Final answer:
The decrease in entropy of 25.0 g of water condensing on a bathroom mirror at 35.0°C can be calculated using the formula ΔS = Q / T. The heat transferred (Q) can be calculated using the latent heat of vaporization (ΔHvap) and the mass of water (m). Plugging in the values, we get ΔS = 0.184 J/K.
Step-by-step explanation:
The decrease in entropy of 25.0 g of water that condenses on a bathroom mirror at a temperature of 35.0° C can be calculated using the formula ΔS = Q / T, where ΔS is the change in entropy, Q is the heat transferred, and T is the temperature in Kelvin.
The heat transferred (Q) can be calculated using the latent heat of vaporization (ΔHvap) and the mass of water (m), as Q = m ΔHvap. In this case, the mass of water is given as 25.0 g. The latent heat of vaporization for water at 25 °C is 44.02 kJ/mol, which can be converted to J/g using molar mass, giving a value of 2.27 J/g.
Using the formula ΔS = Q / T, we can calculate the temperature in Kelvin by adding 273.15 to the given temperature of 35.0 °C, resulting in 308.15 K. Plugging in the values, we get ΔS = (25.0 g)(2.27 J/g) / 308.15 K = 0.184 J/K.