Cinnabar is an ore of mercury that contains only Hg and S. When a 0.350 g sample of cinnabar is heated in oxygen, the ore decomposes completely to yield 0.302 g Hg metal. What is the empirical formula of cinnabar?

HgS

Explanation:

In a 0.350g-sample there are 0.302 g of Hg. Then, there is 0.350 g - 0.302 g = 0.048 g of S. To calculate the empirical formula, we have to follow a series of steps.

Step 1: Calculate the percent composition

Hg: (0.302 g / 0.350 g) * 100% = 86.3%

S: (0.048 g / 0.350 g) * 100% = 13.7%

Step 2: Divide each percentage by the atomic mass of the element

Hg: 86.3 / 200.59 = 0.430

S: 13.7 / 32.07 = 0.427

Step 3: Divide the numbers by the smallest one

Hg: 0.430/0.427 ≈ 1

S: 0.427/0.427 = 1

The empirical formula is HgS.