--- ## Properties - Gasses fill whatever container they are put in and **each molecule or element within a gas is moves independently** in random directions colliding with other particles or the walls of the container *(which causes [[Pressure]])*. These particles move faster when they are hotter which increases the pressure. - Gasses are highly compressible, thermally expandable and have very low viscosity *which allows them to move around quickly and easily.* Gasses also have very low densities compared to their liquid and solid forms. - Gasses are **infinitely miscible** meaning they readily mix when in contact. >[!caution] >##### Important properties >- Collisions between gas particles are **perfectly elastic**. >- Particles within a gas do not [[Chemical reactions|chemically]] react with each other, that is the attractive forces between molecules like the *van-der-walls force and london forces* are statistically **insignificant**. >- Gasses expand to fill whatever container they are put in. >- Gas particles are assumed to occupy **no volume**. >- The average speed of particles within a gas **is its temperature**. --- ## Ideal gas law - The ideal gas law is an equation that allows us to make basic predictions about gasses **assuming that they will evenly fill any given space and exert the same force everywhere**. It is as follows, *R is a constant: 8.31, n is the [[Moles]] of gas, T is temperature in **Kelvin**.* $ PV = nRT$ >[!example] >- The idea gas law can be modified to relate the density of a gas to its molar mass as shown below. Here M is the molar mass of the gas and m is the overall mass of that gas. >$\text{since:}\space\ n=\left(\frac{m}{M}\right)\longrightarrow \space \space PM=\left(\frac{m}{V}\right)RT$ >[!tip] >##### STP >- When making assumptions about the pressure, temperature and volume of a gas it is important to always use an ideal gasses' conditions **at STP: standard temperature and pressure**. This is especially useful when using the ideal gas law to make conclusions about reactions where one only has the chemical formula, that is, no data about the non-relative amount of chemicals used. >- A gas at STP has a temperature of 0 Celsius, a pressure of 1 atm and a volume of 22.42 L *(Most gasses have a volume near 22.42 at STP but others may vary significantly).* ##### *Boyle's law* - Boyles law approximately describes the relationship between pressure and volume of a gas assuming of course that the gas is [[Gasses|ideal]] in nature. - By plotting *1/P* vs V for a given gas **a linear line forms** the slope of this line represents the value *k* which is a constant that is specific for air **at one temperature only** *(and assuming the moles of gas do not change)*. Changing the temperature of air requires one to use a different *k* value. $V=\frac{k}{P} \space\space\space\space\space\space\space k=PV$ ${P_1}{V_1}={P_2}{V_2}$ ##### *Charles' law* - Charles' law states that the volume of a given gas is **directly proportional to the temperature of that gas**. This law unlike Boyle's law assumes **that the [[Pressure]] of the gas and moles of the gas remain constant.** - b is the **proportionality constant between volume and temperature** which like k above is generated from the slope of a graph plotting the temperature *in kelvin* of a gas vs the volume *in liters* it occupies. $V=bT\longrightarrow \frac{V_1}{T_1}=\frac{V_2}{T_2}$ ##### *Avogadro's law* - This law states that for gas **at a constant pressure and temperature the volume is directly proportional to the moles of that gas** multiplied by some proportionality constant *"a"*. $V=an\longrightarrow\frac{V_1}{n}=\frac{V_2}{n}$ ##### *Dalton's law of partial pressures* - This law states that the **sum of the pressures of individual gasses always equals the overall or total pressure of that collection of gasses**.** $P_{total}=P_{1}+P_{2}+P_{3}+\space...=\frac{n_1RT}{V}+\frac{n_2RT}{V}+\frac{n_3RT}{V}\space...$ $hence:(n_1+n_2+n_3+...)(\frac{RT}{V})=n_{total}(\frac{RT}{V})$ - The **mole fraction** of a gas is the **ratio of the number of moles of that gas compared to the moles of *total gas* contained in the system**. This is *not* represented as a percentage or a fraction but rather as a decimal *between 0 and 1*. - The mole fraction of a gas is symbolized by the letter *chi: χ* . - These relationships all combine to create: $\frac{PV}{nT}=\frac{P_1V_1}{n_1T_1}$ --- ## Heat and energy - The heat of a gas is the **average kinetic energy** of the individual particles which can be expressed in the following equations where u is the average velocity of particles and N is the number of particles in a mole (6.022e23). - These equations fall under a general theory about heat, energy and particles known as the **kinetic molecular theory**. $KE=nN(\frac{1}{2}m\mu^2)$ $P=\frac{2}{3}\left(\frac{nN(\frac{1}{2}m\mu^2)}{v}\right)$ $\text{This is the important equation:}$ $(KE)_{avg}=\frac{2}{3}RT$ - The following is the major relationships between pressure, volume and temperature that arises due to these basic laws. $\frac{PV}{n}\propto T$ - The final important relationship is as follows: $\frac{P_1}{T_1}=\frac{P_2}{T_2}$ ##### *Root mean square velocity* - Since every gas particle is moving a different velocity we use the term **u followed by rms** to denote the square root of the average velocity of particles in a specific system of gas. In this equation M is equal to molar mass of the gas. - **The higher the molar mass of a particle the lower its speed** *on average*. $u_{rms}=\sqrt{\frac{3RT}{M}}$ >[!tip] >##### Distribution of molecular speeds >![[Gasses33.png|450]] >![[Gasses333.png|405]] --- ## Effusion and diffusion - **Diffusion** is a term used to describe the mixing of gases. - **Effusion** is a term used to describe the passage of gas through a very small passage into an evacuated chamber *or a chamber of lower pressure*. - Grahams law of effusion allows one to compare the rate of effusion of gasses so long as they are at the same temperature and pressure. M one and M two here represent the molar mass of gas one and two respectively. $\frac{\text{effusion of gas 1}}{\text{effusion of gas 2}}=\frac{\sqrt{M_2}}{\sqrt{M_2}}$ - This "effusion ratio" works with some other properties. For example we can also plug in the equation from the above section thus, showing that the average speed of two gasses also relates to the effusion of the gas. **The faster a gas is moving the more it is able to effuse**. $\frac{\text{effusion of gas 1}}{\text{effusion of gas 2}}=\frac{\sqrt{8RT/\pi M_1}}{\sqrt{8RT/\pi M_2}}=\frac{u_{avg}\space\space\text{gas 1}}{u_{avg}\space\space \text{gas 2}}$ >[!tip] >Surprisingly **both of these equations also work for comparing the diffusion of two different gasses** since the heavier a gas is the slower it is and thus the harder it is for that gas to travel *filling up a space*. This explains why inversely, the faster a gas is traveling the greater it is able to diffuse *second equation*. --- ## Collisions #mainpage