The relationship between velocity(U) of a gas molecules and their relative molecular mass(RAM) is?
Isn't this available in your notes/text?
http://www.chemteam.info/GasLaw/gas-velocity.html
just use v(rms) = (158)[SqrRt(T/M)] meters/sec ... T = Kelvin & M = gms/mole ... 158 is from SqrRt[(3)(8.314)(1000)] ... These are constants factored out of the original equation v(rms) = SqrRt(3RT/M).
The relationship between the velocity (U) of gas molecules and their relative molecular mass (RAM) is described by Graham's law of effusion. According to Graham's law, the rate of effusion or diffusion of two different gases is inversely proportional to the square root of their respective molar masses.
In mathematical terms, the relationship can be expressed as:
U₁ / U₂ = √(M₂ / M₁)
Where U₁ and U₂ represent the velocities of gas molecules, and M₁ and M₂ represent their respective relative molecular masses.
This equation shows that as the relative molecular mass increases, the velocity decreases. Therefore, gas molecules with higher relative molecular masses typically have slower velocities compared to those with lower relative molecular masses.
The relationship between the velocity (U) of gas molecules and their relative molecular mass (RAM) can be explained using the kinetic theory of gases.
According to the kinetic theory, the average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas. This can be expressed using the equation:
KE = (1/2) m U^2
where KE is the average kinetic energy, m is the mass of an individual gas molecule, and U is its velocity.
Rearranging the equation to solve for U, we get:
U = sqrt((2*KE) / m)
Now, considering two gas molecules with different relative molecular masses (RAM1 and RAM2), and assuming the temperature and conditions are the same for both gases, their average kinetic energies would be the same. This means that:
(1/2) m1 U1^2 = (1/2) m2 U2^2
Dividing both sides of the equation by (1/2) and canceling, we get:
m1 U1^2 = m2 U2^2
Dividing both sides of the equation by m2 and taking the square root, we get:
U1 / sqrt(m1) = U2 / sqrt(m2)
This equation shows that the ratio of the velocity of gas molecules to the square root of their relative molecular masses is constant. In other words, the velocity of gas molecules is inversely proportional to the square root of their relative molecular masses.