Which gas law best explains why the volume of a balloon increases when you fill it with helium?

In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation.

A flat tire is not very useful. It does not cushion the rim of the wheel and creates a very uncomfortable ride. When air is added to the tire, the pressure increases as more molecules of gas are forced into the rigid tire. How much air should be put into a tire depends on the pressure rating for that tire. Too little pressure and the tire will not hold its shape. Too much pressure and the tire could burst.

You have learned about Avogadro's hypothesis: equal volumes of any gas at the same temperature and pressure contain the same number of molecules. It follows that the volume of a gas is directly proportional to the number of moles of gas present in the sample. Avogadro's Law states that the volume of a gas is directly proportional to the number of moles (or number of particles) of gas when the temperature and pressure are held constant. The mathematical expression of Avogadro's Law is:

\[V = k \times n\]

\[\dfrac{V_1}{n_1} = \dfrac{V_2}{n_2}\]

where $n$ is the number of moles of gas and $k$ is a constant. Avogadro's Law is in evidence whenever you blow up a balloon. The volume of the balloon increases as you add moles of gas to the balloon by blowing it up.

If the container holding the gas is rigid rather than flexible, pressure can be substituted for volume in Avogadro's Law. Adding gas to a rigid container makes the pressure increase.

Example $\PageIndex{1}$

A balloon has been filled to a volume of $1.90 \: \text{L}$ with $0.0920 \: \text{mol}$ of helium gas. If $0.0210 \: \text{mol}$ of additional helium is added to the balloon while the temperature and pressure are held constant, what is the new volume of the balloon?

Solution

Steps for Problem Solving
Identify the "given"information and what the problem is asking you to "find."	Given: $V_1 = 1.90 \: \text{L}$ $n_1 = 0.0920 \: \text{mol}$ Find: $V_2 = ? \: \text{L}$
List other known quantities	Note that the final number of moles has to be calculated by adding the original number of moles to the moles of added helium. $n_2 = 0.0920 + 0.0210 = 0.1130 \: \text{mol}$
Plan the problem	First, rearrange the equation algebraically to solve for $V_2$. \[V_2 = \frac{V_1 \times n_2}{n_1}\]
Calculate	Now substitute the known quantities into the equation and solve. \[V_2 = \frac{1.90 \: \text{L} \times 0.1130 \: \cancel{\text{mol}}}{0.0920 \: \cancel{\text{mol}}} = 2.33 \: \text{L}\]
Think about your result.	Since a relatively small amount of additional helium was added to the balloon, its volume increases slightly.

Exercise $\PageIndex{1}$

A 12.8 L volume of gas contains .000498 moles of oxygen gas. At constant temperature and pressure, what volume does .0000136 moles of the gas fill?

Answer

0.350 L

Summary

Calculations are shown for relationships between volume and number of moles of a gas.

Contributors and Attributions

Marisa Alviar-Agnew (Sacramento City College)
Henry Agnew (UC Davis)

Find an online tutor for 1-on-1 lessons and master the knowledge you need! Prices from just $5 per hour.

Explore tutors

The balloon shrinks down to practically zero volume when pulled from the liquid nitrogen. It is filled with very cold high density air at that point. As the balloon warms the balloon expands and the density of the air inside the balloon decreases. The volume and temperature kept changing in a way that kept pressure constant. Eventually the balloon ends up back at room temperature (unless it pops).

Now we are in a position to have a quick look at the forces that can cause parcels of air to rise or sink.

Basically it comes down to this - there are two forces acting on a parcel of air in the atmosphere:
1. Gravity pulls downward. The strength of the gravity force depends on the mass of the air inside the parcel. This force is just the weight of the parcel
2. There is an upward pointing pressure difference force. This force is caused by the air outside the parcel (air surrounding the parcel). Pressure decreases with increasing altitude. The pressure of the air at the bottom of a parcel pushing upward is slightly stronger than the pressure of the air at the top of the balloon that is pushing downward. The overall effect is an upward pointing force.

When the air inside a parcel is exactly the same as the air outside, the two forces are equal in strength and cancel out. The parcel is neutrally bouyant and doesn't rise or sink.

