Problem 4 - Chemical Principles: The Quest for Insight

Question

\(\mathbf{L} .4\) The compound diborane, \(\mathrm{B}_{2} \mathrm{H}_{6}\), was at one time considered for use as a rocket fuel. Its combustion reaction is $$ \mathrm{B}_{2} \mathrm{H}_{6}(\mathrm{~g})+3 \mathrm{O}_{2}(\mathrm{l}) \rightarrow 2 \mathrm{HBO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) $$ The fact that \(\mathrm{HBO}_{2}\), a reactive compound, was produced rather than the relatively inert \(\mathrm{B}_{2} \mathrm{O}_{3}\) was a factor in the discontinuation of the investigation of diborane as a fuel. (a) What mass of liquid oxygen (LOX) would be needed to burn \(50.0 \mathrm{~g}\) of \(\mathrm{B}_{2} \mathrm{H}_{6}\) ? (b) Determine the mass of \(\mathrm{HBO}_{2}\) produced from the combustion of \(30.0 \mathrm{~g}\) of \(\mathrm{B}_{2} \mathrm{H}_{6}\).

Step-by-Step Solution

Answer

For part (a), 50.0 g of B2H6 requires 200.96 g of O2. For part (b), combustion of 30.0 g of B2H6 will produce 64.69 g of HBO2.

Step 1: Determine moles of B2H6

Calculate the number of moles of B2H6 using its molar mass. The molar mass of B2H6 is approximately 27.67 g/mol. Using the formula, moles = mass / molar mass, calculate the moles of B2H6.

Step 2: Calculate moles of O2 required

Using the stoichiometry of the given balanced equation, determine the moles of O2 needed to burn B2H6. According to the reaction, 1 mole of B2H6 requires 3 moles of O2. From the moles calculated in Step 1, multiply by 3 to find the moles of O2 required.

Step 3: Determine mass of O2 required

Calculate the mass of O2 needed using its molar mass, 32.00 g/mol. Mass = moles * molar mass. Use the moles of O2 calculated in Step 2 to find the mass of O2 required.

Step 4: Degree of B2H6 conversion to HBO2 in part (b)

First determine the number of moles of B2H6 when 30.0 g is used, as in Step 1. Then, using the balanced equation, determine the moles of HBO2 produced from the combustion of B2H6. The molar ratio is 1 mole of B2H6 to 2 moles of HBO2.

Step 5: Calculate mass of HBO2 produced

Using the moles of HBO2 determined in Step 4, calculate the mass of HBO2 using its molar mass, which is approximately 59.64 g/mol. Mass = moles * molar mass.

Key Concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It's a bit like a recipe: knowing how much of each ingredient you need to make a dish. In a combustion reaction like the one involving diborane fuel, we need to know exactly how much oxygen (the reactant) is needed to completely burn a given amount of diborane (the reactant) to form boric acid (HBO2) and water (the products).

For example, the balanced chemical equation given in the exercise indicates that for each molecule of B2H6 that reacts, three molecules of O2 are required. This ratio is crucial because it tells us that the combustion of 1 mole of diborane requires 3 moles of oxygen. Using stoichiometry, we can calculate not only the amount of oxygen needed but also the amount of products formed, provided we know the starting amount of diborane.

Molar Mass

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It's an essential concept in stoichiometry because it allows us to convert between mass and moles, which is necessary when scaling reactions up or down — like from a lab experiment to an industrial process.

The molar mass is particularly important when dealing with combustion reactions. In the given exercise, the molar mass of diborane (B2H6) is 27.67 g/mol, while for oxygen (O2) it's 32.00 g/mol. These values let us figure out how many grams of oxygen are needed to burn a specific mass of diborane, or conversely, how many grams of diborane would be required to react with a given mass of oxygen.

Chemical Combustion

Chemical combustion refers to a reaction where a substance combines with oxygen, usually releasing heat and light. It's an exothermic process, meaning it gives off energy. In the case of diborane fuel, the combustion involves the reaction of B2H6 with O2 to produce HBO2 and H2O.

Understanding the combustion process of a potential rocket fuel like diborane is critical. The amount of heat released can indicate the fuel's efficiency, while the byproducts, such as the reactive HBO2 mentioned in the exercise, can determine whether it's a practical choice for use. Knowledge of the combustion reaction's products is also important because it impacts the environment and the equipment used.

Diborane Fuel

Diborane (B2H6) is a highly flammable and volatile compound that has been considered as a rocket fuel. Its high energy density made it an interesting choice; however, complexities associated with its use, such as production of reactive byproducts, have limited its practical applications.

In the exercise, the combustion of diborane produces HBO2, a more reactive compound than the expected B2O3, which is relatively inert. This presents safety and material compatibility issues, which is why the use of diborane as a fuel component was eventually discontinued. When assessing diborane as a fuel, one would need to carefully consider the stoichiometry of its combustion reaction, the molar masses of the compounds involved, and the practical implications of the chemical combustion process.