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Chapter 6: Problem 73

The heat capacity of a bomb calorimeter was determined by burning 6.79 g methane (energy of combustion \(=-802 \mathrm{kJ} /\) $\mathrm{mol} \mathrm{CH}_{4}\( in the bomb. The temperature changed by \)10.8^{\circ} \mathrm{C} .$ a. What is the heat capacity of the bomb? b. A 12.6 -g sample of acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2},\) produced a temperature increase of \(16.9^{\circ} \mathrm{C}\) in the same calorimeter. What is the energy of combustion of acetylene (in $\mathrm{kJ} / \mathrm{mol} )$ ?

Short Answer

Expert verified
a. The heat capacity of the bomb calorimeter is -31.53 kJ/°C. b. The energy of combustion of acetylene is approximately -1100.16 kJ/mol.

Step by step solution

01

Determine the moles of methane burned

To determine the number of moles of methane burned, we use the formula: Moles = Mass / Molar mass The molar mass of methane (CH4) is approximately 16 g/mol (12 for C, and 4 for H). Given mass of methane = 6.79 g Moles of methane = 6.79 g / 16 g/mol = 0.4244 mol
02

Calculate the heat released by methane

Now that we know the moles of methane, we can find the heat released by methane during combustion using the given energy of combustion: Heat released by methane (Q) = moles * energy of combustion Given energy of combustion for methane = -802 kJ/mol Q = 0.4244 mol * -802 kJ/mol = -340.49 kJ
03

Calculate the heat capacity of the bomb calorimeter

Now we can calculate the heat capacity of the bomb calorimeter using the formula: Heat capacity (C) = Heat released by methane (Q) / Temperature change Given temperature change = 10.8 °C C = -340.49 kJ / 10.8 °C = -31.53 kJ/°C So, the heat capacity of the bomb calorimeter is -31.53 kJ/°C.
04

Calculate the heat released by acetylene

To find the energy of combustion of acetylene, we first need to calculate the heat released by acetylene using the formula: Heat released by acetylene (Q) = Heat capacity of the bomb calorimeter * Temperature change Given temperature change = 16.9 °C Q = -31.53 kJ/°C * 16.9 °C = -533.14 kJ
05

Determine the moles of acetylene burned

We need to find the moles of acetylene in the 12.6 g sample. The molar mass of acetylene (C2H2) is approximately 26 g/mol (24 for C, and 2 for H). Given mass of acetylene = 12.6 g Moles of acetylene = 12.6 g / 26 g/mol = 0.4846 mol
06

Calculate the energy of combustion of acetylene

Finally, we can calculate the energy of combustion of acetylene using the formula: Energy of combustion of acetylene = Heat released by acetylene / Moles of acetylene Energy of combustion = -533.14 kJ / 0.4846 mol = -1100.16 kJ/mol So, the energy of combustion of acetylene is approximately -1100.16 kJ/mol.

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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 \(\mathrm{O}_{2} ?\) d. How much heat is released when 10.0 \(\mathrm{g}\) Fe and 2.00 $\mathrm{g} \mathrm{O}_{2}$ are reacted?

The standard enthalpy of combustion of ethene gas, $\mathrm{C}_{2} \mathrm{H}_{4}(g),$ is \(-1411.1 \mathrm{kJ} / \mathrm{mol}\) at 298 \(\mathrm{K}\) . Given the following enthalpies of formation, calculate \(\Delta H_{\mathrm{f}}^{\circ}\) for $\mathrm{C}_{2} \mathrm{H}_{4}(g) .$ $$ \begin{array}{ll}{\mathrm{CO}_{2}(g)} & {-393.5 \mathrm{kJ} / \mathrm{mol}} \\\ {\mathrm{H}_{2} \mathrm{O}(l)} & {-285.8 \mathrm{kJ} / \mathrm{mol}}\end{array} $$

A swimming pool, 10.0 \(\mathrm{m}\) by \(4.0 \mathrm{m},\) is filled with water to a depth of 3.0 \(\mathrm{m}\) at a temperature of \(20.2^{\circ} \mathrm{C}\) . How much energy is required to raise the temperature of the water to \(24.6^{\circ} \mathrm{C} ?\)

Photosynthetic plants use the following reaction to produce glucose, cellulose, and so forth: $$6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \frac{\text { Sunlight }}{\longrightarrow} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g)$$ How might extensive destruction of forests exacerbate the greenhouse effect?

Consider the following reaction: $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-572 \mathrm{kJ} $$ a. How much heat is evolved for the production of 1.00 mole of $\mathrm{H}_{2} \mathrm{O}(l) ?$ b. How much heat is evolved when 4.03 g hydrogen are reacted with excess oxygen? c. How much heat is evolved when 186 \(\mathrm{g}\) oxygen are reacted with excess hydrogen? d. The total volume of hydrogen gas needed to fill the Hindenburg was $2.0 \times 10^{8} \mathrm{L}\( at 1.0 atm and \)25^{\circ} \mathrm{C} .$ How much heat was evolved when the Hindenburg exploded, assuming all of the hydrogen reacted?
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