Final answer:
The ratio of the number of molecules of oxygen to nitrogen in a gaseous mixture with a mass ratio of 1:4 is 7:32, calculated by comparing the moles of each gas derived from their molar masses and mass ratio.
Step-by-step explanation:
To determine the ratio of the number of molecules of oxygen to nitrogen in a gaseous mixture with a mass ratio of 1:4, we use the molar masses of oxygen (O2, approximately 32 g/mol) and nitrogen (N2, approximately 28 g/mol). First, we need to calculate the moles of each gas based on their given mass ratio. For oxygen with a mass ratio of 1 and molecular weight of 32 g/mol, we get 1/32 moles; for nitrogen with a mass ratio of 4 and molecular weight of 28 g/mol, we get 4/28 moles.
When simplified, the moles of oxygen are 1/32, and for nitrogen, it's 1/7. To compare these as the number of molecules, since one mole of a substance always contains the same number of molecules (Avogadro's number), we just need to consider the ratio of the moles. Therefore, the ratio of the number of molecules (oxygen to nitrogen) is (1/32)/(1/7) which simplifies to 7:32. Thus, the ratio of the number of their molecules is 7:32.