Question

sulfur tetrafluoride, sf₄, has a mass ratio of sulfur to fluorine of 1.00:2.37. a second, unknown compound containing sulfur and fluorine has a sulfur to fluorine mass ratio of 1.00:3.55. use the law of multiple proportions to determine the chemical formula of the unknown compound.

Explanation:

Step1: Recall the Law of Multiple Proportions

The law of multiple proportions states that when two elements form more than one compound, the masses of one element that combine with a fixed mass of the other element are in the ratio of small whole numbers. Here, we fix the mass of sulfur as 1.00 (so we can consider the moles of fluorine relative to a fixed amount of sulfur).

Step2: Find the ratio of the mass ratios of fluorine

First, we have the mass ratio of F to S in \( SF_4 \) as \( \frac{2.37}{1.00} \) (mass of F per mass of S) and in the unknown compound as \( \frac{3.55}{1.00} \) (mass of F per mass of S). We take the ratio of these two mass ratios of F:
\( \frac{\text{Mass ratio of F in unknown}}{\text{Mass ratio of F in } SF_4} = \frac{3.55}{2.37} \approx 1.5 \)
We can express 1.5 as a fraction \( \frac{3}{2} \). This means that the number of F atoms in the unknown compound compared to \( SF_4 \) (which has 4 F atoms) should be in the ratio of \( \frac{3}{2} \) when the mass of S is fixed.

Step3: Determine the number of F atoms in the unknown compound

Let the number of F atoms in the unknown compound be \( n \). We know that the ratio of the number of F atoms (since the mass ratio is proportional to the number of atoms when the mass of S is fixed) should be equal to the ratio of the mass ratios (from the law of multiple proportions). So:
\( \frac{n}{4} = \frac{3}{2} \)
Solving for \( n \):
\( n = 4\times\frac{3}{2} = 6 \)
Since the compound contains sulfur and fluorine, and we fixed the mass of S as 1 (so the number of S atoms is 1, same as in \( SF_4 \) when we fix the mass of S), the formula of the unknown compound is \( SF_6 \).

Answer:

The chemical formula of the unknown compound is \( \boldsymbol{SF_6} \)