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Aug 14, 2020 · 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.
- The Ideal Gas Law
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- The Ideal Gas Law
Aug 12, 2024 · A gas law is a simple mathematical formula that allows you to model, or predict, the behavior of a gas. This particular gas law ia called Boyle's law , after the English scientist Robert Boyle, who first announced it in 1662.
A gas law is a simple mathematical formula that allows you to model, or predict, the behaviour of a gas. This particular gas law is called Boyle’s law , after the English scientist Robert Boyle, who first announced it in 1662.
Jan 30, 2023 · Simple Gas Laws. The Ideal Gas Law is simply the combination of all Simple Gas Laws (Boyle's Law, Charles' Law, and Avogadro's Law), and so learning this one means that you have learned them all. The Simple Gas Laws can always be derived from the Ideal Gas equation.
- Overview
- What is an ideal gas?
- What is the molar form of the ideal gas law?
- What is the molecular form of the ideal gas law?
- What is the proportional form of the ideal gas law?
- Example 1: How many moles in an NBA basketball?
- Example 2: Gas takes an ice bath
Learn how pressure, volume, temperature, and the amount of a gas are related to each other.
1.Ideal gas molecules do not attract or repel each other. The only interaction between ideal gas molecules would be an elastic collision upon impact with each other or an elastic collision with the walls of the container.
[What is an elastic collision?]
2.Ideal gas molecules themselves take up no volume. The gas takes up volume since the molecules expand into a large region of space, but the Ideal gas molecules are approximated as point particles that have no volume in and of themselves.
If this sounds too ideal to be true, you're right. There are no gases that are exactly ideal, but there are plenty of gases that are close enough that the concept of an ideal gas is an extremely useful approximation for many situations. In fact, for temperatures near room temperature and pressures near atmospheric pressure, many of the gases we care about are very nearly ideal.
If the pressure of the gas is too large (e.g. hundreds of times larger than atmospheric pressure), or the temperature is too low (e.g. −200 C ) there can be significant deviations from the ideal gas law. For more on non-ideal gases read this article.
Gases are complicated. They're full of billions and billions of energetic gas molecules that can collide and possibly interact with each other. Since it's hard to exactly describe a real gas, people created the concept of an Ideal gas as an approximation that helps us model and predict the behavior of real gases. The term ideal gas refers to a hypothetical gas composed of molecules which follow a few rules:
1.Ideal gas molecules do not attract or repel each other. The only interaction between ideal gas molecules would be an elastic collision upon impact with each other or an elastic collision with the walls of the container.
[What is an elastic collision?]
2.Ideal gas molecules themselves take up no volume. The gas takes up volume since the molecules expand into a large region of space, but the Ideal gas molecules are approximated as point particles that have no volume in and of themselves.
If this sounds too ideal to be true, you're right. There are no gases that are exactly ideal, but there are plenty of gases that are close enough that the concept of an ideal gas is an extremely useful approximation for many situations. In fact, for temperatures near room temperature and pressures near atmospheric pressure, many of the gases we care about are very nearly ideal.
If the pressure of the gas is too large (e.g. hundreds of times larger than atmospheric pressure), or the temperature is too low (e.g. −200 C ) there can be significant deviations from the ideal gas law. For more on non-ideal gases read this article.
The pressure, P , volume V , and temperature T of an ideal gas are related by a simple formula called the ideal gas law. The simplicity of this relationship is a big reason why we typically treat gases as ideal, unless there is a good reason to do otherwise.
PV=nRT
Where P is the pressure of the gas, V is the volume taken up by the gas, T is the temperature of the gas, R is the gas constant, and n is the number of moles of the gas.
[What is a mole?]
Perhaps the most confusing thing about using the ideal gas law is making sure we use the right units when plugging in numbers. If you use the gas constant R=8.31JK⋅mol then you must plug in the pressure P in units of pascals Pa , volume V in units of m3 , and temperature T in units of kelvin K .
If you use the gas constant R=0.082L⋅atmK⋅mol then you must plug in the pressure P in units of atmospheres atm , volume V in units of liters L , and temperature T in units of kelvin K .
If we want to use N number of molecules instead of n moles , we can write the ideal gas law as,
PV=NkBT
Where P is the pressure of the gas, V is the volume taken up by the gas, T is the temperature of the gas, N is the number of molecules in the gas, and kB is Boltzmann's constant,
kB=1.38×10−23JK
There's another really useful way to write the ideal gas law. If the number of moles n (i.e. molecules N ) of the gas doesn't change, then the quantity nR and NkB are constant for a gas. This happens frequently since the gas under consideration is often in a sealed container. So, if we move the pressure, volume and temperature onto the same side of the ideal gas law we get,
nR=NkB=PVT= constant
This shows that, as long as the number of moles (i.e. molecules) of a gas remains the same, the quantity PVT is constant for a gas regardless of the process through which the gas is taken. In other words, if a gas starts in state 1 (with some value of pressure P1 , volume V1 , and temperature T1 ) and is altered to a state 2 (with P2 , volume V2 , and temperature T2 ), then regardless of the details of the process we know the following relationship holds.
P1V1T1=P2V2T2
The air in a regulation NBA basketball has a pressure of 1.54 atm and the ball has a radius of 0.119 m . Assume the temperature of the air inside the basketball is 25o C (i.e. near room temperature).
a. Determine the number of moles of air inside an NBA basketball.
b. Determine the number of molecules of air inside an NBA basketball.
We'll solve by using the ideal gas law. To solve for the number of moles we'll use the molar form of the ideal gas law.
PV=nRT(use the molar form of the ideal gas law)
n=PVRT(solve for the number of moles)
A gas in a sealed rigid canister starts at room temperature T=293 K and atmospheric pressure. The canister is then placed in an ice bath and allowed to cool to a temperature of T=255 K .
Determine the pressure of the gas after reaching a temperature of 255 K.
Since we know the temperature and pressure at one point, and are trying to relate it to the pressure at another point we'll use the proportional version of the ideal gas law. We can do this since the number of molecules in the sealed container is constant.
P1V1T1=P2V2T2(start with the proportional version of the ideal gas law)
P1VT1=P2VT2(volume is the same before and after since the canister is rigid)
P1T1=P2T2(divide both sides by V)
P1V1 = P2V2 at constant n and T. 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 behaviour of a gas. This particular gas law is called Boyle’s law, after the English scientist Robert Boyle, who first announced it in 1662.
The ideal gas law allows us to calculate the value of the fourth quantity (P, V, T, or n) needed to describe a gaseous sample when the others are known and also predict the value of these quantities following a change in conditions if the original conditions (values of P, V, T, and n) are known.
