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Empirical Gas Laws

Tag: iit tutorial, gase, chemistry, ideal

Notes:

The ideal gas law may also be used to investigate the behavior of a gas when pressure, volume, the moles of gas and/or temperature are changed. These additional laws are often named after the scientist(s) who investigated these properties.

The relationship between pressure and volume while holding moles and temperature constant is called Boyle's Law. Let's derive this law. Assign subscripts to pressure and volume to indicate two different pressures and volumes:

P₁V₁ = nRT

P₂V₂ = nRT

Since both pressures and volumes are equal to nRT, they are equal to each other:

P₁V₁ = P₂V₂ = nRT (Boyle's Law)

Let's look at a problem dealing with Boyle's Law. Suppose you had gas in a 15.0 L container at 5.00 atmospheres pressure, and the volume is decreased to 0.500 L. What is the new pressure in the container?

To recognize that this is a Boyle's Law problem, make yourself a table of the known quantities and the unknown quantity.

Substitute the know variables into the equation for Boyle's Law. Make sure that the volume units are consistent. In this case, the volume units are both expressed in liters.

(5.00 atm)(15.0 L) = P2(0.500 L)

Solve for the new pressure, P2, by dividing both sides of the equation by the new volume, 0.500 L:

Note that pressure and volume are inversely proportional, so as volume decreases, the pressure increases.

The relationship between volume and temperature while holding moles and pressure constant is called Charles' Law. Let's derive this law from the ideal gas law. Assign subscripts to volume and temperature, and hold moles and pressure constant:

PV₁ = nRT₁

PV₂ = nRT₂

Collect terms. Bring the constants to one side of the equation and the variables to the other side of the equation. Divide both sides of each equation by pressure, P, and by the temperature term, T₁ in the first equation and T₂ in the second equation. This is Charles' Law:

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