Gas Equations - Boyle's Graham's Combined gas law

Gas Equations - Ideal gas law calculator - Download

Ideal gas law - Gas laws - Introduction

In the gas phase the molecules are so energetic that they drift apart rather than connect to each other by intermolecular forces (hydrogen bonds etc.). The gas laws below are about the behavior of gases under different physical conditions.

Boyle's Law - Calculator

Boyle's law is about the relationship between pressure and volume if temperature and the amount of molecules are held constant.

The volume of a fixed mass of gas is inversely proportional to the pressure at a constant temperature.

The relation can also be written as pressure times volume equals a constant:

PV=k

An increasing container volume decreases the pressure.
A decreasing container volume increases the pressure.

When the volume of a container decreases, the distance between the gas molecules shrink. As a result of this they bump into each other more often than if they where farther apart. The increased molecular movements push at the walls inside the container and increases the pressure.

Ideal Gas Law - Calculator

The Ideal Gas Law was first written in 1834 by Emil Clapeyron. Following relations can be expressed as constants (k₁, k₂...k₆) representing six different values.

PV= k₁
V/T = k₂
P/T = k₃
V/n = k₄
P/n = k₅
1/nT = 1/k₆

In order to make one equation that contain them all i.e. P,V,T and n, we can multiply them all.

P³V³ / n³T³ = k₁k₂k₃ k₄k₅ / k₆
Taking the cube root we get:
PV/nT = (k₁k₂k₃k₄ k₅ / k₆)^1/3

An expression in which on the right side of the equation can be presented as a single constant - R - the gas constant. Now we have a single equation representing the relationship between pressure(P), volume(V), mole(n) and temperature(T).

PV/nT = R
or as presented in CHEMIX
PV = nRT

Combined Gas Law - Calculator

The Combined Gas Law can be derived by multiplying Boyle's law by the laws of Charles and Gay-Lussac.

P₁V₁ = P₂V₂
P₁V₁² / T₁ = P₂V₂² / T₂
P₁²V₁² / T₁² = P₂²V₂² / T₂²
By taking the square root of this result we get the combined gas law:
P₁V₁ / T₁ = P₂V₂ / T₂

Kinetic Energy and Graham's Law of Diffusion

Kinetic Energy - Calculator

When the temperature in a gas increases, the gas molecules will become faster and therefore more energetic. We may say that the temperature represent "the average kinetic energy of the particles of a substance". Knowing that two ideal gases with the same amount of molecules occupies the same volume and that the total amount of kinetic energy in these two volumes must be the equal, less massive gases will diffuse more rapidly than more massive gases at equal pressure and temperature. This according to the kinetic energy equation:

E_k=1/2mv²

Graham's Law of Diffusion - Calculator

The relative rates at which two gases under identical conditions of temperature and pressure will diffuse vary inversely as the square roots of the molecular masses of the gases.

Assume following temperature conditions for two different gases:
T₁ = T₂
and by this that these two gases has the same kinetic energy (E_k=1/2mv²)
1/2m₁v₁² = 1/2m₂v₂²
Moving v₂ to the left and m₁ to the right side of the equation we get:
v₁²/v₂² = m₂/m₁
Taking the square root we get:
v₁/v₂ = (m₂/m₁)^1/2

If we know the mass/density and the velocity of a gas, also knowing the mass/density or the velocity of a second gas, we should be able to calculate the velocity or mass/density of the second gas.

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