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Boyles Law Questions

Boyle’s law is also referred to as Boyle–Mariotte law or Mariotte’s law. It tells us about the behaviour of gases. Boyle’s law states that the pressure is inversely proportional to the volume of the gas at constant pressure.

P ∝ 1 / V

Boyles Law Chemistry Questions with Solutions

Q1. Suppose P, V, and T represent the gas’s pressure, volume, and temperature, then the correct representation of Boyle’s law is

• V is inversely proportional to T (at constant P)
• V inversely proportional to P (at constant T)

Answer: (b), If P, V, and T represent the gas’s pressure, volume, and temperature, then the correct representation of Boyle’s law is V inversely proportional to P (at constant T).

V ∝ 1 / P

Q2. What is the nature of Boyle’s Law’s pressure vs volume (P vs V) graph?

• Straight Line
• Rectangular Hyperbola
• None of the above

Answer: (b), The nature of Boyle’s Law’s pressure vs volume (P vs V) graph is a rectangular hyperbola.

Q3. What is the nature of Boyle’s Law’s pressure-volume vs pressure (PV vs P) graph?

• Straight-line parallel to the P axis
• Straight-line parallel to the PV axis
• Straight-line parallel to the V axis

Answer: (a), The nature of Boyle’s Law’s pressure-volume vs pressure (PV vs P) graph is a straight line parallel to the P axis.

Q4. Which of the following quantity is kept constant in Boyle’s law?

• Gas mass only
• Gas Temperature only
• Gas Mass and Gas Pressure
• Gas Mass and Gas Temperature

Answer: (d), In Boyle’s law, the mass of the gas its temperature are kept constant.

Q5. Boyle’s law is valid only for

• Ideal gases
• Non-ideal gases
• Light Gases
• Heavy Gases

Answer: (a), Boyle’s law is valid only for ideal gases.

Q6. What is Boyle’s law?

Answer: Boyle’s law depicts the relationship between the pressure, volume, and temperature of a gas. It states that the pressure of a gas is inversely proportional to its volume at a constant temperature.

Q7. How is Boyle’s law used in everyday life?

Answer: Boyle’s law can be observed in our everyday life. Filling air in the bike tire is one of the significant applications of Boyle’s law. While pumping air into the tyre, the gas molecules inside the tire are compressed and packed closer together. It increases the pressure exerted on the walls of the tyre.

Q8. What is Boyle’s temperature?

Answer: Boyle’s temperature is the temperature at which the real and non-ideal gases behave like an ideal gas over a broad spectrum of pressure. It is related to the Van der Waal’s constant a, b as TB = a / Rb

Q9. Differentiate between Boyle’s law and Charle’s law.

Q10. Match the following gas laws with the equation representing them.

Q11. A helium balloon has a volume of 735 mL at ground level. The balloon is transported to an elevation of 5 km, where the pressure is 0.8 atm. At this altitude, the gas occupies a volume of 1286 mL. Assuming that the temperature is constant, what was the ground level pressure?

Answer: Given

Initial Volume (V 1 ) = 735 mL

Final Pressure (P 2 ) = 0.8 atm

Final Volume (V 2 ) = 1286 mL

To Find: Initial Pressure (P 1 ) = ?

We can calculate the initial pressure of the gas using Boyle’s law.

P 1 V 1 = P 2 V 2

P 1 X 735 = 0.8 X 1286

P 1 = 1028.8 / 735

P 1 = 1.39 ≈ 1.4 atm

Hence the ground level pressure is 1.4 atm.

Q12. A sample of oxygen gas has a volume of 225 mL when its pressure is 1.12 atm. What will the volume of the gas be at a pressure of 0.98 atm if the temperature remains constant?

Initial Volume (V 1 ) = 225 mL

Initial Pressure (P 1 ) = 1.12 atm

Final Pressure (P 2 ) = 0.98 atm

To Find: Final Volume (V 2 ) = ?

We can calculate the final volume of the gas using Boyle’s law.

1.12 X 225 = 0.98 X V 2

252 = 0.98 X V 2

252 / 0.98 = V 2

V 2 = 257.14 mL ≈ 257mL

Hence the final volume of the gas at pressure of 0.98 atm is equivalent to 257 mL.

