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Review of the Gas Laws

- PV nRT

PV nRT

- Boyles Law (isothermal fixed amount)
- Charless Law (isobaric fixed amount)
- Avogadros Law (isothermal isobaric)
- ????? Law (isochoric fixed amount)
- ????? Law (isothermal isochoric)
- ????? Law (isobaric isochoric)

Boyles Law

- Pressure and volume are inversely proportional.
- As pressure increases, volume decreases.
- If pressure increases by 2x, volume cuts in

half.

Charless Law

- Temperature and volume are directly proportional.
- As temperature increases, volume also increases.
- If temperature increases by 2x, volume also

doubles. - Temperature must be measured in Kelvin.

Avogadros Law

- Moles of gas and volume are directly

proportional. - As the number of moles increases, the volume also

increases. - If the number of moles increases by 2x, the

volume also doubles.

????? Law isothermal isochoric

- Moles of gas and pressure are directly

proportional. - As the moles of gas increase, the pressure also

increases. - If the number of moles of gas increases by 2x,

the pressure also doubles.

????? Law isobaric isochoric

- Moles of gas and temperature are inversely

proportional. - As the number of moles of gas increase, the

temperature decreases.

Units of Pressure

- 1 atm 760 torr 760 mmHg
- 1 atm 101.325 kPa
- 1 bar 105 Pa 100 kPa
- 1 Pa

How does 1 atm 101.325 kPa?

Let the area of the base of a cylinder 1 m2

Volume area x height 1 m2 x 0.76 m 0.76 m3

Convert volume to cubic centimeters.

Use the density of mercury and the acceleration

due to gravity to calculate the weight of mercury

in the column.

Continue How does 1 atm 101.325 kPa?

Pressure is force (or weight) per unit area.

Divide the weight of mercury by the area it is

resting on.

Let the area of the cylinder 1cm2

Barometric Formula

As elevation increases, the height of the

atmosphere decreases and its pressure decreases.

Check units.

Continue Derivation of Barometric Formula

Write in differential form.

density

Rewrite PV nRT as

Therefore,

Continue Derivation of Barometric Formula

Substitute the expression for density into the

differential eqn.

Divide both sides of the above equation by P and

integrate.

Continue Derivation of Barometric Formula

Integration of the left side and moving the

constants outside the integral on the right side

of the differential equation gives,

Continue Derivation of Barometric Formula

Evaluating the integral between the limits of Pi

at zero height and Pf at height h, gives

Sample Problem Using the Barometric Formula

Daltons Law of Partial Pressures

Pressure is additive.

Write each pressure as,

Continue Daltons Law of Partial Pressures

Multiply through by V (the combined volume of the

gases) and divide by R T.

Moles are indeed additive.

Mole Fraction Partial Pressure

Therefore,

Continue Mole Fraction Partial Pressure

Show that