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Chapter 2: Problem 2

A sample of liquid butane \(\left(\mathrm{C}_{\mathrm{L}} \mathrm{H}_{10}\right)\) in a pressurized lighter is set up directly beneath an aluminum can, as show in the diagram above. The can contains 100.0 \(\mathrm{mL}\) of water, and when the butane is ignited the temperature of the water inside the can increases from \(25.0^{\circ} \mathrm{C}\) to \(82.3^{\circ} \mathrm{C}\) . The total mass of butane ignited is found to be 0.51 \(\mathrm{g}\) , the specific heat of water is \(4.18 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C},\) and the density of water is \(1.00 \mathrm{g} / \mathrm{mL} .\) (a) Write the balanced chemical equation for the combustion of one mole of butane in air. (i) How much heat did the water gain? (ii) What is the experimentally determined heat of combustion for (ii) Whane based on this experiment? Your answer should be in \(\mathrm{kJ} / \mathrm{mol}\) . (c) Given butane's density of 0.573 \(\mathrm{g} / \mathrm{mL}\) at \(25^{\circ} \mathrm{C},\) calculate how much heat would be emitted if 5.00 \(\mathrm{mL}\) of it were combusted at that temperature. (d) The overall combustion of butane is an exothermic reaction. Explain why this is, in terms of bond energies. (e) One of the major sources of error in this experiment comes from the heat that is aboorbed by the air. Why, then, might it not be a good ide to perform this experiment inside a sealed container to prevent the heat from leaving the system?

Short Answer

Expert verified
The balanced equation for the combustion reaction of butane is: \(2 C_{4}H_{10(g)} + 13 O_{2(g)} \rightarrow 8 CO_{2(g)} + 10 H_{2}O_{(l)}\). The heat gained by water is 23.9 kJ. The experimentally determined heat of combustion for butane is -2732.7 kJ/mol. The heat emitted on combustion of 5 mL butane is -134.4 kJ. The combustion process is exothermic because more energy is released during bond formation than is absorbed during bond breaking.

Step by step solution

01

Write Balanced Chemical Reaction

The balanced chemical equation for the combustion of butane in air to form water and carbon dioxide is: \[2 C_{4}H_{10(g)} + 13 O_{2(g)} \rightarrow 8 CO_{2(g)} + 10 H_{2}O_{(l)}\]
02

Calculate Heat Gain by Water

Using the formula \(q = mc\Delta T\) where \(m\) is the mass of water, \(\Delta T\) is the change in temperature and \(c\) is the specific heat capacity of water, the heat gain by the water is calculated. Since volume of water is 100.0 mL and density is 1.00 g/mL, therefore mass of water \(m = 100.0 g\). Change in temperature \(\Delta T = 82.3^{\circ}C - 25.0^{\circ}C = 57.3^{\circ}C\). Hence \(q = 100g \times 4.18 J/(g \cdot ^{\circ}C) \times 57.3^{\circ}C = 23.9 kJ\)
03

Calculate Moles of Butane Burned

Moles of Butane burned is calculated by dividing mass by molar mass. Molar mass of Butane \(C_{4}H_{10}\) is 58.12 g/mol, hence moles = mass / molar mass = 0.51g / 58.12 g/mol = 8.77 x 10^{-3} mol.
04

Calculate Experimential Heat of Combustion

Experimental heat of combustion is the heat gained by water divided by the moles of butane burned. Hence experimental heat of combustion = 23.9 kJ / 8.77 x 10^-3 mol = -2732.7 kJ/mol
05

Calculate Heat Emitted from Combustion

Given volume of butane is 5.00 mL, hence mass = volume x density = 5.00 mL x 0.573 g/mL = 2.865 g. The number of moles from this mass is 2.865g / 58.12 g/mol = 0.0492 mol. The heat emitted thus = 0..0492 mol x -2732.7 kJ/mol = -134.4 kJ
06

Explain the Exothermic Nature of Combustion

In combustion reactions, bond breaking occurs at a higher energy than bond formation, leading to a net release of energy to the surroundings. Hence, the combustion of butane is an exothermic reaction.
07

Identify Sources of Error in the Experiment

Performing the experiment in a sealed container seems like a good idea to prevent heat loss. However, it may not be viable because pressure build-up due to the production of gaseous products could lead to explosion.

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Most popular questions from this chapter

The enthalpy values for several reactions are as follows: (I) \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2}(g) \rightarrow \mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) \(\quad \Delta H=-131 \mathrm{kJ} / \mathrm{mol}_{\mathrm{rxn}}\) (II) \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow 3 \mathrm{H}_{2}(g)+\mathrm{CO}(g)\) \(\quad \Delta H=206 \mathrm{kJ} / \mathrm{mol}_{\mathrm{rxn}}\) (III) \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)\) \(\quad \Delta H=-41 \mathrm{kJ} / \mathrm{mol}_{\mathrm{rxn}}\) (IV) \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\) \(\quad \Delta H=-890 \mathrm{kJ} / \mathrm{mol}_{\mathrm{rxn}}\) In which of the reactions does the amount of energy released by the formation of bonds in the products exceed the amount of energy necessary to break the bonds of the reactants by the greatest amount? (A) Reaction I (B) Reaction II (C) Reaction III (D) Reaction IV

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