Given that \rm S is the central atom, draw a Lewis structure of \rm OSF_4 in which the formal charges of all atoms are zero.

We can't draw structures on this forum but here is a link where one is drawn for you.

http://www.chem.umass.edu/~dgross/chem111/problems/Chap10.probs.pdf

To draw the Lewis structure of \rm OSF_4 and ensure that the formal charges of all atoms are zero, we need to follow these steps:

Step 1: Determine the total number of valence electrons
To find the total number of valence electrons, we add up the valence electrons of each atom in the molecule.

Oxygen (O) has 6 valence electrons.
Sulfur (S) has 6 valence electrons.
Fluorine (F) has 7 valence electrons.

For each fluorine atom, we need to multiply the number of valence electrons by the number of fluorine atoms in the molecule, which is 4 in this case.

Total valence electrons = (6 + 6 + 4 * 7) = 38

Step 2: Determine the central atom
The central atom is usually the atom with the lowest electronegativity which is sulfur (S) in this case.

Step 3: Connect the atoms
Place the central atom (S) in the center and connect it with the surrounding atoms (O and F) using single lines to represent chemical bonds.

F
|
F--S--O--F
|

Step 4: Distribute the remaining electrons
Place the remaining valence electrons around each atom to satisfy the octet rule, except for hydrogen, which follows the duet rule (2 electrons maximum).

Start by placing lone pairs around each atom until each atom has a full octet or duet. Place any remaining electrons as lone pairs on the central atom.

F
|
F--S--O--F
|
F

Step 5: Check for octet rule and formal charges
Check if all the atoms have a full octet (except hydrogen) or duet.

In this case, the octet rule is not satisfied for the central sulfur (S) atom. It has only 6 electrons around it.

Step 6: Convert lone pairs to bonding pairs
To ensure the central atom has a full octet, we can convert lone pairs on the surrounding atoms to bonding pairs.

Move two lone pairs from one of the fluorine atoms (F) to form a double bond with sulfur (S). This creates a coordinate covalent bond.

F
|
F--S==O--F
|
F

Now, the sulfur atom (S) has a full octet, and all other atoms also have a full octet.

Step 7: Calculate the formal charges
To calculate the formal charges, we need to assign the valence electrons of each atom, lone pairs, and bonding pairs.

The formal charge formula is:
Formal Charge = Valence Electrons - Lone Pairs - (1/2) * Bonding Pairs

Assigning the valence electrons:
Oxygen (O) - Valence Electrons = 6
Sulfur (S) - Valence Electrons = 6
Fluorine (F) - Valence Electrons = 7

Calculating formal charges for each atom:
Formal Charge on O: 6 - 4 - (1/2) * 2 = 0
Formal Charge on S: 6 - 0 - (1/2) * 8 = 0
Formal Charge on F: 7 - 0 - (1/2) * 2 = 0

All the formal charges are zero, which means we have successfully drawn a Lewis structure of \rm OSF_4 with zero formal charges on all atoms:

F
|
F--S==O--F
|
F