You find a compound composed only of element x and hydrogen,and know that it is 91.33% element x by mass. Each molecule has 2.67 times as many H atoms as x atoms. What is element x ?

Answer 1

Take a 100 g sample. That will consist of
91.33 g element X and
8.67 g H. Convert to moles.

91.33/atomic mass X = moles X = (91.33/z) which I am calling the atomic mass z = moles element X. We also know that there are 2.67 x as many x atoms as there are H atoms.
8.67 g H/1 = 8.67 moles H.

So the empirical formula is
X_(91.33/z)H8.67 + we know about the 2.67 so I set
2.67*91.33/z = 8.67 and solve for z.
If I didn't goof, I found z = 28.1 which probably is Si. Then
Si = 91.33/28 = 3.26
H = 8.67/1 = 8.67

Find the ratio and round to whole numbers. The easy way to do this is to divide the smallest number by itself (thus 1.00 for that one) and divide the other number of the same small number.
8.67/3.26 = 2.65. Now multiply each by whole numbers until you get two numbers close enough to round to whole numbers. I think a multiplier of 3 will do it.