Answer:
F₂
Explanation:
Let the R₁ represent the rate of diffusion of Cl₂
Let R₂ represent the rate of diffusion of the gas.
Let M₁ represent the molar mass of Cl₂
Let M₂ represent the molar mass of the gas.
From the question given above, the following data were obtained:
NOTE: Assume the rate of diffusion of Cl₂ is 1.
Rate of diffusion of Cl₂ (R₁) = 1
Rate of diffusion of the gas (R₂) = 1.37 times R1 = 1.37 × 1 = 1.37
Next, we shall determine the molar mass of the gas. This can be obtained as follow:
Rate of diffusion of Cl₂ (R₁) = 1
Molar mass of Cl₂ (M₁) = 35.5 × 2 = 71 g/mol
Rate of diffusion of the gas (R₂) = 1.37
Molar mass of the gas (M₂) =?
R₁/R₂ = √(M₂/M₁)
1/1.37 = √(M₂/71)
Square both side
(1/1.37)² = M₂ /71
1/1.8769 = M₂ /71
Cross multiply
1.8769 × M₂ = 71
Divide both side by 1.8769
M₂ = 71 / 1.8769
M₂ = 37.8 g/mol
Since the gas is a homonuclear (the same element) diatomic molecule, we shall divide the molar mass of the gas molecule by 2 to obtain the molar mass of the element that makes up the molecule. This is illustrated below:
Molar mass of the element = 37.8 / 2
Molar mass of the element = 18.9 g/mol
Comparing the molar mass of the element with those in the periodic table, the element that makes up the gas is fluorine. Thus the molecular formula of the gas F₂.
