Sulfur dioxide gas reacts with hydrogen sulfide gas to produce elemental sulfur (S8) and water vapor. Predict the temperature range over which this reaction is spontaneous.

I would do this.

Write the equation and balance it. It's a little tricky but here it is.
8SO2 + 16H2S ==> 3S8 + 16H2O
Look up delta Hf in tables (probably in yur text or you can find them on the web) and determine delta Hrxn.
deltaHrxn = (n*products of reaction)-(n*reactants)
Do the same thing for delta Srxn the same way.
Then delta G = delta Hrxn -TdeltaSrxn.

Plug in the numbers for deltaHrxn and deltaSrxn and determine T which will give a negative number for delta G.

To determine the temperature range over which a reaction is spontaneous, you can use the concept of Gibbs free energy (ΔG).

The Gibbs free energy change for a reaction is given by the equation:

ΔG = ΔH - TΔS

Where:
ΔG is the change in Gibbs free energy,
ΔH is the change in enthalpy,
T is the temperature in Kelvin,
ΔS is the change in entropy.

In a spontaneous reaction, ΔG is negative, indicating that the reaction can occur without the input of energy. Therefore, to predict the temperature range over which the reaction is spontaneous, we need to find the temperature at which ΔG becomes negative.

1. Start by writing and balancing the chemical equation for the reaction:
SO2(g) + 2H2S(g) -> S8(s) + 2H2O(g)

2. Find the change in standard enthalpy (ΔH) for the reaction. You can look up the standard enthalpies of formation for all the species involved in the reaction and use them to calculate the overall change in enthalpy for the reaction.

3. Determine the change in entropy (ΔS) for the reaction. You can calculate this by subtracting the sum of the standard entropies of the reactants from the sum of the standard entropies of the products.

4. Substitute the values of ΔH and ΔS into the equation for ΔG:

ΔG = ΔH - TΔS

5. Calculate the temperature at which ΔG becomes zero or negative. This can be done by setting ΔG equal to zero and solving for T:

0 = ΔH - TΔS
T = ΔH/ΔS

The temperature calculated in step 5 represents the boundary between a spontaneous and non-spontaneous reaction. If T is lower than this temperature, the reaction is spontaneous; if T is higher, the reaction is non-spontaneous.

Please note that this procedure assumes the reaction is occurring under standard conditions (1 atm pressure, 298 K). If you have specific values for enthalpy and entropy at different temperatures, you can use more precise calculations to determine the temperature range.