# 3.4 The Ideal Gas Law Dalia Savy

Kanya Shah

Gases exert pressure on its surroundings. The key phrase you want to associate with pressure is "the number of times particles hit the walls of the container." If you are ever asked to explain any of the relationships in this key topic, always mention that phrase if pressure is involved!
Standard Pressure: 1.00 atm = 760 mm Hg = 760 torr = 101.3 kPa
Temperature is a function of mass and velocity and it is most often seen as the average kinetic energy on this AP exam.
Standard Temperature: 0 degrees C, 273 K (C + 273 = K)
STP, or Standard Temperature and Pressure, are conditions at 1 atm and 273 K.
Now let's get into it. Don't worry, we're providing some perfect responses to AP questions too🥳.

## P, V, T, n relationships

The following relationships hold true when the amount of gas is constant.
Boyle’s Law (P1V1 = P2V2): describes the relationship between the pressure and volume of an ideal gas under constant temperature.
Boyle's law indicates that there is an inverse relationship between pressure and volume. When volume goes down, the particles collide with the side of the container more often, increasing pressure.
Charles’ Law (V1/T1 = V2/T2): describes the relationship between volume and temperature of an ideal gas under constant pressure.
Charles' law indicates that there is a direct relationship between volume and temperature. When temperature or average kinetic energy increases, particles move faster causing more and stronger collisions with the walls of the container. The volume increases to keep the pressure constant.
Avogadro's Law (V1/n1 = V2/n2): describes the relationship between volume and the moles of gas.
His law indicates a direct relationship between these two concepts. Adding more particles to a container causes more collisions with the walls of the container and the volume increases to keep pressure constant.
🌟Avogadro also found that equal volumes of gases at the same temperature and pressure contain the same number of particles. For example, 5 L of H and 5 L of He at STP contain the same number of particles.
Gay-Lussac’s Law (P1/T1 = P2/T2): describes the relationship between temperature and pressure of an ideal gas under constant volume. Variables that are multiplied are inversely related, variables that are divided are directly related to one another.
His law indicates a direct relationship between pressure and temperature. As temperature increases, particles move faster causing collisions with the sides of the container to happen more often and to be stronger. This increases the pressure.

### The Combined Gas Law

Three of these laws can be expressed in the combined gas law: P1V1/T1 = P2V2/T2. When solving problems, you can ignore any of the variables that aren’t addressed (ex. in a pressure change problem where you find volume, ignore T and do P1V1 = P2V2 which is really Boyle's Law).
In reality, you only have to remember this equation out of the ones we learned so far but you should understand the reasons behind the relationships. Image Courtesy of Online Math Learning

## Ideal Gas Law

The last equation on that chart above is the ideal gas law, or PV=nRT. The following information can be found on the AP Chemistry reference table but it's quick and easy to memorize!
• P = pressure in atm
• V = volume in L
• n = moles of gas
• R = universal gas constant (0.08206 Latm/molK)
• T = temperature in Kelvin
In every case, we must remember to convert temperature to the Kelvin scale, volume to L, and pressure to atm.
💡If you ever forget which units you need for these variables, look at the given units of R!
The ideal gas law is on almost every single AP Examination, so make sure you nail it. Don't worry, it just requires the plugging in of some numbers and sometimes, stoichiometry which you probably mastered by now.

## Dalton's Law of Partial Pressures

"In a sample containing a mixture of ideal gases, the pressure exerted by each component (the partial pressure) is independent of the other components."
According to Dalton's Law of Partial Pressure, the sum of all the partial pressures of each gas in a mixture of gasses is equal to the total pressure. In mathematical notation, this is expressed by saying: P = Pa + Pb + Pc... where a, b, and c are different gasses.
You may be wondering then, how do we calculate partial pressure🤔?
To do this, we use the mole fraction of that gas. Mole fraction is denoted by Xa and equals moles A/total moles. For example, if we have a mixture of 3 mol O2 and 4 mol H2, the mole fraction of O2 = 3/(3+4) = 3/7. Then, partial pressure = Xa * total pressure.
Another way to represent Dalton's Law of Partial Pressures is: All you have to do here is plug in the values you have. Px represents partial pressure and the fraction on the right is the mole fraction itself.

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