Question

Part A: A calorimeter contains 17.0 mL of water at 12.0 ?C . When 2.50 g of X (a substance with a molar mass of 42.0 g/mol ) is added, it dissolves via the reaction

X(s)+H2O(l)?X(aq)

and the temperature of the solution increases to 25.5 ?C .

Calculate the enthalpy change, ?H, for this reaction per mole of X.

Assume that the specific heat of the resulting solution is equal to that of water [4.18 J/(g??C)], that density of water is 1.00 g/mL, and that no heat is lost to the calorimeter itself, nor to the surroundings.

Express the change in enthalpy in kilojoules per mole to three significant figures.

Part B: Consider the reaction

C12H22O11(s)+12O2(g)?12CO2(g)+11H2O(l)

in which 10.0 g of sucrose, C12H22O11, was burned in a bomb calorimeter with a heat capacity of 7.50 kJ/?C. The temperature increase inside the calorimeter was found to be 22.0 ?C. Calculate the change in internal energy, ?E, for this reaction per mole of sucrose.

Express the change in internal energy in kilojoules per mole to three significant figures.

Answer 1

given

volume = 17 ml

density of the solution = 1 g/ml

so

mass of the solution = density x volume

mass of the soltuion = 1 x 17

mass of the solution = 17 g

now

we know that

heat absorbed by the calorimeter = mass x specific heat x temp change

so

Q = m x s x dT

Q = 17 x 4.18 x (25.5 - 12)

Q = 959.31 J

this heat is due to the enthalpy change of the reaction

enthalpy change = - Q

so

the enthalpy change is -959.31 J

given 2.5 g of X

we know that

moles = mass / molar mass

so

moles of X = 2.5 / 42

moles of X = 0.0595

now

change in enthalpy per mole of X = enthalpy change / moles of X

so

change in enthalpy per mole of X = -959.31 / 0.0595

change in enthalpy per mole of X = -16116 J

change in enthalpy per mole of X = -16.116 kJ

so

the change in enthalpy per mole of X is -16.116 kJ/mol

2)

moles = mass / molar mass

so

moles of sucrose = 10/342

moles of sucrose = 0.02924

Heat absorbed by the calorimeter = heat capacity x temp change

so

Q = 7.50 x 22

Q = 165 kJ

so the energy released in the combustion process = -165 kJ

now

change in internal energy per moles of sucrose = change in internal energy / moles of sucrose

change in internal energy per moles of sucrose = -165 / 0.02924

change in internal energy per moles of sucrose = -5643 kJ

so

the change in internal energy per moles of sucrose is -5643 kJ/mol