When the following molecular equation is balanced using the smallest possible integer coefficients, the values of these coefficients are:

_chlorine (g) + _sodium iodide (s) -> _sodium chloride (s) + _iodine (s)

_chlorine (g) + _sodium iodide (s) -> _sodium chloride (s) + _iodine (s)

Cl2 + 2NaI ==> 2NaCl + I2

To balance the given chemical equation:

Cl2 (g) + 2NaI (s) -> 2NaCl (s) + I2 (s)

The balanced equation is obtained by assigning the coefficients as follows:

2 chlorine (g) + 2 sodium iodide (s) -> 2 sodium chloride (s) + 1 iodine (s)

To balance a chemical equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation. In this case, we are given the molecular equation:

_chlorine (g) + _sodium iodide (s) -> _sodium chloride (s) + _iodine (s)

Let's start by counting the number of atoms for each element on both sides of the equation:

On the left side:
- Chlorine (Cl): 1 atom
- Sodium (Na): 0 atoms
- Iodine (I): 1 atom

On the right side:
- Sodium (Na): 1 atom
- Chlorine (Cl): 1 atom
- Iodine (I): 1 atom

To balance the equation, we need to make sure that the number of atoms of each element is the same on both sides. In this case, we can see that we have an imbalance of sodium (Na) and chlorine (Cl) atoms.

Let's balance the equation step by step:

1. Balance the sodium (Na) atoms:
Since there is 1 sodium atom on the right side, we need to add a coefficient of 1 to sodium iodide on the left side:

1 chlorine (g) + 1 sodium iodide (s) -> 1 sodium chloride (s) + _iodine (s)

2. Balance the chlorine (Cl) atoms:
Since there is 1 chlorine atom on the left side, we need to add a coefficient of 1 to chlorine on the right side:

1 chlorine (g) + 1 sodium iodide (s) -> 1 sodium chloride (s) + 1 iodine (s)

3. Balance the iodine (I) atoms:
Since there is 1 iodine atom on the right side, we need to add a coefficient of 1 to iodine on the left side:

1 chlorine (g) + 1 sodium iodide (s) -> 1 sodium chloride (s) + 1 iodine (s)

Therefore, the balanced equation with the smallest possible integer coefficients is:

1 chlorine (g) + 1 sodium iodide (s) -> 1 sodium chloride (s) + 1 iodine (s)