Answer to Question #331363 in General Chemistry for tim

Question

.   If 35.0 g H2O at 22.7°C is combined with 65.0 g H2O at 87.5°C, what is the final temperature of the 

      mixture? The specific heat capacity of water is 4.184 J/g⋅°C.

Answer 1

Solution:

This problem can be summarized thusly:

q_{gained by cold water} = q_{lost by hot water}

 

q = m × C × ΔT

q = m × C × (T_f − T_i),

where:

q = amount of heat energy gained or lost by substance (J)

m = mass of sample (g)

C = specific heat capacity (J °C⁻¹ g⁻¹)

T_f = final temperature (°C)

T_i = initial temperature (°C)

q_{gained by cold water} = (35.0 g) × C_water × (T_f − 22.7°C)

q_{lost by hot water} = (65.0 g) × C_water × (87.5°C − T_f)

Therefore,

(35.0) × C_water × (T_f − 22.7) = (65.0) × C_water × (87.5 − T_f)

(35.0) × (T_f − 22.7) = (65.0) × (87.5 − T_f)

35.0T_f − 794.5 = 5687.5 − 65.0T_f

100T_f = 6482

T_f = 64.82°C

Answer: The final temperature of the mixture is 64.82°C