Question
Question: Tetrafluoroethylene, \({C_2}{F_4}\) , effuses through a barrier at a rate of \(8 \times {10^{ - 6}}m...
Tetrafluoroethylene, C2F4 , effuses through a barrier at a rate of 8×10−6mol/hr . An unknown gas (X ) consisting only of boron and hydrogen; effuses at the rate of 10×10−6mol/hr under the same conditions. The molecular mass of X is [At. Weight of F=19amu ].
Solution
Graham's law of effusion (also called Graham's law of diffusion) was formulated by Scottish physical chemist Thomas Graham in 1848. Graham found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles or the molar mass of the gas.
Complete step by step answer:
Graham's law states that the rate of diffusion or of effusion of a gas is inversely proportional to the square root of its molecular weight. Thus, if the molecular weight of one gas is four times that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other (heavier gases diffuse more slowly). Mathematically, Graham’s law can be represented as:
R∝Mw1
Where, R= rate of effusion of gas
Mw= molecular weight of the gas
Thus, for tetrafluoroethylene, C2F4, and the unknown gas, the mathematical relation can be represented by:
RXRC2F4=MC2F4MX…(i)
Where, RC2F4=8×10−6mol/hr = rate of effusion of tetrafluoroethylene gas
RX=10×10−6mol/hr= rate of effusion of unknown gas
MC2F4=(2×12)+(4×19)=100amu = molecular mass of tetrafluoroethylene gas
MX=? = molecular mass of unknown gas
Substituting the values in the equation (i), we have:
⇒10×10−68×10−6=100MX
Thus, on solving, we have:
⇒10064=100MX
Hence, MX=64amu .
Note:
A complete theoretical explanation of Graham's law was provided years later by the kinetic theory of gases. Graham's law provides a basis for separating isotopes by diffusion which is a method that came to play a crucial role in the development of the atomic bomb.