Elementary Gas Laws and the Ideal Gas Law

Gay-Lussac’s Law Remember the relationship between P and T? Pressure and Temperature are directly related when the volume and number of moles are held constant. Mathematically: P = kT (linear/direct relationship) Rearranged:

Gay-Lussac’s Law So if you have some initial pressure and temperature: And if you have some final pressure and temperature: so… *note: temperature for ALL calculations must always be in Kelvin! Always!

Practice If a gas has a pressure of 0.95 atm at 25oC, what will its pressure be at 125oC if the volume and moles stay constant? Givens: Pi = 0.95 atm, Ti = 25oC = 298 K Tf = 125oC = 398 K Unknown: Pf = ? Equation: Substitute: Solve: 1.3 atm *note: temperature for ALL calculations must always be in Kelvin! Always!

Boyle’s Law Remember the relationship between P and V? Pressure and Volume are inversely related when the temperature and number of moles are held constant. Mathematically: (linear/direct relationship) Rearranged: PV = k

Boyle’s Law So if you have some initial pressure and temperature: PiVi = k And if you have some final pressure and temperature: PfVf = k so… PiVi = PfVf

Charles’ Law Volume and Temperature are directly related when the temperature and number of moles are held constant. Using the same logic we used with Gay-Lussac’s Law: *note: temperature for ALL calculations must always be in Kelvin! Always!

Avogadro’ Law Volume and the number of moles are directly related when the temperature and pressure are held constant. Using the same logic we used with Gay-Lussac’s Law:

Tying It All Together: Ideal Gas Law If you notice, P and V were always in the numerator of the previous equations whereas T and n were always in the denominator. We can combine all of these gas laws together and create what is know as the Ideal Gas Law. R is the Universal Gas Constant. It is always the same for every gas! R = 0.0821

Ideal Gas Law Using similar logic to all the previous gas laws: This version of the ideal gas law will allow you to solve for any unknown variable. Any variable that stays constant in the problem can be eliminated from the equation. For instance, if the number of moles stays constant in the problem, the equation becomes:

Practice 1 PiVi = PfVf (12.2 psi)(3.9L) = (14.8 psi)Vf Vf = 3.2 L If Pi = 12.2 psi Vi = 3.9 L ni = 1.2 mol Ti = 128 K Pf = 14.8 psi nf = 1.2 mol Tf = 128 K What is Vf? Because both n and T stay constant in the problem, we can eliminate those from the equation. PiVi = PfVf (12.2 psi)(3.9L) = (14.8 psi)Vf Vf = 3.2 L

Practice 2 If 4.3 L of a gas has a pressure of 83 kPa at 200. K, what volume would have a pressure of 162 kPa at 300. K? Answer: 3.3 L