The rate of Diffusion of a gas to hydrogen is 12x and the RMM of Hydrogen gas is 2 find the RMM of the other gass
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Step-by-step solution
4 stepsLet's solve this using Graham's Law of Diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its relative molecular mass (RMM).
Graham's Law of Diffusion:
(Rate₁)/(Rate₂) = √(RMM₂)/(RMM₁)
Identify the given information.
- Let Gas 1 be Hydrogen (H₂) and Gas 2 be the unknown gas.
- RMM of Hydrogen (RMM₁) = 2
- The problem states "The rate of Diffusion of a gas to hydrogen is 12x". This phrasing can be ambiguous. However, since hydrogen (H₂) is the lightest gas (RMM = 2), it will diffuse faster than any other gas. Therefore, it is logical to assume that hydrogen's rate of diffusion is 12x times faster than the unknown gas. So, (Rate of H₂)/(Rate of unknown gas) = 12x
Apply Graham's Law.
Using the interpretation from Step 1:
(Rate of H₂)/(Rate of unknown gas) = √(RMM of unknown gas)/(RMM of H₂)Substitute the known values into the equation.
12x = √(RMM of unknown gas)/(√(2))
Solve for the RMM of the unknown gas.
Multiply both sides by √(2):
12x · √(2) = √(RMM of unknown gas)Square both sides to eliminate the square root:
(12x · √(2))² = RMM of unknown gas
(12x)² · (√(2))² = RMM of unknown gas
144x² · 2 = RMM of unknown gas
RMM of unknown gas = 288x²The relative molecular mass of the other gas is 288x².
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