Q13. An ideal gas occupying a 2.0 L flask at 760 torrs is allowed to expand to a volume of 6,000 mL. Calculate the final pressure

Initial Volume (V 1 ) = 2 L

Initial Pressure (P 1 ) = 760 torrs

Final Volume (V 2 ) = 6000 mL = 6 L

To Find: Final Pressure (P 2 ) = ?

We can calculate the final pressure of the gas using Boyle’s law.

760 X 2 = P 2 X 6

1520 = P 2 X 6

P 2 = 1520 / 6

P 2 = 253.33 torrs ≈ 253 torrs

Hence the final pressure of the gas at volume of 6 L is equivalent to 253 torrs.

Q14. A gas occupies a volume of 1 L and exerts a pressure of 400 kPa on the walls of its container. What would be the pressure exerted by the gas if it is completely transferred into a new container having a volume of 3 litres (assuming that the temperature and amount of the gas remain the same.)?

Initial Volume (V 1 ) = 1 L

Initial Pressure (P 1 ) = 400 kPa

Final Volume (V 2 ) = 3 L

400 X 1 = P 2 X 3

P 2 = 400 / 3

P 2 = 133.33 ≈ 133 kPa

Hence the final pressure of the gas at of volume 3 L is equivalent to 133 kPa.

Q15. A gas exerts a pressure of 3 kPa on the walls of container 1. When container one is emptied into a 10 litre container, the pressure exerted by the gas increases to 6 kPa. Find the volume of container 1. Assume that the temperature and amount of the gas remain the same.

Initial Pressure (P 1 ) = 3 kPa

Final Volume (V 2 ) = 10 L

Final Pressure (P 2 ) = 6 kPa

To Find: Initial Volume (V 1 ) = ?

We can calculate the initial volume of the gas using Boyle’s law.

3 X V 1 = 6 X 10

3 X V 1 = 60

V 1 = 60 / 3

Hence the initial volume of the gas at pressure of 3 kPa is equivalent to 20 L.

Practise Questions on Boyle’s Law

Q1. A gas is initially in a 5 L piston with a pressure of 1 atm. What is the new volume if the pressure changes to 3.5 atm by moving the piston down?

Q2. A balloon of volume 0.666 L at 1.03atm is placed in a pressure chamber where the pressure becomes 5.68atm. Determine the new volume.

Q3. A gas in a 30.0 mL container is at a pressure of 1.05 atm and is compressed to a volume of 15.0 mL. What is the new pressure of the container?

Q4. If a gas occupies 3.60 litres at a pressure of 1.00 atm, what will be its volume at a pressure of 2.50 atm?

Q5. A gas occupies 12.3 litres at a pressure of 40.0 mmHg. What is the volume when the pressure is increased to 60.0 mmHg?

Click the PDF to check the answers for Practice Questions. Download PDF

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Boyle's Law Explained With Example Problem

Volume's inversely proportional to pressure if temperature's constant

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Boyle's gas law states that the volume of a gas is inversely proportional to the pressure of the gas when the temperature is held constant. Anglo-Irish chemist Robert Boyle (1627–1691) discovered the law and for it he is considered the first modern chemist. This example problem uses Boyle's law to find the volume of gas when pressure changes.

Boyle's Law Example Problem

• A balloon with a volume of 2.0 L is filled with a gas at 3 atmospheres. If the pressure is reduced to 0.5 atmospheres without a change in temperature, what would be the volume of the balloon?

Since the temperature doesn't change, Boyle's law can be used. Boyle's gas law can be expressed as:

• P i V i = P f V f
• P i = initial pressure
• V i = initial volume
• P f = final pressure
• V f = final volume

To find the final volume, solve the equation for V f :

• V f = P i V i /P f
• V i = 2.0 L
• P i = 3 atm
• P f = 0.5 atm
• V f = (2.0 L) (3 atm) / (0.5 atm)
• V f = 6 L / 0.5 atm
• V f = 12 L

The volume of the balloon will expand to 12 L.

