AP Chem Chapter 5 - Gases

Density Variation

D = m/v = g/L

MP = dRT

R

universal gas law constant

.0821 atm•L/K•mol

Ideal Gas Law

R = PV/nT or PV = nRT

Combined Gas Law

VP/T = VP/T (changed over time)

Avogadro’s Law

V/n = V/n (changed over time)

Direct Relationship

^n, ^collisions, ^P, ^V (flexible container)

Avg. KE is the same in 2 gases if

Temperature is constant

if Volume is = at STP

The number of moles is =

(avogadro’s law)

a

attractive forces between particles (real gas)

b

the volume of the gas particle itself (real gas)

Van der Waals Equation

\left\lbrack P+a\left(\frac{n}{V}\right)^2\rbrack\right.\cdot\left(V-nb\right)=nRT

Attractive Forces (T)

Intermolecular attractive forces tend to pull the particles toward one another, significantly reducing space

Attractive Forces (P)

High pressure creates more opportunities for collisions between particles

Real gases acting like ideal gases

Low pressure and high temperatures

Diffusion

the mixing of gases

the rate of diffusion = the rate of the mixing gases

Effusion

the passage of a gas through a tiny orifice (hole) into a evacuated chamber

Graham’s Law of Effusion

“graham cracker”

\frac{Rate_{a}}{Rate_{b}} = \sqrt{\frac{M_{b}}{M_{a}}}

Gay-Lussac’s Law

P/T = P/T (changed over time)

Direct Relationship in kelvin!!

^T, ^KE, ^collisions, ^P (rigid container)

Charles’ Law

V/T = V/T (changed over time)

Direct Relationship *KELVIN!!!*

^T, ^KE, ^collisions, ^P, ^V (increasing volume keeps pressure =)

(flexible container)

Boyle’s Law

VP = VP

Inverse Relationship

vV, ^collisions, ^P

Root Mean Square Velocity

u=\sqrt{\frac{3RT}{M}}

Collecting gas over water

Pgas(dry) = Ptotal - Ph2o

Mole fractions

X = n/n(total)

X = P/P(total)

Dalton’s Law

Ptotal = Pgas(a) + Pgas(b) + …

STP

V = 22.4L

T = 0*C = 273K

P = 1 atm = 760mmHg

Molar mass variation

n = m/M

PV = nRT \rightarrow PV = mRT/M

Density variation

d = m/V

d = MP/RT or MP = dRT

Kinetic Molecular Theory (KMT) 1

Gases are mostly empty space

Kinetic Molecular Theory (KMT) 2

Gases move rapidly and randomly in all directions and exert pressure in their collisions.

Kinetic Molecular Theory (KMT) 3

Gas particles are assumed to act independently of each other

Kinetic Molecular Theory (KMT) 4

the avg. KE of gas particles is assumed to be directly proportional to Kelvin temp. (KEave \alpha T)

\overline{u^2}

the average of the squares of the particle velocities

Kinetic Energy

KE = ½ m \overline{u^{}}^2

KEavg = 3/2 RT