The spontaneity of a reaction can be determined using the Gibb's free energy equation:

In this formula,  is enthalpy,  is entropy, and  is the temperature in Kelvin. In order for a reaction to be spontaneous, Gibb's free energy must be negative. Looking at the equation, we can see that the value for  will ALWAYS be negative if enthalpy is negative and entropy is positive.

These are the requirements for a reaction that is always spontaneous, regardless of temperature,

The first thing we need to do in order to solve this problem is determine at what temperature  is equal to zero. When  is equal to zero, the reaction is at equilibrium and will not go one way or the other. Using the Gibb's free energy equation, we can determine the temperature where the reaction is at equilibrium.

The question tells us the enthalpy and entropy values, allowing us to solve for the equilibrium temperature. Remember to convert the enthalpy from kilojoules to Joules.

At , the reaction is at equilibrium. In order to make the reaction spontaneous, do we need to raise or lower from this temperature? Notice how entropy in this case is positive. By increasing temperature, the negative portion of the equation will become larger, and will result in a negative value. This means that the above reaction is spontaneous at temperatures higher than . You can check you work by solving for the Gibb's free energy at a higher temperature.

Since the value is negative, the reaction is spontaneous at this higher temperature.

Given the above conditions, we can use the Gibb's free energy equation in order to determine the reaction's spontaneity.

Convert the temperature to Kelvin and the enthalpy to Joules.

Use the given values to solve for the Gibb's free energy.

Since  is positive at these conditions, we can conclude that the reaction is nonspontaneous and will not take place.

The sign of the change in Gibb's free energy,  tells us whether a reaction is spontaneous or not (whether the reaction requires the net input of energy or not). For a spontaneous reaction, the  value is always less than zero. This is because the free energy of the products is less than that of the reactants. This indicates that there is a net release of energy, as opposed to a net energy consumption. When the products are at a lower energy than the reactants, the reaction can proceed spontaneously, and is known as exothermic.

Gibbs free energy is used to determine if a reaction will occur spontaneously. If the Gibbs free energy is negative for the given process, then the reaction will occur spontaneously.

In the given scenario, ice will always melt spontaneously when the temperature is above 0^oC. As a result, we can state that the Gibbs free energy will always be negative for this process.

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If a process is endothermic, is positive.

If a process involves a decrease in entropy, is negative.

Under these conditions, the only way can be negative is if is below absolute zero, which is impossible. Catalysts do not effect , rather they only affect reaction kinetics, not thermodynamics.