Answer to Question #217464 in Physical Chemistry for Thea

Question

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).

Answer 1

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

$$Q = m * c * ΔT$$

substituting the given information in this formula we have

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

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

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

$$moles \ of \ CaCl_2 = 1.75 \ \cancel{g \ of \ CaCl_2} \ * \ \frac{1 \ mol \ CaCl_2}{110.984 \ \cancel{g \ of \ CaCl_2} }$$

$$moles \ of \ CaCl_2 = 0.015768 \ g/mol$$

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.

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

$$= - \frac{1274.9 \ Joules}{ 0.015768 \ mol \ of \ CaCl_2 }$$

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

in Kilojoules per mol, the answer will be

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

$$= -80.853 \ \ kiloJoules$$

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.