The final temperature will be approximately 119.63 K.
According to Charles's Law, which states that for a given amount of gas at constant pressure, the volume of the gas is directly proportional to its temperature in kelvin, we can use the formula:
V1/T1 = V2/T2
Where V1 is the initial volume, T1 is the initial temperature, V2 is the final volume, and T2 is the final temperature.
In this case, the initial pressure is 1580 mmHg and the initial temperature is 389°C (662 K).
If the pressure is reduced to 287 mmHg, we can substitute these values into the formula to find the final temperature:
(V1/T1) = (V2/T2)
(1580 mmHg / 662 K) = (287 mmHg / T2)
Simplifying the equation, we can solve for T2: T2 = (287 mmHg * 662 K) / 1580 mmHg
Calculating this, we find that the final temperature will be approximately 119.63 K.