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Chapter 7: Problem 13

Assuming gasoline is pure \(\mathrm{C}_{8} \mathrm{H}_{18}(l),\) predict the signs of \(q\) and \(w\) for the process of combusting gasoline into \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\).

Short Answer

Expert verified
The signs of q (heat) and w (work) for the combustion of gasoline into CO2 and H2O are both negative, as the reaction is exothermic (\(q < 0\)) and the system does work on the surroundings by causing an expansion (\(w < 0\)).

Step by step solution

01

Write down the balanced combustion equation for gasoline

We need to write the balanced combustion reaction for gasoline (C8H18) which reacts with oxygen (O2) to form carbon dioxide (CO2) and water (H2O) as products. The balanced equation is: \[ C_8H_{18}(l) + \frac{25}{2}O_2(g) \rightarrow 8CO_{2}(g) + 9H_{2}O(g) \]
02

Determine the sign of q (heat) for the combustion process

Combustion reactions are generally exothermic, meaning they release heat to the surroundings. In this case, the combustion of gasoline into CO2 and H2O is also an exothermic reaction. Since heat is being released to the surroundings, the sign of q (heat) will be negative. So, q < 0.
03

Determine the sign of w (work) for the combustion process

Since gasoline (C8H18) is combusted with oxygen (O2), the number of moles of gas in the products (8 moles of CO2 and 9 moles of H2O) is greater than the number of moles of gas in the reactants (12.5 moles of O2). When the number of moles of gaseous products is greater than the number of moles of gaseous reactants, the system does work on the surroundings, causing an expansion. In such cases, the work (w) done by the system is negative. So, w < 0. In conclusion:
04

Predict the signs of q and w for the combustion process

Based on the steps above, we can predict that the signs of q (heat) and w (work) for the combustion of gasoline into CO2 and H2O are both negative: q < 0 (Heat is released to the surroundings, exothermic reaction) w < 0 (Work is done by the system on the surroundings, expansion)

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Most popular questions from this chapter

The overall reaction in a commercial heat pack can be represented as $$4 \mathrm{Fe}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \quad \Delta H=-1652 \mathrm{kJ}$$ a. How much heat is released when 4.00 moles of iron are reacted with excess \(\mathrm{O}_{2} ?\) b. How much heat is released when 1.00 mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is produced? c. How much heat is released when \(1.00 \mathrm{g}\) iron is reacted with excess \(\mathbf{O}_{2} ?\) d. How much heat is released when \(10.0 \mathrm{g}\) Fe and \(2.00 \mathrm{g} \mathrm{O}_{2}\) are reacted?

Write reactions for which the enthalpy change will be a. \(\Delta H_{\mathrm{f}}^{\circ}\) for solid aluminum oxide. b. the standard enthalpy of combustion of liquid ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\). c. the standard enthalpy of neutralization of sodium hydroxide solution by hydrochloric acid. d. \(\Delta H_{\mathrm{f}}^{\circ}\) for gaseous vinyl chloride, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}(g)\). e. the enthalpy of combustion of liquid benzene, \(C_{6} \mathrm{H}_{6}(l)\). f. the enthalpy of solution of solid ammonium bromide.

Give the definition of the standard enthalpy of formation for a substance. Write separate reactions for the formation of NaCl, \(\mathrm{H}_{2} \mathrm{O}, \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) and \(\mathrm{PbSO}_{4}\) that have \(\Delta H^{\circ}\) values equal to \(\Delta H_{\mathrm{f}}^{\circ}\) for each compound.

If the internal energy of a thermodynamic system is increased by \(300 .\) \(\mathrm{J}\) while \(75 \mathrm{J}\) of expansion work is done, how much heat was transferred and in which direction, to or from the system?

It takes \(585 \mathrm{J}\) of energy to raise the temperature of \(125.6 \mathrm{g}\) mercury from \(20.0^{\circ} \mathrm{C}\) to \(53.5^{\circ} \mathrm{C}\). Calculate the specific heat capacity and the molar heat capacity of mercury.
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