What happens to the pressure of a gas if its volume is increased?

How cool is it to change your state?

Freeze me; I am ice.

Heat me; I am water.

Boil me; I am steam.

I have different forms and states: I am Matter!

The Different States of Matter (Photo Credit : VectorMine/Shutterstock)

Recommended Video for you:

Why Do Bubbles Form In A Glass Of Water?

If you wish to buy/license this video, please write to us at .

The versatility of ‘Matter’

Simply put, the definition of matter is something that carries mass and occupies space.

There are four fundamental states of matter: Solid, Liquid, Gas, and Plasma.

Arrangement of molecules in different states of matter (Photo Credit : udaix/Shutterstock)

Solids:

These are rigid and incompressible with a definite shape and volume. Strong inter-molecular forces hold the molecules together with no or negligible inter-molecular spaces. The molecules in solids have low kinetic energy and low vibrational energy. Solids can exist in two forms: crystalline or amorphous.

Solid carbon exists in a crystalline form as diamond, and in amorphous form as charcoal.

Liquids:

These are fluidic, have a definite volume, no definite shape (takes the shape of the container), and are incompressible. Moderate intermolecular forces hold the molecules together with weak intermolecular spaces. The molecules in liquid move with moderate kinetic energy. Liquids possess properties of capillary action, viscosity, and surface tension.

Gases:

Inter- molecular spaces in gases (Photo Credit : Arisa_J/Shutterstock)

These are also highly fluidic, have indefinite shape and volume, and are easily compressible. The intermolecular forces in a gas are very weak and the intermolecular distances are large. Thus, gases are free-flowing, and the molecules in a gas move with high kinetic energy.

Plasma:

The most abundant state of matter in the universe is plasma or superheated matter. 99% of the matter in the Universe is in the plasma state. When energy is passed through neutral gas, the electrons are removed to form both positively and negatively charged ions. It has neither shape nor volume. Plasma makes up the sun and stars.

(Photo Credit : Quardia/Shutterstock)

What determines the state of Matter?

Matter has a specific state at a given temperature and pressure. The two factors that regulate its state are:

1. Temperature (explained by Charles’ Law)
2. Pressure (explained by Boyles’ Law)

Understanding the effect of temperature on the States of Matter

At atmospheric pressure, water exists as a liquid at temperatures between 0ᵒC to 100ᵒC, as water vapor (gas) beyond 100ᵒC, and as ice (solid) at 0ᵒC and below. The temperature ranges in which substances exist in a particular state vary for each substance.

We know that water has three states, but what about other elements and compounds? Do iron, oxygen, and calcium chloride exist in three states?

The emphatic answer is: “All matter exists in different states, depending on the temperature and pressure”.

From the above, oxygen is a gas at > -182ᵒC, while iron is a gas at 2860ᵒC. All matter can exist in the three states, but the temperatures at which they attain each state vary broadly.

Charles’s Law governs the States of Matter

Charles’s Law states that the volume of a fixed amount of gas is directly proportional to its absolute temperature if the pressure remains constant.

Charles’s Law postulating the relationship between Temperature and Volume (Photo Credit : udaix/Shutterstock)

At constant pressure, if the temperature of a solid (i.e., ice) is increased, its volume correspondingly increases. With the increased volume, molecules move farther, increasing the inter-molecular distance, and thereby decreasing the intermolecular forces. When this happens, the solid ice slowly undergoes a phase transition to liquid water.

A further increase in temperature will proportionally increase the volume, making the molecules move farther away from each other. This increases the intermolecular distance, and decreases the intermolecular force of attraction, thus causing the shift from water (liquid) to steam (gas).

Understanding the effect of pressure on the States of Matter

As mentioned earlier, pressure is another critical factor that determines the state of matter. This principle is used in the manufacture of liquid N2 and dry ice (solid carbon dioxide). Gaseous Nitrogen will become a liquid when pressure is increased on the gas.

On the other hand, you can make water boil at room temperature by decreasing the pressure enough.

So, pressure and temperature are in an inverse relationship. Liquid N2 and dry ice are manufactured by applying pressure on the gases N2 and CO2 to change their state from gas to liquid and gas to solid, respectively.

Liquid N2 (Photo Credit : Suslov Denis/Shutterstock)

Dry Ice (Photo Credit : Kollawat Somsri/Shutterstock)

Boyle’s Law governs the States of Matter

As mentioned earlier, there is an inverse relationship between pressure and temperature, which is governed by Boyle’s law. According to the law, the volume of a gas increases as the pressure decreases, at a constant temperature.

