Problem 29 - Chemistry Matter and Change

Question

Calculate How much heat is released by the combustion of 206 g of hydrogen gas? \(\Delta H_{\text { comb }}=-286\) kl/mol

Step-by-Step Solution

Answer

14,729 kJ of heat is released by the combustion of 206 g of hydrogen gas.

Step 1: Understanding the Chemical Reaction

The problem involves the combustion of hydrogen gas. The reaction for the combustion of hydrogen gas is \( 2H_2 (g) + O_2 (g) \rightarrow 2H_2O (l) \). The given \( \Delta H_{\text{comb}} \) is the enthalpy change for this reaction, which is \(-286\, \text{kJ/mol}\) for the formation of water from hydrogen.

Step 2: Moles of Hydrogen

We need to convert the mass of hydrogen gas into moles. The molar mass of hydrogen \( H_2 \) is 2 g/mol. The formula for converting mass to moles is: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \]. Substituting in the values, we get: \[ \text{moles of } H_2 = \frac{206 \text{ g}}{2 \text{ g/mol}} = 103 \text{ mol} \].

Step 3: Heat Released Calculation

Since the reaction \(2H_2\) releases \(-286\, \text{kJ/mol of reaction}\), it involves 2 moles of \( H_2 \). Therefore, the heat released per mole of \( H_2\) is \(-143\, \text{kJ/mol H}_2\). Thus, to find the heat released by 103 moles of \( H_2\), we multiply by the heat released per mole of \( H_2\): \[ \text{Heat released} = 103 \text{ mol} \times (-143 \text{ kJ/mol}) = -14729 \text{ kJ} \].

Step 4: Final Result Interpretation

The negative sign indicates heat is released (exothermic reaction). Thus, the combustion of 206 g of hydrogen gas releases 14,729 kJ of energy.

Key Concepts

Chemical Reaction

In this exercise, we're looking at the **combustion of hydrogen gas**. This involves a chemical reaction where hydrogen gas reacts with oxygen. The result is the formation of water. The balanced chemical equation for this reaction is:

• \[ 2H_2 (g) + O_2 (g) \rightarrow 2H_2O (l) \]

This equation shows that two molecules of hydrogen gas react with one molecule of oxygen gas, producing two molecules of water.
The given enthalpy change, \( \Delta H_\text{comb} = -286 \, \text{kJ/mol} \), tells us the amount of heat involved in this reaction under standard conditions.
In simple terms, this is the energy change when hydrogen is burned completely to form water.

Moles of Hydrogen

To understand how much heat is released, we first need to determine the **amount of hydrogen gas** we're dealing with in terms of moles.

• The molar mass of hydrogen gas, \( H_2 \), is 2 g/mol.
• Given mass of hydrogen gas = 206 g.
• We use the formula: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \]

Substituting in our values gives:

• \[ \text{moles of } H_2 = \frac{206 \text{ g}}{2 \text{ g/mol}} = 103 \text{ mol} \]

So, we have 103 moles of hydrogen gas. By converting mass into moles, we can apply the enthalpy change to calculate the heat released.

Heat Released Calculation

With the number of **moles of hydrogen** known, we can now calculate the total heat released. The reaction shows that combustion of 2 moles of hydrogen gas releases \(-286 \, \text{kJ}\) of heat, therefore:

• The heat released per mole of \( H_2 \) is \(-143 \, \text{kJ/mol} \).

Since we have 103 moles of hydrogen gas, the total heat released is calculated as:

• \[ \text{Heat released} = 103 \text{ mol} \times (-143 \text{ kJ/mol}) = -14729 \text{ kJ} \]

This calculation tells us the total energy released when 206 g of hydrogen gas undergoes complete combustion.

Exothermic Reaction

The negative sign in the enthalpy change indicates an **exothermic reaction**. This means that energy is released into the surroundings.
In chemical reactions, exothermic processes are ones where the resulting products have lower energy than the reactants, resulting in the release of energy usually as heat.

• This causes the surroundings to warm up, which is typical of many combustion reactions.

In our example, the combustion of 206 g of hydrogen gas results in a release of 14,729 kJ of energy.
This not only shows the amount of energy produced but also reinforces the nature of combustion reactions as being highly energetic and exothermic.