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Calculate the heat of mixing when 25 grams of ethanol is added to 75 grams of water at 25°C. The heat of mixing of ethanol in water is -4.4 kJ/mol. Assume the densities of ethanol and water to be 0.789 g/mL and 1 g/mL, respectively, and the specific heat of the mixture to be 4.184 J/g°C.

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First, we need to find the number of moles of ethanol and water in the mixture.The molar mass of ethanol  C2H5OH  is approximately 46.07 g/mol.Moles of ethanol = mass / molar massMoles of ethanol = 25 g / 46.07 g/mol = 0.542 molesThe molar mass of water  H2O  is approximately 18.015 g/mol.Moles of water = mass / molar massMoles of water = 75 g / 18.015 g/mol = 4.164 molesNow, we can calculate the heat of mixing for the ethanol and water.Heat of mixing = moles of ethanol * heat of mixing per moleHeat of mixing = 0.542 moles * -4.4 kJ/mol = -2.3848 kJSince the heat of mixing is negative, it means that the process is exothermic and heat is released during the mixing of ethanol and water.Now, let's calculate the temperature change of the mixture due to the heat of mixing.First, we need to find the total mass of the mixture.Total mass = mass of ethanol + mass of waterTotal mass = 25 g + 75 g = 100 gNext, we need to convert the heat of mixing from kJ to J.Heat of mixing = -2.3848 kJ * 1000 J/kJ = -2384.8 JNow, we can use the specific heat formula to find the temperature change.q = mcTWhere q is the heat, m is the mass, c is the specific heat, and T is the temperature change.T = q /  mc T = -2384.8 J /  100 g * 4.184 J/gC T = -2384.8 J / 418.4 J/CT = -5.7CSince the initial temperature was 25C, the final temperature of the mixture will be:Final temperature = initial temperature + TFinal temperature = 25C - 5.7C = 19.3CSo, the heat of mixing when 25 grams of ethanol is added to 75 grams of water at 25C is -2.3848 kJ, and the final temperature of the mixture is 19.3C.

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