How many atoms do mercury vapour molecules consist of if the density of mercury vapour relative to air is \(6.92\) ? The average mass of air is \(29 \mathrm{~g}\) per mole. \((\mathrm{Hg}=200)\) (a) 1 (b) 2 (c) 4 (d) Infinite

Short Answer

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Answer: (a) 1

Step by step solution

01

Determine the molecular weight of air

We are given that the average mass of air is 29 g per mole. We will refer to the molecular weight of air as M_air: M_air = 29 g/mol
02

Calculate the molecular weight of mercury vapor

We are given the relative density of mercury vapor to air, which is 6.92. We can use this information to find the molecular weight of mercury vapor (M_Hg_vapor): M_Hg_vapor = relative density * M_air M_Hg_vapor = 6.92 * 29 g/mol M_Hg_vapor = 200.68 g/mol
03

Determine the number of mercury atoms in a mercury vapor molecule

Now, we want to determine how many atoms of mercury are in each mercury vapor molecule. To do this, we will divide the molecular weight of the mercury vapor (M_Hg_vapor) by the atomic weight of mercury (Hg = 200): Number of mercury atoms = M_Hg_vapor / Atomic weight of Hg Number of mercury atoms = 200.68 g/mol / 200 g/mol Number of mercury atoms ≈ 1 Since the number of mercury atoms is approximately 1, the correct answer is: (a) 1

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