Boyle’s Law postulating the relationship between Pressure and Volume (Photo Credit : udaix/Shutterstock)

From the above illustration, we observe that the pressure and volume of a gas are inversely proportional.

When the pressure is increased, the volume decreases, bringing the molecules closer together. This increases the intermolecular force of attraction and decreases the intermolecular distance. This will promote the transition from a gaseous to a liquid state.

A further increase in pressure reduces the volume even more, thus transiting liquids into solids.

How is dry ice formed?

In dry ice manufacturing, the pressure on CO2 gas is reduced from 1 atmospheric (1 atm) to 5.11. At this pressure, and at a constant -56ᵒC, gaseous CO2 becomes solid CO2 with a very transient liquid state.

The specific temperature and pressure at which three states of any matter are in equilibrium is called its triple point.

Triple point: The temperature and pressure at which the solid, liquid, and vapor phases of a pure substance can coexist in equilibrium (Photo Credit : magnetix/Shutterstock)

A slight decrease in temperature will phase transform gaseous CO2 to solid CO2.

Conclusions

The states of matter are continuously recycled, and temperature and pressure control the phase transitions. The temperature and pressure at which all the states coexist is called the triple point. A finely orchestrated process between temperature, volume, and pressure determines the state of any matter.

Suggested Reading

References

1. Scientific American (Link 1)
2. Scientific American (Link 2)

Was this article helpful?

Learning Objectives

• To understand the relationships among pressure, temperature, volume, and the amount of a gas.

Early scientists explored the relationships among the pressure of a gas (P) and its temperature (T), volume (V), and amount (n) by holding two of the four variables constant (amount and temperature, for example), varying a third (such as pressure), and measuring the effect of the change on the fourth (in this case, volume). The history of their discoveries provides several excellent examples of the scientific method.

As the pressure on a gas increases, the volume of the gas decreases because the gas particles are forced closer together. Conversely, as the pressure on a gas decreases, the gas volume increases because the gas particles can now move farther apart. Weather balloons get larger as they rise through the atmosphere to regions of lower pressure because the volume of the gas has increased; that is, the atmospheric gas exerts less pressure on the surface of the balloon, so the interior gas expands until the internal and external pressures are equal.

The Irish chemist Robert Boyle (1627–1691) carried out some of the earliest experiments that determined the quantitative relationship between the pressure and the volume of a gas. Boyle used a J-shaped tube partially filled with mercury, as shown in Figure \(\PageIndex{1}\). In these experiments, a small amount of a gas or air is trapped above the mercury column, and its volume is measured at atmospheric pressure and constant temperature. More mercury is then poured into the open arm to increase the pressure on the gas sample. The pressure on the gas is atmospheric pressure plus the difference in the heights of the mercury columns, and the resulting volume is measured. This process is repeated until either there is no more room in the open arm or the volume of the gas is too small to be measured accurately. Data such as those from one of Boyle’s own experiments may be plotted in several ways (Figure \(\PageIndex{2}\)). A simple plot of \(V\) versus \(P\) gives a curve called a hyperbola and reveals an inverse relationship between pressure and volume: as the pressure is doubled, the volume decreases by a factor of two. This relationship between the two quantities is described as follows:

\[PV = \rm constant \label{6.2.1}\]

Dividing both sides by \(P\) gives an equation illustrating the inverse relationship between \(P\) and \(V\):

\[V=\dfrac{\rm const.}{P} = {\rm const.}\left(\dfrac{1}{P}\right) \label{6.2.2}\]

or

\[V \propto \dfrac{1}{P} \label{6.2.3}\]

where the ∝ symbol is read “is proportional to.” A plot of V versus 1/P is thus a straight line whose slope is equal to the constant in Equation 6.2.1 and Equation 6.2.3. Dividing both sides of Equation 6.2.1 by V instead of P gives a similar relationship between P and 1/V. The numerical value of the constant depends on the amount of gas used in the experiment and on the temperature at which the experiments are carried out. This relationship between pressure and volume is known as Boyle’s law, after its discoverer, and can be stated as follows: At constant temperature, the volume of a fixed amount of a gas is inversely proportional to its pressure.

