Problem 58 - General Chemistry

Question

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 gram of hydrogen?

Step-by-Step Solution

Answer

The enthalpy change is \(-119.80 \text{ kJ/g}\) for hydrogen.

Step 1: Determine the Molar Mass of Hydrogen

First, calculate the molar mass of hydrogen. Since hydrogen (\( ext{H}_2\)) is diatomic, each molecule consists of 2 hydrogen atoms. The atomic mass of hydrogen is approximately 1.01 g/mol. Thus, the molar mass of \( ext{H}_2\) is \(2 \times 1.01 = 2.02 \text{ g/mol}\).

Step 2: Calculate the Amount of Heat per Mole

From the given chemical reaction, burning 2 moles of hydrogen gas releases 484 kJ of energy. Therefore, the enthalpy change per mole of hydrogen gas is \( \frac{-484 \text{ kJ}}{2 \text{ moles}} = -242 \text{ kJ/mol}\).

Step 3: Convert the Enthalpy Change to Per Gram

Now convert the enthalpy change from per mole to per gram. Use the molar mass of hydrogen to do the conversion: \(-242 \text{ kJ/mol} \div 2.02 \text{ g/mol} = -119.80 \text{ kJ/g}\).

Step 4: Present the Final Answer

Thus, the enthalpy change per gram of hydrogen burned is \(-119.80 \text{ kJ/g}\).

Key Concepts

Thermochemistry

Thermochemistry is an important branch of chemistry that deals with the study of energy changes, particularly heat, during chemical reactions. One key aspect is understanding how heat is absorbed or released when substances react.
In this exercise, the focus is on the reaction of hydrogen with oxygen. This reaction results in the formation of water vapor, and it releases energy in the form of heat. The amount of energy exchanged during this reaction is expressed by the enthalpy change (\(\Delta H\)).
In our given equation, \(2 \text{H}_2(g) + \text{O}_2(g) \rightarrow 2 \text{H}_2\text{O}(g); \Delta H = -484 \text{ kJ}\), this negative enthalpy value indicates that the reaction is exothermic, meaning it releases heat.
Understanding exothermic reactions is essential because it helps us harness energy efficiently, as seen in applications like rocket fuel, where hydrogen is used for its high-energy output.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationships between the reactants and the products in a chemical reaction. It allows us to determine how much of each substance is consumed or produced in a reaction.
In our problem, the balanced chemical equation shows us the stoichiometry:

• 2 moles of hydrogen react with 1 mole of oxygen.
• This produces 2 moles of water vapor.

Using this stoichiometric relationship, we can deduce that the enthalpy change provided (-484 kJ) relates to the consumption of 2 moles of hydrogen. This stoichiometric data is crucial in understanding and calculating energy changes per specific quantities, such as per mole or per gram, as demonstrated in the exercise.

Molar Mass Calculation

The concept of molar mass is fundamental in chemistry and is used to convert between the mass and amount (in moles) of a substance. Molar mass is the mass of one mole of a given substance and is typically expressed in grams per mole (g/mol).
For hydrogen gas (\(\text{H}_2\)), calculating the molar mass involves summing the atomic masses of the component elements. Hydrogen's atomic mass is approximately 1.01 g/mol. Since \(\text{H}_2\) consists of two hydrogen atoms, the molar mass is \(2 \times 1.01 = 2.02 \text{ g/mol}\).
This calculated molar mass is crucial for converting the enthalpy change from a per-mole basis to a per-gram basis, helping us understand the energy changes in terms of gram quantities. This conversion is essential for practical applications where specific weights of substances are used.

Energy Release per Gram

To grasp the energy output of a reaction fully, we may need to express energy changes on a per-mass basis. This is especially useful in practical scenarios, like fuel assessments. The enthalpy change per gram provides insight into the efficiency of a fuel.
In the given exercise, we convert the enthalpy change from kJ per mole to kJ per gram using the molar mass of hydrogen calculated previously. The conversion goes as follows:\(-242 \text{ kJ/mol} \div 2.02 \text{ g/mol} = -119.80 \text{ kJ/g}\).
This calculation tells us that -119.80 kJ of energy is released for every gram of hydrogen burned. Such quantifications are vital for evaluating the suitability of hydrogen as an efficient fuel type, particularly in applications like aeronautics and rocketry, where energy density is crucial.