Question

Consider the reaction \(\mathrm{B}_{2} \mathrm{H}_{6}(g)+3 \mathrm{O}_{2}(g) \longrightarrow \mathrm{B}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2} \mathrm{O}(g) \quad \Delta H=-2035 \mathrm{~kJ}\) Calculate the amount of heat released when \(54.0 \mathrm{~g}\) of diborane is combusted.

Short answer

The amount of heat released when 54.0 g of diborane is combusted is -4070 kJ.

Step-by-step solution

Calculate the number of moles of diborane

We have 54.0g of diborane (B2H6), and we need to find the number of moles. Use the molar mass of diborane to convert mass to moles: Molar mass of B2H6 = 2 × (Molar mass of Boron) + 6 × (Molar mass of Hydrogen) Molar mass of B2H6 = 2 × (10.81 g/mol) + 6 × (1.01 g/mol) Moles of B2H6 = \( \frac{mass}{molar~mass} \) Moles of B2H6 = \( \frac{54.0 g}{2 \times 10.81 ~ g/mol + 6 \times 1.01 ~ g/mol} \)

Calculate the heat released during the combustion

The balanced chemical equation states that when 1 mole of B2H6 is reacted, the heat released is -2035 kJ. Now we need to find the heat released for the number of moles of B2H6 that we calculated in step 1. Heat released = moles of B2H6 × heat released per mole Heat released = (moles of B2H6) × (-2035 kJ) Note that the negative sign in the heat value indicates that heat is released (exothermic reaction).

Calculate the final answer

Now we have all the values needed to find the amount of heat released during the combustion. Perform the calculations using the values obtained in Step 1 and Step 2: Moles of B2H6 = \( \frac{54.0 g}{2 \times 10.81 ~ g/mol + 6 \times 1.01 ~ g/mol} \) = 2 moles Heat released = 2 moles × (-2035 kJ) = -4070 kJ Hence, the amount of heat released when 54.0 g of diborane is combusted is -4070 kJ.

Key concepts

Understanding Molar Mass

Molar mass is a key concept in chemistry that helps us connect the mass of a substance to the amount of substance in moles.
The molar mass of a compound is the sum of the atomic masses of all the atoms in a molecule of that compound. For instance, in the exercise above, we calculated the molar mass of diborane (B\(_2\)H\(_6\)), which consists of boron and hydrogen atoms.

• The atomic mass of a boron atom is 10.81 g/mol
• The atomic mass of a hydrogen atom is 1.01 g/mol

By multiplying the atomic masses by the number of atoms each, we find that the molar mass of diborane is:\[\text{Molar mass of } B_2H_6 = 2 \times 10.81\, \text{g/mol} + 6 \times 1.01\, \text{g/mol}\]This calculation is crucial because it transforms the physical measurement of 54 grams of diborane into a chemical measurement of moles, which is needed for further calculations.

Basics of Chemical Reactions

Chemical reactions are processes where substances, called reactants, are transformed into different substances, called products.
During a chemical reaction, bonds between atoms are broken, rearranged, and reformed. The reaction given in the exercise is a perfect example:\[\mathrm{B}_{2} \mathrm{H}_{6}(g)+3 \mathrm{O}_{2}(g) \longrightarrow \mathrm{B}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2} \mathrm{O}(g)\]This equation represents the combustion of diborane in the presence of oxygen to form boron oxide and water.
It's balanced, meaning the number of each type of atom is the same on both sides. Balancing chemical equations is fundamental because it reflects the law of conservation of mass, affirming that mass is neither created nor destroyed in a chemical reaction.

What is Combustion?

Combustion is a specific type of chemical reaction where a substance combines with oxygen to release energy.
It often produces heat and light, making it easily recognizable in everyday experiences, like burning wood or gasoline.In the given exercise, the combustion of diborane (B\(_2\)H\(_6\)) with oxygen results in the formation of boron oxide and water, while releasing energy:

• Diborane and oxygen are reactants
• Boron oxide and water are the products
• Heat energy is a byproduct

The combustion reaction, such as in this scenario, tends to be quick and can release a significant amount of energy, fueling many of the processes that power our daily lives.

Understanding Exothermic Reactions

In an exothermic reaction, energy is released into the surroundings, usually in the form of heat.
The negative sign associated with \(\Delta H\) in the equation, \(-2035 \text{kJ/mole}\) for diborane combustion, indicates it is exothermic.
When we calculate the heat released from the reaction of 54 grams of diborane, we are assessing how this reaction transfers energy to its environment.Exothermic reactions are key in many practical applications, providing energy for heating, cooking, and even generating electricity. Defining features of exothermic reactions include:

• Energy release
• Product formation with higher stability
• Temperature increase of the surroundings

These reactions contrast with endothermic reactions, where energy is absorbed rather than released, resulting in a temperature drop.