At standard condition, gaseous chlorine is heavier than gaseous fluorine by? (Compare using density)?

density is directly proportional to the molar mass, which, because both are diatomic, means it is proportional to the atomic mass.

35.5/19 = 1.87 times heavier

Gases have the same molar volume at a given temperature and pressure. Therefore, the density is proportional to the mass of each mole (or molecule).

F has molar mass 18.998 g mol⁻¹, and Cl is 35.453 g mol⁻¹. Therefore F₂ is 37.996 g mol⁻¹, Cl₂ 70.906 g mol⁻¹.

The density ratio is ρ(Cl₂)/ρ(F₂) = M(Cl₂)/M(F₂) = 70.906 g mol⁻¹/35.453 g mol⁻¹ = 1.8661

Where M is molar mass.

Therefore Cl₂ gas is 86.6% denser than F₂.

Additional info:

Density of a gas is proportional to the molar mass because gas molecules are far apart enough that the molecular forces between them are negligible. Therefore, under given temperature (average speed of molecules) and pressure (push on the molecules at boundaries), increasing the number of molecules will increase the volume by the same amount. Each molecule simply take up the same amount of space, regardless of what the molecule is (its mass, shape, etc).

So to increase the density of a gas, you cannot just add more molecules (if you don't change temperature and pressure). You can only make each molecule heavier.

Making each molecule heavier is the same as making each mole of molecules heavier. Therefore, to find the relative density of gases, you compare their molecular masses or molar masses.

Or if you prefer algebra:

ρ₁/ρ₂ = (m₁/V₁)/(m₂/V₂) = (M₁n₁/V₁)/(M₂n₂/V₂)

Since V₁/n₁ = V₂/n₂ = Vm (molar volume) under given temperature and pressure,

ρ₁/ρ₂ = M₁/M₂

ps. Since PV = nRT, Vm (molar volume) = V/n = RT/P. Under STP, Vm = 22.42 m³ mol⁻¹.