If you replace the air inside the balloon with warm low density air, it won't weigh as much. The gravity force is weaker. The upward pressure difference force doesn't change, because it is determined by the air outside the balloon which hasn't changed, and ends up stronger than the gravity force. The balloon will rise.

Conversely if the air inside is cold high density air, it weighs more. Gravity is stronger than the upward pressure difference force and the balloon sinks.

We can modify the demonstration that we did earlier to demonstrate Charles' Law. In this case we use balloons filled with helium (or hydrogen). Helium is less dense than air even when the helium has the same temperature as the surrounding air. A helium-filled balloon doesn't need to warmed up in order to rise.

We dunk the helium-filled balloon into some liquid nitrogen to cool it and to cause the density of the helium to increase. When removed from the liquid nitrogen the balloon doesn't rise, the cold helium gas is denser than the surrounding air (the purple and blue balloons in the figure above). As the balloon warms and expands its density of the helium decreases. The balloon at some point has the same density as the air around it (green above) and is neutrally bouyant. Eventually the balloon becomes less dense that the surrounding air (yellow) and floats up to the ceiling.

Something like this happens in the atmosphere.

At (1) sunlight reaching the ground is absorbed and warms the ground. This in turns warms air in contact with the ground (2) Once this air becomes warm and its density is low enough, small "blobs" of air separate from the air layer at the ground and begin to rise. These are called "thermals." (3) Rising air expands and cools (this is something we haven't covered yet). If it cools enough (to the dew point) a cloud will become visible as shown at Point 4. This whole process is called free convection. Many of southern Arizona's summer thunderstorms start this way.

The relative strengths of the downward graviational force and the upward pressure difference force determine whether a parcel of air will rise or sink. Archimedes Law is another way of trying to understand this topic.

A gallon of water weighs about 8 pounds (lbs).

If you submerge a 1 gallon jug of water in a swimming pool, the jug becomes, for all intents and purposes, weightless. Archimedes' Law (see figure below, from p. 53a in the photocopied ClassNotes) explains why this is true.

The upward bouyant force is really just another name for the pressure difference force covered earlier today (higher pressure pushing up on the bottle and low pressure at the top pushing down, resulting in a net upward force). A 1 gallon bottle will displace 1 gallon of pool water. One gallon of pool water weighs 8 pounds. The upward bouyant force will be 8 pounds, the same as the downward force on the jug due to gravity. The two forces are equal and opposite.

Now we imagine pouring out all the water and filling the 1 gallon jug with air. Air is about 1000 times less dense than water;compared to water, the jug will weigh practically nothing.

If you submerge the jug in a pool it will displace 1 gallon of water and experience an 8 pound upward bouyant force again. Since there is no downward force the jug will float.

One gallon of sand (which is about 1.5 times denser than water) jug will weigh 12 pounds.

The jug of sand will sink because the downward force is greater than the upward force.

You can sum all of this up by saying anything that is less dense than water will float in water, anything that is more dense than water will float in water.

The same reasoning applies to air in the atmosphere.

Air that is less dense (warmer) than the air around it will rise. Air that is more dense (colder) than the air around it will sink.

There's a colorful demonstration of how small differences in density can determine whether an object floats or sinks.

Cans of both regular and Diet Pepsi are placed in beakers filled with water (Coke and Diet Coke can also be used). Both cans are made of aluminum which has a density almost three times higher than water. The drink itself is largely water. The regular Pepsi also has a lot of high-fructose corn syrup, the Diet Pepsi doesn't. The mixture of water and corn syrup has a density greater than plain water. There is also a little air (or perhaps carbon dioxide gas) in each can. The average density of the can of regular Pepsi (water & corn syrup + aluminum + air) ends up being slightly greater than the density of water. The average density of the can of diet Pepsi (water + aluminum + air) is slightly less than the density of water.

In some respects people in swimming pools are like cans of regular and diet soda. Some people float (they're a little less dense than water), other people sink (slightly more dense than water).

Many people can fill their lungs with air and make themselves float, or they can empty their lungs and make themselves sink. People must have a density that is about the same as water.