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Propane, \(\mathrm{C}_{3} \mathrm{H}_{8}\), is a common fuel gas. Use the following to calculate the grams of propane you would need to provide \(369 \mathrm{~kJ}\) of heat. $$ \begin{aligned} \mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) & \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g) ; \\ \Delta H &=-2043 \mathrm{~kJ} \end{aligned} $$

Short Answer

Expert verified
You need approximately 7.94 grams of propane to provide 369 kJ of heat.

Step by step solution

01

Understanding the Reaction

The combustion of propane is an exothermic reaction, releasing heat energy. The given reaction for the combustion is: \( \mathrm{C}_{3} \mathrm{H}_{8}(g) + 5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g) + 4 \mathrm{H}_{2} \mathrm{O}(g) \) with \( \Delta H = -2043 \mathrm{~kJ} \), indicating that 2043 kJ of heat is released per mole of propane burned.
02

Calculating Moles of Heat Released

We need to calculate how many moles of propane correspond to the release of 369 kJ of energy. Based on the reaction, 1 mole of propane releases 2043 kJ. The requirement is to release 369 kJ. The number of moles of propane needed is calculated using the ratio: \( \text{Moles of propane} = \frac{369 \text{ kJ}}{2043 \text{ kJ/mol}} \approx 0.18 \text{ mol} \).
03

Calculating Molar Mass of Propane

The molar mass of propane (\( \mathrm{C}_{3} \mathrm{H}_{8} \)) is calculated by summing the atomic masses of its constituent elements: Carbon (C) and Hydrogen (H). The molar mass is \( 3 \times 12.01 \text{ g/mol} + 8 \times 1.01 \text{ g/mol} = 44.11 \text{ g/mol} \).
04

Calculating Grams of Propane Needed

Using the number of moles needed from Step 2 and the molar mass from Step 3, calculate the grams of propane required. The formula is \( \text{Grams of propane} = 0.18 \text{ mol} \times 44.11 \text{ g/mol} \approx 7.94 \text{ g} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Exothermic Reaction
An exothermic reaction is one that releases energy into the surroundings, usually in the form of heat. This energy release occurs because the total energy required to break bonds in the reactants is less than the energy released when new bonds are formed in the products. In the case of the combustion of propane, the reaction equation is: \[ \mathrm{C}_{3} \mathrm{H}_{8}(g) + 5 \mathrm{O}_{2}(g) \rightarrow 3 \mathrm{CO}_{2}(g) + 4 \mathrm{H}_{2} \mathrm{O}(g) \]The enthalpy change (\(\Delta H\)) is negative, \(-2043\,\text{kJ}\), indicating that energy is released as the propane reacts with oxygen. This makes it an exothermic process. Such reactions are crucial in fuels, as they provide the heat energy necessary for power applications.
Whenever a chemical reaction has a negative enthalpy change, it is a sign of an exothermic reaction. Always remember, the more exothermic a reaction, the larger the negative value of \(\Delta H\).
  • Negative \(\Delta H\) signifies an exothermic reaction.
  • Combustion reactions often fall under exothermic categories.
Stoichiometry
Stoichiometry is the study of quantitative relationships or ratios in chemical reactions. It's like a recipe that tells you how much of each ingredient (or reactant) you need to get a desired amount of product. In the case of this exercise, we used stoichiometry to figure out how much propane is needed to release a certain amount of heat. Using the balanced equation: \[ \mathrm{C}_{3} \mathrm{H}_{8}(g) + 5 \mathrm{O}_{2}(g) \rightarrow 3 \mathrm{CO}_{2}(g) + 4 \mathrm{H}_{2} \mathrm{O}(g) \]We know that 1 mole of \(\mathrm{C}_{3} \mathrm{H}_{8}\) releases \(2043\,\text{kJ}\) of heat. We calculated that to produce \(369\,\text{kJ}\) of heat, approximately 0.18 moles of propane are required. This kind of calculation is common in chemistry and is essential for converting quantities of one substance into another, particularly when calculating how much of a compound is needed or produced in a reaction.
  • Relies on balanced chemical equations.
  • Helps in converting between moles, mass, and number of particles.
Molar Mass Calculation
Molar mass is a crucial concept that links chemical formulas to measurable quantities. It denotes the mass of one mole of a substance and is calculated using the atomic masses of the elements in the molecule. For propane \(\mathrm{C}_{3} \mathrm{H}_{8}\), we must sum the masses of all the carbon and hydrogen atoms in the molecule.Propane consists of 3 carbon atoms and 8 hydrogen atoms: \[3 \times 12.01\,\text{g/mol} + 8 \times 1.01\,\text{g/mol} = 44.11\,\text{g/mol} \]This tells us that one mole of propane weighs 44.11 grams. Using this information alongside stoichiometry, we calculated that the 0.18 moles of propane needed to release \(369\,\text{kJ}\) of energy corresponds to approximately 7.94 grams. This calculation is vital in laboratory settings where precise amounts of chemicals are necessary.
  • Calculated by summing atomic masses from the periodic table.
  • Used to convert between moles and grams.

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Most popular questions from this chapter

The sugar arabinose, \(\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{5},\) is burned completely in oxygen in a calorimeter. $$ \mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{5}(s)+5 \mathrm{O}_{2}(g) \longrightarrow 5 \mathrm{CO}_{2}(g)+5 \mathrm{H}_{2} \mathrm{O}(l) $$ Burning a 0.548 -g sample caused the temperature to rise from \(20.00^{\circ} \mathrm{C}\) to \(20.54^{\circ} \mathrm{C}\). The heat capacity of the calorimeter and its contents is \(15.8 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\). Calculate \(\Delta H\) for the combustion reaction per mole of arabinose.

A soluble salt, \(\mathrm{MX}_{2}\), is added to water in a beaker. The equation for the dissolving of the salt is: $$ \mathrm{MX}_{2}(s) \longrightarrow \mathrm{M}^{2+}(a q)+2 \mathrm{X}^{-}(a q) ; \quad \Delta H>0 $$ a) Immediately after the salt dissolves, is the solution warmer or colder? b) Indicate the direction of heat flow, in or out of the beaker, while the salt dissolves. c) After the salt dissolves and the water returns to room temperature, what is the value of \(q\) for the system?

Describe a simple calorimeter. What measurements are needed to determine the heat of reaction?

When \(21.45 \mathrm{~g}\) of potassium nitrate, \(\mathrm{KNO}_{3}\), was dissolved in water in a calorimeter, the temperature fell from \(25.00^{\circ} \mathrm{C}\) to \(14.14^{\circ} \mathrm{C}\). What is the \(\Delta H\) for the solution process? $$ \mathrm{KNO}_{3}(s) \longrightarrow \mathrm{K}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) $$ The heat capacity of the calorimeter and its contents is \(682 \mathrm{~J} /{ }^{\circ} \mathrm{C} .\)

Hydrogen, \(\mathrm{H}_{2}\), is used as a rocket fuel. The hydrogen is burned in oxygen to produce water vapor. $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) ; \Delta H=-484 \mathrm{~kJ} $$ What is the enthalpy change per kilogram of hydrogen?

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