# Show to to find the volume of one mole of Cl2 at 200kPa at 0 degrees Celsius using Avogadro's theory and molar mass of gases

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### 1 Answer

Avogadro's Theory states that equal volumes of gas have an equal number of moles. One mole of any gas always expands into 22.4 liters.

Pressure, volume, temperature, and amount of gas are all related by the Ideal Gas Formula:

(Pressure)(Volume) = (#moles)(gas amount)(Temperature) or

PV=nRT

However, the units must be as follows: Pressure in Atmospheres, Volume in Liters, Gas amount in Moles, and Temperature in Kelvins.

We can determine the Pressure, Volume, Temperature or amount of a gas (n) when the others are known. For this we must use Pressure in Atmospheres (atm), Volume in Liters (l), amount of gas in moles, and Temperature in Kelvin (k),

1 kPA = .00987 atm, so 200 kPA = 1.974 atm

0 Celsius = 273 Kelvin, so

(1.974 atm)(V) = (1 mole)(0.082 atm l / mole k)(273 k)

(1.974 atm)(V) = 22.386 (atm l)

V = 11.34 liters

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