Suppose that 0.50 g of water at 25 ∘c condenses on the surface of a 51-g block of aluminum that is initially at 25 ∘c. if the heat released during condensation goes only toward heating the metal, what is the final temperature (in ∘c) of the metal block? (the specific heat capacity of aluminum is 0.903 j/g∘c and the heat of vaporization of water at 25 ∘c is 44.0 kj/mol.)

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Physics

Gidget

15 November, 00:35

Suppose that 0.50 g of water at 25 ∘c condenses on the surface of a 51-g block of aluminum that is initially at 25 ∘c. if the heat released during condensation goes only toward heating the metal, what is the final temperature (in ∘c) of the metal block? (the specific heat capacity of aluminum is 0.903 j/g∘c and the heat of vaporization of water at 25 ∘c is 44.0 kj/mol.)

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Lucky · Answer 1

Moles water = 0.50 g / 18.02 g/mol=0.0277

heat lost by water = 0.0277 mol x 44.0 kJ/mol=1.22 kJ = > 1220 J

heat gained by aluminum = 1220 J

1220 = 51 x 0.903 (T - 25) = 46.05 T - 1151

1220 + 1151 = 46.05T

46.05T = 2371

T = 51.48 °C (51 °C at two significant figures)