Problem 117 - Chemistry An Atoms First Approach

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.

Step-by-Step Solution

Answer

The amount of heat released when \(54.0 \mathrm{g}\) of diborane is combusted is \(3973 \mathrm{kJ}\).

Step 1: Calculate the molar mass of diborane (B2H6)

To calculate the molar mass of diborane, we need to add up the atomic masses of its constituent elements. Look for the molar mass of boron (B) and hydrogen (H) in the periodic table: Molar mass of B = 10.81 g/mol Molar mass of H = 1.008 g/mol Now, let's calculate the molar mass of diborane: Molar mass of B2H6 = (2 x molar mass of B) + (6 x molar mass of H) Molar mass of B2H6 = (2 x 10.81 g/mol) + (6 x 1.008 g/mol) = 27.66 g/mol

Step 2: Convert the mass of diborane into moles

To convert the mass of diborane into moles, we will use the following formula: moles of B2H6 = mass of B2H6 / molar mass of B2H6 Given mass of B2H6 = 54.0 g moles of B2H6 = 54.0 g / 27.66 g/mol = 1.95 mol

Step 3: Determine the heat released per mole of diborane using the given ∆H value

The given ∆H value for the reaction is: ∆H = -2035 kJ/mol Since the ∆H value is negative, it indicates that the reaction is exothermic and releases heat. The -2035 kJ/mol value represents the heat released when 1 mole of diborane is combusted.

Step 4: Calculate the total heat released for the given mass of diborane

To calculate the total heat released when 1.95 moles of diborane is combusted, multiply the moles of diborane by the heat released per mole of diborane: Total heat released = moles of B2H6 x ∆H Total heat released = 1.95 mol x -2035 kJ/mol = -3973 kJ Therefore, the amount of heat released when 54.0 g of diborane is combusted is 3973 kJ.

Key Concepts

Enthalpy Change

When considering chemical reactions, the concept of enthalpy change is extremely important. Enthalpy change (\( \Delta H \)) represents the total energy change inside a system at constant pressure.
It indicates whether a reaction absorbs or releases heat, which is crucial in understanding thermochemical processes. When examining the reaction of diborane (\( \mathrm{B}_2 \mathrm{H}_6 \)) with oxygen, the enthalpy change is given as\( \Delta H = -2035 \text{ kJ/mol} \), suggesting that the reaction releases energy.
This negative value tells us that the reaction is exothermic. Each mole of diborane combusted releases 2035 kJ of energy. Such information helps us predict energy exchanges in chemical reactions. Key points about enthalpy change:

• A positive \( \Delta H \) indicates an endothermic reaction, where heat is absorbed.
• A negative \( \Delta H \) signifies an exothermic reaction, where heat is released.
• It helps in calculating the amount of energy exchanged at any given condition of pressure and temperature.

Molar Mass Calculation

Understanding how to calculate molar mass is a necessary skill in chemistry. Molar mass tells you how much one mole of a chemical compound weighs and it is typically expressed in g/mol.
For instance, to find the molar mass of diborane \( \mathrm{B}_2 \mathrm{H}_6 \), you add up the atomic masses of its constituent elements, boron (B) and hydrogen (H).
Here's a simple breakdown:

• Boron, \( \mathrm{B} \), has a molar mass of 10.81 g/mol.
• Hydrogen, \( \mathrm{H} \), has a molar mass of 1.008 g/mol.

Thus, the calculation becomes:

• Molar mass of \( \mathrm{B}_2 \mathrm{H}_6 \) = (2 x 10.81 g/mol) + (6 x 1.008 g/mol)
• Resulting in 27.66 g/mol

Using this molar mass, you can convert between the mass of a substance and the number of moles, essential for stoichiometric calculations in reactions.

Exothermic Reactions

Exothermic reactions are those that release energy, usually in the form of heat. These reactions are characterized by a negative enthalpy change (\( \Delta H \)).
In the example provided, the combustion of diborane is exothermic as indicated by a \( \Delta H \) of -2035 kJ/mol.
Here’s why exothermic reactions are significant:

• They often result in an increase in temperature of the surroundings.
• Most spontaneous reactions are exothermic, as they naturally progress towards a state of lower energy.
• Fuels undergo exothermic reactions when burnt—they release large amounts of energy, which is a basis for power generation.

Using the example, if 1.95 mol of diborane is combusted, you would calculate the total heat released by multiplying the number of moles by the energy per mole (\(-2035 \)>\( \mathrm{kJ/mol} \)A key characteristic of exothermic reactions is that they help us understand energy distributions in chemical processes, impacting industries and heating requirements.