Question

part a.

The air in an inflated balloon (defined as the system) is warmed over a toaster and absorbs 110 J of heat. As it expands, it does 79 kJ of work.

What is the change in internal energy for the system? Express the energy in kilojoules to two significant figures.

part b.

When fuel is burned in a cylinder equipped with a piston, the volume expands from 0.235 L to 1.350 L against an external pressure of 1.02 atm . In addition, 857 J is emitted as heat. What is ΔE for the burning of the fuel?

Express the energy to three significant figures and include the appropriate units.

part c.

A calorimeter is an insulated device in which a chemical reaction is contained. By measuring the temperature change, ΔT, we can calculate the heat released or absorbed during the reaction using the following equation:

q=specific heat×mass×ΔT

Or, if the calorimeter has a predetermined heat capacity, C, the equation becomes

q=C×ΔT

At constant pressure, the enthalpy change for the reaction, ΔH, is equal to the heat, qp; that is,

ΔH=qp

but it is usually expressed per mole of reactant and with a sign opposite to that of q for the surroundings. The total internal energy change, ΔE (sometimes referred to as ΔU), is the sum of heat, q, and work done, w:

ΔE=q+w

However, at constant volume (as with a bomb calorimeter) w=0 and so ΔE=qv.

A calorimeter contains 23.0 mL of water at 11.0 ∘C . When 2.00 g of X (a substance with a molar mass of 67.0 g/mol ) is added, it dissolves via the reaction

X(s)+H2O(l)→X(aq)

and the temperature of the solution increases to 30.0 ∘C .

Calculate the enthalpy change, ΔH, 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 d.

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, ΔE, for this reaction per mole of sucrose.

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

Answer 1

Part A.

According to the first law of thermodynamics:

Amount of heat absorbed (q) = change in internal energy ($\Delta$E) + work done by the system (-w)

i.e. (110/1000) kJ = $\Delta$E + 79 kJ

i.e. $\Delta$E = 0.11 - 79 = -78.89 kJ ~ -79 kJ