Boyle’s Law: https://youtu.be/lu86VSupPO4

Hot air rises, which is why hot-air balloons ascend through the atmosphere and why warm air collects near the ceiling and cooler air collects at ground level. Because of this behavior, heating registers are placed on or near the floor, and vents for air-conditioning are placed on or near the ceiling. The fundamental reason for this behavior is that gases expand when they are heated. Because the same amount of substance now occupies a greater volume, hot air is less dense than cold air. The substance with the lower density—in this case hot air—rises through the substance with the higher density, the cooler air.

The first experiments to quantify the relationship between the temperature and the volume of a gas were carried out in 1783 by an avid balloonist, the French chemist Jacques Alexandre César Charles (1746–1823). Charles’s initial experiments showed that a plot of the volume of a given sample of gas versus temperature (in degrees Celsius) at constant pressure is a straight line. Similar but more precise studies were carried out by another balloon enthusiast, the Frenchman Joseph-Louis Gay-Lussac (1778–1850), who showed that a plot of V versus T was a straight line that could be extrapolated to a point at zero volume, a theoretical condition now known to correspond to −273.15°C (Figure \(\PageIndex{3}\)).A sample of gas cannot really have a volume of zero because any sample of matter must have some volume. Furthermore, at 1 atm pressure all gases liquefy at temperatures well above −273.15°C. Note from part (a) in Figure \(\PageIndex{3}\) that the slope of the plot of V versus T varies for the same gas at different pressures but that the intercept remains constant at −273.15°C. Similarly, as shown in part (b) in Figure \(\PageIndex{3}\), plots of V versus T for different amounts of varied gases are straight lines with different slopes but the same intercept on the T axis.

The significance of the invariant T intercept in plots of V versus T was recognized in 1848 by the British physicist William Thomson (1824–1907), later named Lord Kelvin. He postulated that −273.15°C was the lowest possible temperature that could theoretically be achieved, for which he coined the term absolute zero (0 K).

We can state Charles’s and Gay-Lussac’s findings in simple terms: At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature (in kelvins). This relationship, illustrated in part (b) in Figure \(\PageIndex{3}\) is often referred to as Charles’s law and is stated mathematically as

\[V ={\rm const.}\; T \label{6.2.4}\]

or

\[V \propto T \label{6.2.5}\]

with temperature expressed in kelvins, not in degrees Celsius. Charles’s law is valid for virtually all gases at temperatures well above their boiling points.

Charles’s Law: https://youtu.be/NBf510ZnlR0

We can demonstrate the relationship between the volume and the amount of a gas by filling a balloon; as we add more gas, the balloon gets larger. The specific quantitative relationship was discovered by the Italian chemist Amedeo Avogadro, who recognized the importance of Gay-Lussac’s work on combining volumes of gases. In 1811, Avogadro postulated that, at the same temperature and pressure, equal volumes of gases contain the same number of gaseous particles (Figure \(\PageIndex{4}\)). This is the historic “Avogadro’s hypothesis.”

A logical corollary to Avogadro's hypothesis (sometimes called Avogadro’s law) describes the relationship between the volume and the amount of a gas: At constant temperature and pressure, the volume of a sample of gas is directly proportional to the number of moles of gas in the sample. Stated mathematically,

\[V ={\rm const.} \; (n) \label{6.2.6}\]

or

\[V \propto.n \text{@ constant T and P} \label{6.2.7}\]

This relationship is valid for most gases at relatively low pressures, but deviations from strict linearity are observed at elevated pressures.

Note

For a sample of gas,

• V increases as P decreases (and vice versa)
• V increases as T increases (and vice versa)
• V increases as n increases (and vice versa)

The relationships among the volume of a gas and its pressure, temperature, and amount are summarized in Figure \(\PageIndex{5}\). Volume increases with increasing temperature or amount but decreases with increasing pressure.

 Avogadro’s Law: https://youtu.be/dRY3Trl4T24

The volume of a gas is inversely proportional to its pressure and directly proportional to its temperature and the amount of gas. Boyle showed that the volume of a sample of a gas is inversely proportional to its pressure (Boyle’s law), Charles and Gay-Lussac demonstrated that the volume of a gas is directly proportional to its temperature (in kelvins) at constant pressure (Charles’s law), and Avogadro postulated that the volume of a gas is directly proportional to the number of moles of gas present (Avogadro’s law). Plots of the volume of gases versus temperature extrapolate to zero volume at −273.15°C, which is absolute zero (0 K), the lowest temperature possible. Charles’s law implies that the volume of a gas is directly proportional to its absolute temperature.