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Answer :
Yes, the ammonium sulfate will dissolve completely in the water, and the solution will be unsaturated.
This is because the solubility of ammonium sulfate is 5.79 M, which means that 5.79 moles of ammonium sulfate can dissolve in 1 liter of water. The amount of ammonium sulfate added to the water is 37.6 g, which is equivalent to 0.28 moles. The amount of water is 105 g, which is equivalent to 0.105 liters. Therefore, the concentration of the solution is 0.28 moles / 0.105 liters = 2.67 M, which is less than the solubility of ammonium sulfate. This means that the solution is unsaturated and can still dissolve more ammonium sulfate.
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