A gases mixture contains oxygen and nitrogen in the ratio `1 : 4` by weight. Therefore, the ratio of the number of molecules is:

Options

A. (a)1:4
B. (b)1:8
C. (c )7:32
D. (d)3:16

Answer

C

Explanation

Let mass of oxygen `=1 g`, Then mass of nitrogen `=4 g`
Mol. Wt. of `N_(2)=28 g`, Mol. Wt. of `O_(2)=32 g`
`28 g` of `N_(2)` has`=6.02xx10^(23)` molecules of nitrogen
`4 g` of `N_(2)` has`=(6.02xx10^(23))/28xx4` molecules of nitrogen
`=(6.02xx10^(23))/7` molecules of nitrogen
`32 g` of `O_(2)` has`=6.02xx10^(23)` molecules of oxygen
`:. 1 g of O_(2)` has`=(6.02xx10^(23))/32xx1=(6.02xx10^(23))/32` molecules of oxygen
Thus, ratio of molecules of oxygen: nitrogen
`=(6.02xx10^(23)//32)/(6.02xx10^(23)//7)=7:32`.