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You know the entropy of the system because the reactants have 3 moles of gas while the products have 2 moles of gas. Since the moles of gas decreases from reactants to products, you know that the entropy of the system must be decreasing, so the change in entropy of the system must be negative and therefore less than zero. Since the reaction is spontaneous, you know that the total change in entropy must be positive or greater than zero. The total change in entropy is equal to sum of the change in entropy of the system and the change in entropy of the surroundings. Since it was already determined that the change in entropy of the system is negative from the first part, the change in entropy of the surroundings must be positive in order to give a total positive change in entropy.
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