Question

Methylhydrazine, \(\mathrm{CH}_{6} \mathrm{~N}_{2}\), is commonly used as a liquid rocket fuel. The heat of combustion of methylhydrazine is \(-1.30 \times 10^{3} \mathrm{~kJ} / \mathrm{mol}\). How much heat is released when \(100.0 \mathrm{~g}\) of methylhydrazine is burned?

Short answer

The heat released when 100.0g of Methylhydrazine is burnt is \(-4.33 \times 10^{3} \mathrm{~kJ}\).

Step-by-step solution

Calculate the molar mass of Methylhydrazine

The molecular formula for Methylhydrazine is \(\mathrm{CH}_{6} \mathrm{~N}_{2}\). Thus, we need to calculate the molar mass as: (1.0 x 1) + (1 x 6) + (14 x 2) = 30g/mol.

Convert grams to moles

Use the molar mass to convert the given 100.0g of Methylhydrazine to moles: 100.0g / 30g/mol = 3.33 moles.

Calculate heat released

Use the heat of combustion (per mole) and the calculated number of moles to compute the total heat released: 3.33 moles x -1.30 x 10^3 kJ/mol = -4.33 x 10^3 kJ.

Key concepts

Heat of Combustion

The heat of combustion is a key concept in thermochemistry. It refers to the energy released as heat when a substance undergoes complete combustion with oxygen under standard conditions. This value is usually given in kilojoules per mole \((\text{kJ/mol})\). For methylhydrazine, the heat of combustion is \(-1.30 \times 10^3 \, \text{kJ/mol}\), indicating the energy released per mole burned.

When considering heat of combustion, it’s important to realize that negative values reflect an exothermic process. This means energy is released during the reaction. When calculating how much heat is released in practical terms, we must first determine how many moles of the substance we have. This requires knowledge of the molar mass, highlighting the interconnected nature of these chemical concepts.

Molar Mass Calculation

Calculating the molar mass is a fundamental aspect of chemistry that allows you to convert between grams and moles. The molar mass of a compound is the mass of one mole of its molecules, often expressed in grams per mole \((\text{g/mol})\). To find this for methylhydrazine \(\text{CH}_6\text{N}_2\), you add up the atomic masses of all atoms in its molecular formula.

Here’s how the calculation works for methylhydrazine:

• Carbon (C): 1 atom × 12 g/mol = 12 g/mol
• Hydrogen (H): 6 atoms × 1 g/mol = 6 g/mol
• Nitrogen (N): 2 atoms × 14 g/mol = 28 g/mol

Adding these gives a total molar mass of \30\, \text{g/mol}. This value enables the conversion of mass to moles, vital for calculating the total energy released in a reaction.

Mole Concept

The mole concept is one of the cornerstones of chemistry. It allows chemists to count particles by weighing them. A mole is defined as exactly \(6.022 \times 10^{23}\) entities (Avogadro's number), be these atoms, molecules, or other particles. This concept connects macroscopic measurements (grams) to the atomic scale (moles).

In practical applications, knowing how to convert between mass and moles is crucial. Using the molar mass of methylhydrazine \(30 \, \text{g/mol}\), we see that \(100.0 \, \text{g}\) of the substance equates to roughly \(3.33 \, \text{moles}\). This conversion allows us to calculate the quantity of heat released by using the heat of combustion value. Understanding these steps helps solve not just exercises but also real-world chemical challenges, highlighting the utility of the mole concept in balancing chemical equations, stoichiometry, and in calculating reaction energies.