More Examples of Boyle's Law

As long as the temperature and number of moles of gas remain constant, Boyle's law means doubling the pressure of a gas halves its volume. Here are more examples of Boyle's law in action:

• When the plunger on a sealed syringe is pushed, the pressure increases and the volume decreases. Since the boiling point is dependent on pressure, you can use Boyle's law and a syringe to make water boil at room temperature.
• Deep-sea fish die when they're brought from the depths to the surface. The pressure decreases dramatically as they are raised, increasing the volume of gases in their blood and swim bladder. Essentially, the fish pop.
• The same principle applies to divers when they get "the bends." If a diver returns to the surface too quickly, dissolved gases in the blood expand and form bubbles, which can get stuck in capillaries and organs.  
• If you blow bubbles underwater, they expand as they rise to the surface. One theory about why ships disappear in the Bermuda Triangle relates to Boyle's law. Gases released from the seafloor rise and expand so much that they essentially become a gigantic bubble by the time they reach the surface. Small boats fall into the "holes" and are engulfed by the sea.

Walsh C., E. Stride, U. Cheema, and N. Ovenden. " A combined three-dimensional in vitro–in silico approach to modelling bubble dynamics in decompression sickness ." Journal of the Royal Society Interface , vol. 14, no. 137, 2017, pp. 20170653, doi:10.1098/rsif.2017.0653

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• Boyle's Law Definition in Chemistry
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• Pressure Definition and Examples

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High School Chemistry : Using Boyle's Law

Study concepts, example questions & explanations for high school chemistry, all high school chemistry resources, example questions, example question #11 : gases and gas laws.

Since the volume of the gas is the only variable that has changed, we can use Boyle's law in order to find the final pressure. Since pressure and volume are on the same side of the ideal gas law, they are inversely proportional to one another. In other words, as one increases, the other will decrease, and vice versa.

Boyle's law can be written as follows:

Use the given volumes and the initial pressure to solve for the final pressure.

Example Question #1 : Using Boyle's Law

What law is the following formula?

Charles's law

Boyle's law

Combined gas law

Ideal gas law

Gay-Lussac's law

Boyle's law relates the pressure and volume of a system, which are inversely proportional to one another. When the parameters of a system change, Boyle's law helps us anticipate the effect the changes have on pressure and volume.

Example Question #13 : Gases And Gas Laws

To solve this question we will need to use Boyle's law:

We are given the final pressure and volume, along with the initial volume. Using these values, we can calculate the initial pressure.

Example Question #14 : Gases And Gas Laws

The graph depicted here represents which of the gas laws?

The graph shows that there is an inverse relationship between the volume and pressure of a gas, when kept at a constant temperature. This was described by Robert Boyle and can be represented mathematically as Boyle's law:

Gay-Lussac's law shows the relationship between pressure and temperature. Charles's law shows the relationship between volume and temperature. Hund's rule (Hund's law) is not related to gases, and states that electron orbitals of an element will be filled with single electrons before any electrons will form pairs within a single orbital.

We are given the initial pressure and volume, along with the final pressure. Using these values, we can calculate the final volume.

A gas is initially in a 5L piston with a pressure of 1atm.

If pressure changes to 3.5atm by moving the piston down, what is new volume?

Use Boyle's Law:

Plug in known values and solve for final volume.

Use Boyle's law and plug in appropriate parameters:

Boyle's Law is:

Notice the answer has 3 significant figures.

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Boyle’s Law – Definition, Formula, Example

Boyle’s law or Mariotte’s law states that pressure of an ideal gas is inversely proportional to volume under conditions of constant mass and temperature. When the gas volume increases, pressure decreases. When the volume decreases, pressure increases. Boyle’s law takes its name from chemist and physicist Robert Boyle , who published the law in 1862.

Boyle’s law states that the absolute pressure of an ideal gas is inversely proportional to its volume under conditions of constant mass and temperature.

Boyle’s Law Formula

There are three common formulas for Boyle’s law:

P ∝ 1/V PV = k P 1 V 1 = P 2 V 2

P is absolute pressure, V is volume, and k is a constant.

Graphing Boyle’s Law

The graph of volume versus pressure has a characteristic downward curved shape that shows the inverse relationship between pressure and volume. Boyle used the graph of experimental data to establish the relationship between the two variables.

Richard Towneley and Henry Power described the relationship between the pressure and volume of a gas in the 17th century. Robert Boyle experimentally confirmed their results using a device constructed by his assistant, Robert Hooke. The apparatus consisted of a closed J-shaped tube. Boyle poured mercury into the tube, decreasing the air volume and increasing its pressure. He used different amounts of mercury, recording air pressure and volume measurements, and graphed the data. Boyle published his results in 1662. Sometimes the gas law is called the Boyle-Mariotte law or Mariotte’s law because French physicist Edme Mariotte independently discovered the law in 1670.

