The question; The mass of element Q found in 1.00 mole of each of four different compounds is 38.0 grams, 57.0 grams, 76.0 grams, and 114 grams, respectively. A possible atomic weight of Q is;
Answer;
Atomic weight of Q = 19 g
Solution and explanation; 
A possible atomic mass of Q has to be a factor of 38, 57, 76, and 114. 
Because the number of atoms of Q in any compound must be a whole number.
-Finding a greatest common Divider of 38, 57, 76, and 114 
38 = 2(19) 
57 = 3(19) 
76 = 4(19) 
114 = 6(19)
Thus; the greatest common divider is 19 
Hence, the possible atomic mass of Q is 19 g