Find the simplest formula of a substance containing (by weight) 39.66% sodium, 27.59% sulfur and 41.38% oxygen

Given:
w (Na) = 39.66%;
w (S) = 27.59%;
w (O) = 41.38%.
To find:
NaSO =?
Decision:
We denote the numbers of sodium, sulfur, and oxygen atoms in the simplest formula of a substance by x, y, and z, respectively. The atomic masses of these elements are 23, 32, and 16, respectively. Therefore, the masses of sodium, sulfur, and oxygen in the composition of the substance are 23x: 32y: 16z. By the condition of the problem, this relation has the form: 39.66: 27.59: 41.38. Hence:
23x: 32y: 16z = 39.66: 27.59: 41.38.
Where from
x: y: z = (39.66 / 23): (27.59 / 32): (41.38 / 16) = 1.72: 0.86: 2.59.
To express the resulting ratio in whole numbers, we divide all three of its terms into the smallest of them:
x: y: z = (1.72 / 0.86): (0.86 / 0.86): (2.59 / 0.86) = 2: 1: 3.
Thus, the simplest formula of the substance NaxSyOz will be: Na2SO3.
Answer: Na2CO3.

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