Examples of Boyle’s Law in Everyday Life

There are examples of Boyle’s law in everyday life:

• The bends : A diver ascends to the water surface slowly to avoid the bends. As a diver rises to the surface, the pressure from the water decreases, which increases the volume of gases in the blood and joints. Ascending too quickly allows these gases to form bubbles, blocking blood flow and damaging joints and even teeth.
• Air bubbles : Similarly, air bubbles expand as they rise up a column of water. If you have a tall glass, you can watch bubble expand in volume as pressure decreases. One theory about why ships disappear in the Bermuda Triangle relates to Boyle’s law. Gases released from the seafloor rise and expand so much that they essentially become a gigantic bubble by the time they reach the surface. Small boats fall into the bubbles and are engulfed by the sea.
• Deep-sea fish : Deep-sea fish die if you bring them up to the surface. As outside pressure drops, the volume of gas within their swim bladder increases. Essentially, the fish blow up or pop.
• Syringe : Depressing the plunger on a sealed syringe decreases the air volume inside it and increases its pressure. Similarly, if you have a syringe containing a small amount of water and pull back on the plunger, the volume of air increases, but it’s pressure decreases. The pressure drop is enough to boil the water within the syringe at room temperature.
• Breathing: The diaphragm expands the volume of the lungs, causing a pressure drop that allows outside air to rush into the lungs (inhalation). Relaxing the diaphragm reduces the volume of the lungs, increasing the gas pressure within them. Exhaling occurs naturally to equalize pressure.

Boyle’s Law Example Problem

For example, calculate the final volume of a balloon if it has a volume of 2.0 L and pressure of 2 atmospheres and the pressure is reduced to 1 atmosphere. Assume temperature remains constant.

P 1 V 1 = P 2 V 2 (2 atm)(2.0 L) = (1 atm)V 2 V 2 = (2 atm)(2.0 L)/(1 atm) V 2 = 4.0 L

It’s a good idea to check your work to make sure the answer makes sense. In this example, the balloon pressure decreased by a factor of two (halved). The volume increased and doubled. This is what you expect from an inverse proportion relationship.

Most of the time, homework and test questions require reasoning rather than math. For example, if volume increases by a factor of 10, what happens to pressure? You know increasing volume decreases pressure by the same amount. Pressure decreases by a factor of 10.

See another Boyle’s law example problem .

• Fullick, P. (1994).  Physics . Heinemann. ISBN 978-0-435-57078-1.
• Holton, Gerald James (2001). Physics, The Human Adventure: From Copernicus to Einstein and Beyond . Rutgers University Press. ISBN 978-0-8135-2908-0.
• Tortora, Gerald J.; Dickinson, Bryan (2006). ‘Pulmonary Ventilation’ in Principles of Anatomy and Physiology (11th ed.). Hoboken: John Wiley & Sons, Inc. pp. 863–867.
• Walsh, C.; Stride, E.; Cheema, U.; Ovenden, N. (2017). “A combined three-dimensional in vitro–in silico approach to modelling bubble dynamics in decompression sickness.” Journal of the Royal Society Interface . 14(137). doi: 10.1098/rsif.2017.0653
• Webster, Charles (1965). “The discovery of Boyle’s law, and the concept of the elasticity of air in seventeenth century”. Archive for the History of Exact Sciences . 2(6) : 441–502.

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11.4: Boyle’s Law: Pressure and Volume

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Learning Objectives

• Learn what is meant by the term gas laws .
• Learn and apply Boyle’s Law.

When seventeenth-century scientists began studying the physical properties of gases, they noticed some simple relationships between some of the measurable properties of the gas. Take pressure ( P ) and volume ( V ), for example. Scientists noted that for a given amount of a gas (usually expressed in units of moles [ n ]), if the temperature ( T ) of the gas was kept constant, pressure and volume were related: as one increases, the other decreases. As one decreases, the other increases. This means that pressure and volume are inversely related .

