Using Charles's law, we can determine the new volume of chlorine gas at 600 K. Charles's law states that the volume of a gas is directly proportional to its temperature, assuming constant pressure. Mathematically, it can be expressed as:

```

V1/T1 = V2/T2

```

where:

- V1 is the initial volume of the gas (25.0 mL)

- T1 is the initial temperature of the gas (300 K)

- V2 is the final volume of the gas (what we're trying to find)

- T2 is the final temperature of the gas (600 K)

Rearranging the equation to solve for V2, we get:

```

V2 = V1 * T2/T1

```

Substituting the given values:

```

V2 = 25.0 mL * 600 K / 300 K

```

```

V2 = 50.0 mL

```

Therefore, the chlorine gas will occupy a volume of 50.0 mL at 600 K.