Final answer:
The ratio of the number of molecules of O₂ to N₂ in a gaseous mixture with a mass ratio of 1:4 is found by converting the mass ratio to moles using molecular weights and is approximately 1: 4.57. Rounding to the nearest given option, the molecule ratio is 1:5.
Step-by-step explanation:
The question asks to find the ratio of the number of molecules of O₂ and N₂ in a gaseous mixture given their mass ratio which is 1:4. For O₂ (molecular weight = 32 g/mol) and N₂ (molecular weight = 28 g/mol), the ratio of molecules can be calculated by dividing the mass of each gas by its molecular weight to get the number of moles, and then using Avogadro's number to find the number of molecules. Since both O₂ and N₂ have the same Avogadro's number of molecules per mole, the ratio of moles will be the same as the ratio of the number of molecules.
First, we find the number of moles of each gas by mass ratio:
- 1 g of O₂ / 32 g/mol = 0.03125 moles of O₂
- 4 g of N₂ / 28 g/mol = 0.14286 moles of N₂
Next, we find the ratio of moles, which gives us the ratio of molecules since the number of molecules in a mole is a constant (Avogadro's number):
Ratio of moles = 0.03125 moles of O₂ : 0.14286 moles of N₂ ≈ 1 : 4.5714
The closest integer ratio to this value is 1 : 4.57, which, when rounding to whole numbers for the options given in the multiple-choice question, results in a ratio of 1 : 5.
Therefore, the correct answer is: (d) 1:5.