Question #217464

When 1.75 g of CaCl2 dissolves in 125 g of water in a coffee-cup calorimeter, the temperature increases by 2.44°C. What is the heat change per mole of CaCl2 dissolved in water? Assume that all the heat is absorbed by the water (c = 4.18 J/g×°C).


1
Expert's answer
2021-07-16T01:29:08-0400

Q217464

 Deadline: 15.07.21, 19:38

When 1.75 g of CaCl2 dissolves in 125 g of water in a coffee-cup calorimeter, the temperature increases by 2.44°C. What is the heat change per mole of CaCl2 dissolved in water? Assume that all the heat is absorbed by the water (c = 4.18 J/g×°C).


Solution :


Step 1: To find the heat absorbed by the water


We have to assume that all the heat is absorbed by the water.


specific heat capacity of water, c = 4.18 J/g×°C


mass of water, m = 125 g


change in temperature of the water, ΔT = 2.44°C


The formula for finding the heat absorbed by the water is given as


Q=mcΔTQ = m * c * ΔT



substituting the given information in this formula we have



Q=125 g  4.18 J/g°C  2.44°CQ = 125 \ g \ * \ 4.18 \ J/g°C \ * \ 2.44°C


Q = 1274.9 Joules.Q \ = \ 1274.9 \ Joules.

Step 2: Convert 1.75 g of CaCl2 to moles by using the molar mass of CaCl2.


Molar mass of CaCl2 = 110.984 g/mol



moles of CaCl2=1.75 g of CaCl2  1 mol CaCl2110.984 g of CaCl2moles \ of \ CaCl_2 = 1.75 \ \cancel{g \ of \ CaCl_2} \ * \ \frac{1 \ mol \ CaCl_2}{110.984 \ \cancel{g \ of \ CaCl_2} }



moles of CaCl2=0.015768 g/molmoles \ of \ CaCl_2 = 0.015768 \ g/mol



Step 3: Find the Heat change per mole of CaCl2.


The temperature of the water has increased. This means the reaction is exothermic.

For exothermic reaction.


Heat change per mole, ΔH=Qmoles of CaCl2Heat \ change \ per \ mole, \ ΔH = - \frac{Q}{ moles \ of \ CaCl_2 }



=1274.9 Joules0.015768 mol of CaCl2= - \frac{1274.9 \ Joules}{ 0.015768 \ mol \ of \ CaCl_2 }

Heat change per mole, ΔH=80,853.4 Joules/molHeat \ change \ per \ mole, \ ΔH = - 80,853.4 \ Joules / mol


in Kilojoules per mol, the answer will be



=80,853.4 Joules/mol1 kiloJoules1000 Joules= - 80,853.4 \ \cancel{Joules} / mol * \frac{1 \ kiloJoules }{1000 \ \cancel{Joules}}


=80.853  kiloJoules= -80.853 \ \ kiloJoules


The quantities given in the question are in 3 significant figures, so our final answer must also be in 3 significant figures.


In correct, significant figures, the answer is - 80.9 kilojoules per mole. Hence heat change per mole of CaCl2 in water = - 80.9 kilojoules per mole.





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