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Chapter 6: Problem 13

Assuming gasoline is pure \(\mathrm{C}_{8} \mathrm{H}_{1 \mathrm{~s}}(l)\), predict the signs of \(q\) and \(w\) for the process of combusting gasoline into \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) .\)

Short Answer

Expert verified
In the combustion of gasoline (\(\mathrm{C}_{8} \mathrm{H}_{18}(l)\)) into \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\), the signs of \(q\) and \(w\) are both negative. This is because it is an exothermic reaction, releasing heat to the surroundings (q < 0), and the system does work on the surroundings by expanding the gaseous products against the pressure exerted by the surroundings (w < 0).

Step by step solution

01

Combustion Reaction

Combustion is an exothermic reaction, meaning it releases heat to the surroundings. The balanced chemical equation for the combustion of gasoline is: \( C_{8}H_{18}(l) + \frac{25}{2} O_{2}(g) \rightarrow 8 CO_{2}(g) + 9 H_{2}O(g) \)
02

Determine the Sign of \(q\) (Heat)

Since combustion is an exothermic reaction, heat is released by the system (reaction) to the surroundings. Therefore, the sign of \(q\) is negative. q < 0
03

Determine the Sign of \(w\) (Work)

In the combustion reaction, the system (reaction) does work on the surroundings by expanding the products (8 moles of CO₂ and 9 moles of H₂O) against the pressure exerted by the surroundings (since more moles of gaseous products are formed than the moles of gaseous reactants). This means work is done by the system on the surroundings. Therefore, the sign of \(w\) is negative. w < 0 In conclusion, both \(q\) and \(w\) are negative for the process of combusting gasoline into \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\).

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Most popular questions from this chapter

The standard enthalpy of formation of \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(298 \mathrm{~K}\) is \(-285.8\) \(\mathrm{kJ} / \mathrm{mol} .\) Calculate the change in internal energy for the following process at \(298 \mathrm{~K}\) and 1 atm: $$ \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \quad \Delta E^{\circ}=? $$ (Hint: Using the ideal gas equation, derive an expression for work in terms of \(n, R\), and \(T\).)

Consider the following changes: a. \(\mathrm{N}_{2}(g) \longrightarrow \mathrm{N}_{2}(l)\) b. \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)\) c. \(\mathrm{Ca}_{3} \mathrm{P}_{2}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 3 \mathrm{Ca}(\mathrm{OH})_{2}(s)+2 \mathrm{PH}_{3}(g)\) d. \(2 \mathrm{CH}_{3} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)\) e. \(\mathrm{I}_{2}(s) \longrightarrow \mathrm{I}_{2}(g)\) At constant temperature and pressure, in which of these changes is work done by the system on the surroundings? By the surroundings on the system? In which of them is no work done?

Calculate \(\Delta H^{\circ}\) for each of the following reactions using the data in Appendix 4: $$ \begin{array}{c} 4 \mathrm{Na}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Na}_{2} \mathrm{O}(s) \\ 2 \mathrm{Na}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g) \\ 2 \mathrm{Na}(s)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{Na}_{2} \mathrm{O}(s)+\mathrm{CO}(\mathrm{g}) \end{array} $$ Explain why a water or carbon dioxide fire extinguisher might not be effective in putting out a sodium fire.

The complete combustion of acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\), produces 1300\. kJ of energy per mole of acetylene consumed. How many grams of acetylene must be burned to produce enough heat to raise the temperature of \(1.00\) gal water by \(10.0^{\circ} \mathrm{C}\) if the process is \(80.0 \%\) efficient? Assume the density of water is \(1.00 \mathrm{~g} / \mathrm{cm}^{3}\)

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 \(4.00 \mathrm{~mol}\) iron is reacted with excess \(\mathrm{O}_{2}\) ? b. How much heat is released when \(1.00 \mathrm{~mol} \mathrm{Fe}_{2} \mathrm{O}_{3}\) is produced? c. How much heat is released when \(1.00 \mathrm{~g}\) iron is reacted with excess \(\mathrm{O}_{2} ?\) d. How much heat is released when \(10.0 \mathrm{~g} \mathrm{Fe}\) and \(2.00 \mathrm{~g} \mathrm{O}_{2}\) are reacted?
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