There is more to it, however: pressure and volume of a given amount of gas at constant temperature are numerically related. If you take the pressure value and multiply it by the volume value, the product is a constant for a given amount of gas at a constant temperature:

\[P × V = \text{ constant at constant n and T} \nonumber \]

If either volume or pressure changes while amount and temperature stay the same, then the other property must change so that the product of the two properties still equals that same constant. That is, if the original conditions are labeled \(P_1\) and \(V_1\) and the new conditions are labeled \(P_2\) and \(V_2\), we have

\[P_1V_1 = \text{constant} = P_2V_2 \nonumber \]

where the properties are assumed to be multiplied together. Leaving out the middle part, we have simply

\[P_1V_1 = P_2V_2 \text{ at constant n and T} \nonumber \]

This equation is an example of a gas law. A gas law is a simple mathematical formula that allows you to model, or predict, the behavior of a gas. This particular gas law is called Boyle's Law , after the English scientist Robert Boyle, who first announced it in 1662. Figure \(\PageIndex{1}\) shows two representations of how Boyle’s Law works.

Boyle’s Law is an example of a second type of mathematical problem we see in chemistry—one based on a mathematical formula. Tactics for working with mathematical formulas are different from tactics for working with conversion factors. First, most of the questions you will have to answer using formulas are word-type questions, so the first step is to identify what quantities are known and assign them to variables. Second, in most formulas, some mathematical rearrangements (i.e., algebra) must be performed to solve for an unknown variable. The rule is that to find the value of the unknown variable, you must mathematically isolate the unknown variable by itself and in the numerator of one side of the equation. Finally, units must be consistent. For example, in Boyle’s Law there are two pressure variables; they must have the same unit. There are also two volume variables; they also must have the same unit. In most cases, it won’t matter what the unit is, but the unit must be the same on both sides of the equation.

Example \(\PageIndex{1}\)

A sample of gas has an initial pressure of 2.44 atm and an initial volume of 4.01 L. Its pressure changes to 1.93 atm. What is the new volume if temperature and amount are kept constant?

Exercise \(\PageIndex{1}\)

If P 1 = 334 torr, V 1 = 37.8 mL, and P 2 = 102 torr, what is V 2 ?

As mentioned, you can use any units for pressure and volume, but both pressures must be expressed in the same units, and both volumes must be expressed in the same units.

Example \(\PageIndex{2}\):

A sample of gas has an initial pressure of 722 torr and an initial volume of 88.8 mL. Its volume changes to 0.663 L. What is the new pressure?

Exercise \(\PageIndex{2}\)

If V 1 = 456 mL, P 1 = 308 torr, and P 2 = 1.55 atm, what is V 2 ?

• The behavior of gases can be modeled with gas laws.
• Boyle’s Law relates the pressure and volume of a gas at constant temperature and amount.

V 1 / T 1 = V 2 / T 2

V 1 T 2 = V 2 T 1

(2.00 L) / 294.0 K) = (1.00 L) / (x) cross multiply to get: 2x = 293 x = 147.0 K Converting 147.0 K to Celsius, we find -126.0 °C, for a total decrease of 147.0 °C, from 21.0 °C to -126.0 °C.

(600.0 mL) / (293.0) = (x) / (333.0 K) x = 682 mL

(900.0 mL) / (300.0 K) = (x) / (405.0 K) x = 1215 mL

(60.0 mL) / (306.0 K) = (x) / (278.00 K) Cross multiply to get: 306x = 16680 x = 54.5 mL The volume decreases by 5.5 mL.

In cross-multiplied form, it is this: V 1 T 2 = V 2 T 1 V 2 = (V 1 T 2 ) / T 1 1 x = [(300.0 mL) (283.0 K)] / 290.0 K

In cross-multiplied form, it is this: V 1 T 2 = V 2 T 1 V 2 = (V 1 ) [T 2 / T 1 ] x = (1.00 L) [(606.0 K) / (273.0 K)] x = 2.22 L

(6.00 L) / (300.0 K) = (x) / (423.0 K) or (6.00 L) (423.0 K) = (x) (300.0 K)

V 2 = (V 1 ) [T 2 / T 1 ] x = (400.0 mL) [(400.0 K) / (498.0 K) x = 321 mL

(400.0 mL) / (498.0 K) = (x) / (400.0 K)

(8.00 L) / (483.0 K) = (x) / (250.0 K) Note how you can have a negative Celsius temperature, but not a negative Kelvin temperature.

V 1 / T 1 = V 2 / T 2 x / 588 K = 852 mL / 725 K (x) (725 K) = (852 mL) (588 K) x = 691 mL

2.05 L / 278 K = V 2 / 294 K Calculate V 2 . The volume that "escapes" is V 2 minus 2.05 L