify the mercury level to a certain level as in AB by sliding the tube CD. To measure the upper convex peak of mercury, utilize a set square.
- Take note of the metre scale readings matching to the enclosed tube P's upper end and level Q's curve just ending.
- Elevate CD to the point where the mercury levels in pipes AB and CD are not the same. In tubes AB and CD, use the set square to carefully examine the mercury bubble X and Y. Take note of the distinction.
- Perform the CD modification for 5 more 'h' values. Gradually and without jerking should be done. Boyle's section applies if the orientation of the CD with regard to AB is slowly changed. Else, the temp will change.
- Compute the diameter of the sealed tube AB using the Vernier Callipers, and thus 'r', its radii 1/ 3 PQ =1/3 r.
- Make a note of your findings in the Table.
- Plot and analyse graphs I P vs V and (ii) P versus 1/V.
Also Read: Kinetic Theory of Gases
Variation in Volume with Pressure: Experiment Observations
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Following Observations are made through the experiment:
- The temperature in the room is... °C.
- As measured by the Fortins Barometer, air density is... cm Hg.
- Due to the curved segment of tube AB, there is a correction in level l.
- The measurement for the sealed tube's top is AB (P) =... cm.
- Identifying the point on the tube AB where the equal portion starts (or the curved section finishes) (Q) =... cm.
- (P – Q) difference = r =... cm
- P1 is the initial air pressure in millimetres of mercury.
- P2 =......cm Hg final air pressure
- P0 = P 1 + P 2/ 2 = 75.0 c m o f H g is the mean air pressure.
The graph involving P and V is a curve with experimental limitations.
The PV output is consistent (from the computation) within experimental limitations.
Variation in Volume with Pressure: Experiment Calculations
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Through the Table
To determine the differential pressure, compare the Hg levels in tubes A and B. (p).
To get the total pressures P(= P0 + p) of air in pipe A, add air density P0(75.0 cm of Hg) to force difference p.
Write the volume V of air in tube A.
Fill in the values for 1/V and PV in the appropriate columns.
With Graph
Make a graph connecting P and V, with P on the X-axis and V on the Y-axis. A hyperbola is the chart.
Some other graph involving P and 1/V, this time with P on the X-axis and y on the Y-axis. The graph is a positive sloped straight line.
Variation in Volume with Pressure: Experiment Precautions
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The following points should be kept in mind while Conducting the Experiment:
- When not being used, the equipment should be secured.
- During observations, the device should not be moved.
- Adjustment for the curved part of the enclosed tube must be taken into consideration when calculating the volume of air.
- The mercurial should be pure and leave no traces on the glass.
- While not being used, the open pipe should be sealed with cotton wool.
- To measure the level of the mercury, the set square should indeed be positioned parallel to the uppermost meniscus.
Also Read: Ideal Gas law
Things to Remember
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- The two transparent tubes' diameters may well not be the same, but the apparatus must be vertical.
- The temp of the enclosed air should be maintained by gradually raising or lowering the open tube CD.
- The readings (along each atmospheric pressure) should be taken in that sequence. This ensures a broader range of observation, and if they are taken slowly enough.
- The atmospheric pressure and density will remain constant throughout the observation period. As a result, there should be no squandering of time.
Sample Questions
Ques. Given 2 Examples of Boyle’s law. (2 Marks)
Ans. The two examples are:
- When you squeeze an inflated balloon, the space represented by the air within the balloon shrinks. As a result of Boyle's law, this is characterised by an elevation in the pressure imposed by the air on the balloon. As the balloon is pressed tighter, the pressure builds up until it pops.
- The drop in pressure caused by a scuba diver quickly ascending from a deeper zone to the level of the sea can force the gas molecules in his or her system to expand. These bubbles have the potential to harm the diver's organs and perhaps lead to death. Other example of Boyle's law is the inflation of the gas generated by the scuba diver's ascent.
