 The problem reads at what temperature is the following reaction spontaneous, bromide 2 liquid going to bromide 2 gas. Where the change in enthalpy is 30.91 kilojoules per mole and the change in entropy is 93.2 joules per mole kelvin. So we're looking for something that gives us spontaneous, that means we're looking for Gibbs free energy. So we're looking for a formula that relates delta G, that's this, with delta H and delta S. And of course that would be this formula. So let's just check this formula out. Let's do a test for when temperature is room temperature, so that would be 298 kelvin. So how much is delta G theta then? 298 kelvin. It equals 30.91 kilojoules per mole minus 298 kelvin times 93.2 joules per mole kelvin. We see that all our units are correct. What would we get? Let's move this into joules. So this is 30,910 and we need this multiplied. So 298 times 93.2. So that's 27,774. 27,774. So how much would that be? So we need 30,910 minus that answer. And that is 3,136 joules per mole. 1,136 joules per mole. And what that is is greater than zero, so not spontaneous. Remember spontaneous is anything that's under zero. So how are we going to solve this? We're going to set delta G theta equal to zero and see what T we get. So solution delta G theta equals zero means that T times delta S theta equals delta H theta or T equals delta H theta divided by delta S theta. So now we can calculate that. This is 30,910 joules per mole divided by 93.2 joules per mole kelvin. So we expect to get kelvin here. So let's get our calculator up. So we have 30,910 divided by 93.2 equals so 331.7 kelvin 331.7 kelvin. So at 298 it was not spontaneous at 331.7 delta G theta becomes zero. So our answer is for T greater than or equal to 331.7 kelvin, which would be minus 273.58.7 Celsius. This reaction is spontaneous.