A gas made up of homonuclear diatomic molecules escapes through a pinhole 1.37 times as fast as cl2 gas. Write the chemical formula of the gas.

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.

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