## Graham Law of Diffusion:

After comparing the rates of diffusion for different gases, Graham found that under similar conditions of temperature and pressure, the rates of diffusion of gases are inversely proportional to the square roots of their densities. This is called Graham’s law of diffusion. Mathematically, it can be expressed as-

r_{1}/r_{2} = √d_{2}/d_{1} ………………(I) |

Where, r_{1} and r_{2} are the rates of diffusion of two gases and d_{1} and d_{2} stand for their densities.

Rate of diffusion = Volume diffused/Time taken |

Noe if V_{1} is the volume of a certain gas diffusing in time t_{1} and V_{2} is the volume of another gas diffusing in time t_{2}, then we have-

r_{1} = V_{1}/t_{1} and r_{2} = V_{2}/t_{2}Thus, r _{1}/r_{2} = V_{1}/t_{1} / V_{2}/t_{2} = √d_{2}/d_{1} ………………….(II) |

When volume is the same, i.e., V_{1} = V_{2}, the above relation becomes-

t_{2}/t_{1} = √d_{2}/d_{1} or t_{1}/t_{2} = √d_{1}/d_{2} …………………..(III) |

If different volumes, V_{1} and V_{2}, of two gases diffuse in same time t, then we have,

r_{1}/r_{2} = V_{1}/t / V_{2}/t = √d_{2}/d_{1} or V_{1}/V_{2} = √d_{2}/d_{1} |

Since, molecular weight = 2 x Vapour density, Graham’s law equation (I) can be written as-

r_{1}/r_{2} = √d_{2}/d_{1} = √2d_{2}/2d_{1} = √M_{2}/M_{1}i.e. r _{1}/r_{2} = √M_{2}/M_{1} |

Where, r_{1} and r_{2} are the rates of diffusion and M_{1} and M_{2} the molecular weights of two gases, respectively.

Thus, the rates of diffusion of two gases are inversely proportional to the square roots of their miolecular weights.

**Graham law of diffusion find application-**

- In the separation of gases from their mixture.
- In the determination of the densities and molecular weights of gases.

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