Chapter 15: Problem 29
Calculate How much heat is released by the combustion of 206 g of hydrogen gas \(? \Delta H_{\text { comb }}=-286 {k} / / {mol}\)
Short Answer
Expert verified
The heat released by the combustion of 206 g of hydrogen gas is -29458 kJ.
Step by step solution
01
Convert the mass of hydrogen gas into moles
To find the moles of hydrogen gas, we need to divide the given mass (206 g) by the molar mass of hydrogen gas. The molar mass of hydrogen gas (Hâ‚‚) is 2 g/mol since there are 2 atoms of hydrogen in one molecule of hydrogen gas, and each hydrogen atom has a molar mass of 1 g/mol.
Therefore, moles of hydrogen gas = \( \frac{206 \text{ g}}{2 \text{ g/mol}} \) = 103 mol.
02
Calculate the heat released
We are given that the enthalpy change for the combustion of hydrogen gas is -286 kJ/mol. To find the heat released by the combustion of 206 grams of hydrogen gas, we will use the formula:
\( q = n \times \Delta H_{\text { comb }} \)
where q is the heat released, n is the number of moles of hydrogen gas, and \( \Delta H_{\text { comb }}\) is the enthalpy change for the combustion of hydrogen gas.
Plugging in the values, we get:
\( q = 103 \text{ mol} \times -286 \frac{\text{kJ}}{\text{mol}} \)
03
Calculate the result
Multiply the number of moles by the enthalpy change:
\( q = 103 \text{ mol} \times -286 \frac{\text{kJ}}{\text{mol}} = -29458 \text{ kJ} \)
The heat released by the combustion of 206 g of hydrogen gas is -29458 kJ. The negative sign indicates that heat is being released (exothermic reaction).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Understanding Combustion
Combustion is a chemical reaction between a fuel and an oxidant, often oxygen. This reaction produces heat and light, primarily in the form of flame. In the case of hydrogen gas combustion, the reaction combines hydrogen \( (H_2) \) with oxygen \( (O_2) \) to form water \( (H_2O) \). This process releases a significant amount of energy, making it very efficient as a fuel.
- Hydrogen Combustion: Hydrogen gas is ideal for combustion because it's clean, producing only water as a byproduct.
- Energy Release: The energy output is high, making hydrogen a powerful energy source.
The Role of Molar Mass
Molar mass is the mass of one mole of a substance, expressed in grams per mole. For hydrogen gas \( (H_2), \) the molar mass is 2 g/mol. This is calculated because each hydrogen atom has a molar mass of 1 g/mol, and there are two atoms in a molecule of hydrogen gas. To find out how many moles are in a given mass, you simply divide by the molar mass.
- Importance: Knowing the molar mass allows you to convert between mass and moles, a critical step in stoichiometric calculations.
- Application: In this exercise, the mass of hydrogen is divided by its molar mass to find the number of moles (103 mol).
Exothermic Reaction Explained
Exothermic reactions release heat, making them feel warm or hot to the touch. In such reactions, the energy required to break bonds in the reactants is less than the energy released when new bonds are formed in the products. This results in a net release of energy.
- Heat Release: The negative sign in the enthalpy value \( (\Delta H = -286 \text{kJ/mol}) \) indicates heat release.
- Relevance: Exothermic reactions are essential for power generation and heating processes.
Heat Calculation in Reactions
Calculating the heat change in reactions involves using the formula \( q = n \times \Delta H, \) where \( q \) is the heat change, \( n \) is the number of moles, and \( \Delta H \) is the enthalpy change per mole. This equation helps determine how much heat is absorbed or released during a chemical reaction.
- Formula Application: In this problem, we calculate the heat released by multiplying the moles of hydrogen (103 mol) by the enthalpy change (-286 kJ/mol).
- Outcome: The result, -29,458 kJ, represents the total heat released, with the negative sign indicating the exothermic nature of the reaction.