Two 20.0 g ice cubes at –16.0 °C are placed into 215 g of water at 25.0 °C. Assuming no energy is transferred to or from thesurroundings, calculate the final temperature, Tf, of the water after all the ice melts.heat capacity of H,O(s)37.7 J/(mol·K)T; :°Cheat capacity of H,O(1)75.3 J/(mol·K)- TOOLSx10enthalpy of fusion of H,O6.01 kJ/mol

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Chemistry

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ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

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Two 20.0 g ice cubes at –16.0 °C are placed into 215 g of water at 25.0 °C. Assuming no energy is transferred to or from the
surroundings, calculate the final temperature, Tf, of the water after all the ice melts.
heat capacity of H,O(s)
37.7 J/(mol·K)
T; :
°C
heat capacity of H,O(1)
75.3 J/(mol·K)
- TOOLS
x10
enthalpy of fusion of H,O
6.01 kJ/mol

Expert Solution

Step 1

$m a s s o f i c e, m_{1} = 20 g m a s s o f w a t e r, m_{2} = 215 g t e m p o f i c e, T_{1} = - 16 ° C t e m p o f w a t e r, T_{2} = 25 ° C h e a t c a p a c i t y o f i c e (H_{2} O s o l i d), c_{1} = 37.7 J / (m o l K) h e a t c a p a c i t y o f l i q (H_{2} O l i q), c_{1} = 75.3 J / (m o l K) e n t h a l p y o f f u s i o n = 6.01 J / (m o l K)$

$f o r s p e c i f i c v a l u e i n t e r m s o f g r a m H e a t c a p a c i t y o f 1 m o l e o f i c e = 37.7 J / (m o l K) h e a t c a p a c i t y o f 18 g o f i c e = 37.7 J / (m o l K) h e a t c a p a c i t y o f 1 g o f i c e = \frac{37.7}{18} J / (g K) = 2.09 J / (g K) t h i s i s c a l l e d s p e c i f i c h e a t c a p a c i t y t h e r e f o r e, h e a t c a p a c i t y f o r i c e, c_{1} = 2.094 J / (g K) s i m i l a r l y f o r H_{2} O (l) H e a t c a p a c i t y o f 1 m o l e o f H_{2} O (l) = 75.3 J / (m o l K) h e a t c a p a c i t y o f 18 g o f H_{2} O (l) = 75.3 J / (m o l K) h e a t c a p a c i t y o f 1 g o f H_{2} O (l) = \frac{75.3}{18} J / (g K) = 4.18 J / (g K) t h i s i s c a l l e d s p e c i f i c h e a t c a p a c i t y t h e r e f o r e, h e a t c a p a c i t y f o r H_{2} O (l), c_{2} = 4.184 J / (g K) s i m i l a r l y e n t h a p l y o f f u s i o n = 6.01 J / (m o l K) = \frac{6.01}{18} J / (g K) = 0.33 J / (g K)$

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