Let’s tackle about ideal gasses

• First, what is gas? Gas is a state of matter that has no fixed shape and no fixed volume. Gasses
have a lower density than other states of matter such as solids and liquids.

• If we make a couple guesses about gas there are easy predictions about it:
1. Particles are points in random motion - the movement of the gas is irrelevant they can move
anywhere
2. Particles don’t interact with each other - the particles of gas are bouncing from each other

Before we look at the Ideal Gas Equation, let us state the four gas variables and one constant for a
better understanding. The four gas variables are pressure (P), volume (V), number of moles of gas
(n), and temperature (T).

• 1st Pressure - all gasses exert pressure, pressure is the amount of force exerted per area, it refers
to how often the particles hit each other.
• 2nd Temperature - this is the amount of heat energy available to to be transferred into kinetic
energy of motion, the higher the temperature the faster the particles move
• 3rd Volume - volume refers on how much space an object or substance takes up
• 4th Moles - how many particles are there in the container or the amount of substance

The relationships between these variables have developed into laws

Let’s say that the temperature and the number of moles are constant in a container with gas inside.
Now if we will compress the container, the gas particles will hit each other more often which means
that the pressure increases while the volume decreases. This is expressed in Boyle’s law which
states that the volume of a given amount of gas held at constant temperature varies inversely with the
applied pressure when the temperature and mass are constant.

Volume and Temperature are also related to each other. At constant pressure, a balloon will increase
its volume when the temperature increases. The particles inside the balloon will move faster, the
balloon will expand to keep the pressure constant. This is expressed in Charles’ law which states that
the volume of a given amount of gas is directly proportional to its temperature on the Kelvin scale
when pressure is constant.
When we do calculations involving temperature, we must always use an absolute temperature scale
called the Kelvin Scale. 1-degree kelvin is the same magnitude as 1-degree celsius, but 0 Kelvin is
absolute zero, the lowest temperature possible, a complete absence of heat energy

In order to get Kelvin from Celsius you just need to add 273 and if you need to get Celsius from
Kelvin you just need to subtract 273

The combined Gas Law is like a combination of Boyle’s and Charles’s law

Avogadro’s law says that equal volumes of gas at the same temperature and pressure contain the
same number of molecules.
.
For example, one mole of an ideal gas occupies 22.4 liters at standard temperature and pressure
regardless of the identity of the gas

All the variables correlate in one equation called the ideal gas law. This also contains the gas
constant R which makes these calculations intelligible in our manmade units. There are a number of
values for R depending on the units.

This equation is useful when we aren’t looking for a change but just to know the value of the four
variables at once.

So, if you are looking at a sample of gas and you have three of the four variables, you can solve for
the fourth using the ideal gas law.

The ideal gas equation, is PV=nRT

In plain English, this means that for a given amount of gas, the temperature goes up as the gas is
compressed into a smaller volume, and the temperature goes down as the gas is allowed to expand
into a larger volume.

Some examples where ideal gas law is present are refrigerator and air conditioners.
Coolant gas is compressed, causing its temperature to increase. The hot gas is passed through a
radiator, allowing excess heat to escape, and then the gas is allowed to expand into the refrigerator.
As it expands, it cools off, and heat is drawn from the interior of the refrigerator.

The exact same system is used in air conditioner. Except the inside of your home take the place of the
inside of the refrigerator.
For the word problem related to Ideal Gas Law, Determine the volume of occupied by 2.34 grams of
carbon dioxide gas at STP (Standard Temperature and Pressure).

Given:
𝐿 𝑔
𝑅 = 0.08206 𝑚𝑜𝑙 𝐾 𝑀 = 44.01 𝑚𝑜𝑙 𝑚 = 2.34 𝑔 𝑇 = 0℃ 𝑜𝑟 273.15𝐾 𝑃 = 1 𝑎𝑡𝑚

Solution:

1) Rearrange PV = nRT to this:

𝑉 = 𝑛𝑅𝑇 / 𝑃

2) Substitute:

𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒
(𝑛 = ) 𝑅𝑇
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑜𝑛𝑒 𝑚𝑜𝑙𝑒
𝑉=
𝑃
2.34 𝑔 𝑎𝑡𝑚 − 𝐿
( 𝑔 ) (0.08206 𝑚𝑜𝑙 − 𝐾 ) (273.15 𝐾)
44.01
𝑚𝑜𝑙
𝑉 =
1 𝑎𝑡𝑚
𝑎𝑡𝑚 − 𝐿
(0.053169734 𝑚𝑜𝑙) (0.08206 ) (273.15 𝐾)
𝑉 = 𝑚𝑜𝑙 −𝐾
1 𝑎𝑡𝑚
(0.053169734 ) (0.08206 𝐿)(273.15 )
𝑉 =
1
𝑉 = (0.004363108384 𝐿)(273.15)

𝑉 = 1.191783055 𝐿 𝑜𝑟 1.19 𝐿