Ques. Explain the Relation between Volume & temperature. (2 Marks)
Ans. When we inflate and enclose a balloon with gas, the balloon holds a specified volume of air pressure, say 1 atm. When we put the balloon in the fridge, the gas within condenses and the balloon contracts. Chilled balloon shrinks a lot and then expands when it heats up again. In principle, as the temp rises, the volume rises, and as the temp falls, the volume falls.
Ques. What is the Relation between Temperature & Pressure? (2 Marks)
Ans. Consider filling a hard container connected to a pressure sensor with air and then covering it to prevent the gas from escaping. When the vessel is cooled, the gas within cools as well, and the temperature inside drops. The quantity and molar mass of gas stay unchanged since the vessel is stiff and tightly sealed. When the sphere is heated, the gas inside becomes hotter, and the pressure rises. Any specimen of gas constrained to a constant volume exhibits this correlation between pressure and temperature.
Ques. Upon the sidewalls of box 1, a gas produces a pressure of 3 kPa. The pressure applied by the gas grows to 6 kPa when box 1 is discharged into a 10-liter container. Calculate box 1's volume. Consider that the gas's pressure and temperature remain unchanged. (3 Marks)
Ans. Given,
P1 = 3kPa is the initial pressure.
P2 = 6kPa final pressure
V2 = 10L final volume
V1 = (P2V2)/P1 as per Boyle's law
V1 = (6 kPa * 10 L)/3 kPa = 20 L
As a result, box 1 has a volume of 20 L.
Ques. What is Ideal Gas Law? (4 Marks)
Ans. The universal gas equation, commonly known as the ideal gas law, is the fundamental equation of a theoretical ideal gas. Although it has significant drawbacks, it is a fair estimate of the behaviour of various gases under several settings. Benoît Paul Émile Clapeyron initially articulated it in 1834 as a mixture of experimental Boyle's equation, Charles' law, Avogadro's law, and Gay-law. Lussac's The actual form of the ideal gas law is as follows:
The tension, volume, and temperature of a given amount of gas define its condition. The contemporary formulation of the equation merely connects these in two ways. The temp in the equation of value is absolute, and the kelvin is the relevant SI unit.
Ques. What is the Importance of Boyle’s law? (3 Marks)
Ans. When the temp is held constant, Boyle's Law asserts that the connection between pressure and volume is directly proportional. The pressure is increased as the volume drops, implying that when one increases, the other halves. This law contributed in the development of needles and explains how balloons, planes, and bubbles work.
Boyle's law provides valuable insight into the behaviour of gases. In this situation, we discover that a gas's mass and density are inversely related, which means that if we squeeze it really hard, it squeezes into a smaller amount.
Ques. A valve separates two bulbs of different amounts. The valve here between 2.00 L bulb, which has a 1.00 atm gas pressure, and the 3.00 L bulb, which has a 1.50 atm gas pressure, is unlocked. What really is the final volume in the two bulbs if the temp in both bulbs is steady and the same? (5 Marks)
Ans. The following is a solution based on Boyle's Law:
P1V1 is equal to P2V2 twice.
- atm) (2.00 L) = (x) (5.00 L) x is equal to 0.400 atm
- (1.50 atm) (3.00 L) (5.00 L) is equal to (y)
- 0.900 atm= y
- Let’s Calculate all of them.
- 1.30 atm = 0.400 atm + 0.900 atm
Ques. What are the limitations of Boyle’s law? (3 Marks)
Ans. Only ideal gases are covered by Boyle's law. Only at low temperatures and high pressures does the law hold true. At extreme pressures, the law breaks down. At elevated pressure, the merchandise of pressure and volume does not stay unchanged, but exhibits a little increase. This increase is due to a rise in volume, which is presented by repulsive forces between molecules. The law could also be established theoretically using hypotheses about velocity and completely elastic interactions, as well as the assumed presence of subatomic particles.
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