**The Gas Laws**

Today we're going to talk about the three gas laws (in order): __Boyle's Law__, __Charles Law__, and __Avogadro's Law__.

Then, we'll move on to the __Combined Gas Law__ and the __Ideal Gas Law__.

First, the three gas laws...

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**Boyle's Law**

__Boyle's Law__ ➞ **PV = k** , at constant temperature (T)

P = pressure of the gas

V = volume of the gas

k = "some constant" (value unimportant)

➞ *balloon scenario* = squeezing a balloon decreases its volume...

➞ so **PV = k** (as P**↑**, V**↓** ) -- they are __inversely proportional__.

**Boyle's Law Calculations** will always involve a "situation 1" and a "situation 2." So this is the formula to remember: **P _{1}V_{1} = P_{2}V_{2}**

*ex:* Consider a 1.53L sample of SO

_{2}(g) at a pressure of 5.6 x 10

^{3}Pa. If the pressure is increased to 1.5 x 10

^{4}Pa at a constant temperature, what's the new volume of the gas?

➞ start with Boyle's Law, then "plug and chug" so to speak...

The above image nicely shows the flow of how to do the problem:

P_{1}V_{1} = P_{2}V_{2}

( 5.6 x 10^{3} Pa ) (1.53 L ) = ( 5.6 x 10^{4} Pa ) ( V_{2} )

**V _{2} = 0.57 L**

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**Charles' Law**

__Charles' Law__ ➞ **V / T = k** , at constant pressure (P)

V = volume of the gas

T = temperature of the gas (in Kelvin!)

k = "some constant" (value unimportant)

➞ *balloon scenario* = as you increase the temperature of the gas in a balloon, you also increase the gas' volume.

➞ think of a limp hot air balloon -- what happens when heat (fire torch) is turned on? Yes, the balloon expands.

➞ so **V / T = k** (as T**↑**, V**↑** ) -- they are __directly proportional__.

**Charles' Law Calculations** will always involve a "situation 1" and a "situation 2." So this is the formula to remember: **V _{1} / T_{1} = V_{2} / T_{2} **

*ex:* A sample of gas at 15°C and 1atm has a volume of 2.58L. What volume will this gas occupy at 38°C and 1atm?

➞ convert Celsius to Kelvin temperature, then plug in values...

15 + 273 = 288K

38 + 273 = 311K

Here it is again:

V_{1} / T_{1} = V_{2} / T_{2}

( 2.58 L ) **/** (288 K ) = ( V_{2} ) **/** ( 311 K )

**V _{2} = 2.79 L**

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**Avogadro's Law**

__Avogadro's Law__ ➞ **V / n = k** , at constant pressure (P) and temperature (T)

V = volume of the gas

n = number of moles of the gas

k = "some constant" (value unimportant)

➞ for a gas at constant temperature and pressure, the __volume__ is directly proportional to the __number of moles__ of the gas.

➞ so **V / n = k** (as n**↑**, V**↑** ) -- they are __directly proportional__.

**Avogadro's Law Calculations** will always involve a "situation 1" and a "situation 2." So this is the formula to remember: **V _{1} / n_{1} = V_{2} / n_{2} **

*ex:* Suppose you have 12.2 L of O

_{2}gas, containing 0.50 mol at a pressure of 1 atm and temperature of 25°C.

If all of this O_{2} were converted to ozone, O_{3}, at the same temperature and pressure, what would be the volume of the ozone?

-- okay, the question is asking for the volume of O_{3}.

-- assuming this is V_{2}, we need to calculate n_{2} for O_{3} (* not* O

_{2}) before applying Avogadro's Law. So,

Now, putting all 3 laws together to get the __combined gas law__ and the __ideal gas law__.

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**The Combined Gas Law**

__Combined Gas Law__ = take a look at the image below. In each of the 3 gas laws, the P's and V's are in the ** numerator**, while the n's and T's are in the

**.**

*denominator*Putting them all together, we get: **P _{1}V_{1} / n_{1}T_{1} = P_{2}V_{2} / n_{2}T_{2}**

Or, **PV / nT = k**

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Take a look at the "far right" equation in the image above: **PV / nT = k**

If we define "k" as the **universal gas constant (R)**, we get:

Alright, now we just need to substitute **R** in for **k** to get the **Ideal Gas Law**.

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**The Ideal Gas Law**

__The Ideal Gas Law__ does * NOT* have a "situation 1" and "situation 2," so there's no subscripts 1 and 2.

### PV = nRT

Unlike Boyle's Law, Charles' Law, Avogadro's Law, and the Combined Gas Law, the __Ideal Gas Law__ contains the universal gas constant, "R".

And "R" has ** specific units**!

The units of "R" __force__ us to have:

- Pressure in atm

- Volume in liters

- Moles in moles (duh)

- Temperature in Kelvin

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In my next post on this topic, we'll do a TON of gas law and gas stoichiometry practice problems together.

So stick around and check out my next video post from **SECTION 5 - Gases.**

We'll go over a bunch of Ideal Gas Law Examples and Gas Law Practice Problems...