final temperature of water if no heat is lost?

Question

A 0.551g sample of steam at 103.4 C is condensed into a container with 5.63g of water at 14.0 C. What is the final temperature of the water mixture if no heat is lost? The specific heat of water is 4.18 j/g x c , the specific heat of steam is 2.01 j/g x c, and ΔH_vap= -40.7 kj/mol

Answer 1

heat lost by steam = heat gained by liquid

heat to convert 0.551 g steam @ 103.4º to 100 º = mC∆T = (0.551 g)(2.01 J/gº)(3.4º) = 3.77 J

heat to convert 0.551 g steam @ 100º to liquid @100º = m∆Hvap = (0.551 g)(1mol/18g)(40.7 kJ/mol) = 1.25 kJ

Total heat lost by steam = 1250 J + 3.77 J = 1253.77 J

Heat gained by water = q = mC∆T = 1253.77 J

1253.77 J = (5.63 g)(4.18 J/gº)(∆T)

∆T = 53.3º

Final temperature of water = 53.5º + 14.0º = 67.3ºC