Pressure

The **force** exerted **per** **unit** **area** by gas molecules as they **strike** the **surfaces** around them

Pressure = force/area = F/A

Pressure units & conversion factors

760 mmHg = 760 torr = 1 atm = 101,325 Pa

Elements that exist as gases at 25°C and 1 atm

1A: H

5A: N

6A: O

7A: F, Cl

8A: (all)

Force (formula)

mass × acceleration

SI units of force and pressure

Force: 1 newton (N)

Pressure: 1 pascal (Pa)

Newton

1 newton = 1 kg×m/s^{2}

Pascal

1 pascal = 1N/m^{2} = 1 kg/(m×s^{2})

Barometer

Atmospheric pressure measurment tool

Inverted tube of Hg over open dish of Hg;

height of Hg in mm is equal to atmospheric pressure

Manometer

Instrument used to measure pressure of gas trapped in container

Gas pressure is determined by difference in liquid levels in U-shaped tube

(Pressure is high if it pushes down on liquid;

low if it cannot push down on liquid)

Simple Gas Laws: Four* basic properties of a gas

P, pressure

V, volume

T, temperature (Kelvin)

t, temperature (°C)

n, amount in moles

Boyle's law

**Inverse** relationship between **volume** and **pressure**

*n is constant

*T is constant

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

Charles' law

**Direct** relationship between **volume** and **temperature** (**Kelvin**).

*P is constant

*n is constant

__V _{1}__ =

__V__

_{2}T

_{1}T

_{2}

Avogadro's law

Direct relationship between **volume** and **quantity** (number of moles)

*P is constant

*T is constant

__V _{1}__ =

__V__

_{2}n n

Ideal Gas Law

How a hypothetical gas behaves

PV = nRT

Where R is the ideal gas constant

R, ideal gas constant

R = 0.08206 L atm/mol K

Molar volume

The volume occupied by one mole of a substance

Ideal gas molar volume

22.414 L at STP of an ideal gas

STP

standard temperature and pressure

pressure = 1 atm at STP

temperature = 0°C or 273.15 K at STP

Density of a gas (formula)

d = __P M__

RT

Where d = density

P = pressure in atm

*M* = molar mass

R = gas constant

T = temperature in Kelvin

Molar mass of a gas (formula)

*M* = __dRT__

P

Where *M* = molar mass

d = density

R = gas constant

T = temperature in Kelvin

P = pressure in atm

Dalton's law

Partial pressures, P_{n}

P_{n} = n_{n}__RT__

V

P_{total} = P_{x} + P_{y} + P_{z}

*volume and temperature are constant

Mole fraction

*X*_{n} = __n _{n}__

n

_{total}

Thus, with Dalton's law:

P_{n} = *X*_{n}P_{total}

Vapor pressure

The partial pressure of water vapor in a system

Gas stoichiometry

General conceptual plan:

P, V, T / mass or volume of gas A --> moles of gas A -->

moles of gas B --> P, V, T / mass or volume of gas B

Kinetic molecular theory

1. Particle **size** is **negligible**, even those they have mass

2. Constant motion, random directions, **no overall loss of energy, just a transfer of energy **(known as being ** elastic**)

3. **Average** **kinetic** **energy** is **directly** proportional to **temperature** in **Kelvin**

4. Gas particles exert **neither** **attractive** nor **repulsive** forces

Average kinetic energy

average kinetic energy = KE

( KE = 1/2×mv^{2} )

At **same** **temperature**, gases have **same** **average** **kinetic** **energy**

Boyle's law explained (KMT)

Decreasing volume forces gas particles into a smaller space, thus increasing collisions, and hence, pressure

*n and T are constant

Charle's law explained (KMT)

Temperature increase increases average kinetic energy

The higher the average kinetic energy, the greater the area particles will move around

Thus, volume increases

*P & n constant

Avogadro's law explained (KMT)

Increasing number of particles causes more collisions

To keep pressure constant, volume must then increase

*P and T are constant

Dalton's law explained (KMT)

Because average kinetic energy is the same (at same temperature), the total pressure of the collisions is the same