Problem 58 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following will impart highest specific impulse? (a) \(\mathrm{NH}_{3}+\mathrm{F}_{2}\) (b) \(\mathrm{H}_{2}+\mathrm{O}_{2}\) (c) Alcohol \(+\mathrm{O}_{2}\) (d) \(\mathrm{H}_{2}+\mathrm{F}_{2}\)

Step-by-Step Solution

Answer

The combination \( \mathrm{H}_{2} + \mathrm{F}_{2} \) will impart the highest specific impulse.

Step 1: Understand Specific Impulse

Specific impulse ( I_{sp} ) is a measure of how effectively a rocket uses propellant. It is defined as the thrust produced per unit weight flow rate of the propellant. The unit is seconds (s), and higher specific impulse indicates more efficient propulsion.

Step 2: Analyze the Propellants

Compare the given propellant combinations: (a) \(\mathrm{NH}_{3} + \mathrm{F}_{2}\), (b) \(\mathrm{H}_{2} + \mathrm{O}_{2}\), (c) Alcohol + \(\mathrm{O}_{2}\), and (d) \(\mathrm{H}_{2} + \mathrm{F}_{2}\). Hydrogen usually participates in reactions that release a lot of energy due to its low molar mass.

Step 3: Consider the Energy Release and Molarmass

Hydrogen, when combined with oxygen or fluorine, generates a significant amount of energy because of its high enthalpy of combustion and low molecular weight. \( \mathrm{F}_{2} \) when combined with \( \mathrm{H}_{2} \) tends to give very high specific impulse values due to the energetic reaction and lower molecular mass of products.

Step 4: Compare Options and Identify

Option (d) \( \mathrm{H}_{2} + \mathrm{F}_{2} \) will impart the highest specific impulse among the options due to the extremely high energy release and low molar mass of resulting products, maintaining efficient propulsion characteristics.

Key Concepts

Rocket Propellant Efficiency

Efficiency is a key factor in designing and selecting rocket propellants. It determines how well a rocket can utilize its fuel to produce thrust. The measure used to express this efficiency is called the **Specific Impulse** \( (I_{sp}) \). Specific impulse is essentially the amount of thrust generated per unit of fuel consumed over time. This means: the higher the specific impulse, the more thrust for the same amount of fuel. What makes a propellant efficient?

• High energy release during combustion – more energy means more thrust.
• Low molecular weight of combustion products – lighter gases result in faster speeds.

In evaluating efficiency, propellants like hydrogen-oxygen (H₂ + O₂) and hydrogen-fluorine (H₂ + F₂) are known for their high specific impulses due to their favorable energy and mass properties. Hence, choosing the right propellants is crucial for maximizing the efficiency of rockets.

Energy Release in Chemical Reactions

The energy released during chemical reactions is a crucial consideration in determining the effectiveness of rocket propellants. In chemical reactions, energy is a result of bonds forming and breaking; this energy release manifests as heat and propellant gas to propel the rocket. Combustion reactions, particularly those involving hydrogen and oxygen or fluorine, release considerable amounts of energy. **Why is this energy important?**

• More energy means more force is available to push the rocket upwards.
• The rapid release of gases at high temperatures generates thrust – a key factor in effective propulsion.

Assessing the reaction energy entails examining each reactant's enthalpy of combustion. Hydrogen with fluorine is notably strong, as it liberates a significant amount of energy, thus providing exceptional thrust and making it ideal for missions requiring high efficiency.

Chemical Propellants in Rockets

Rockets rely on chemical propellants due to their high energy release and ability to produce thrust rapidly. A typical rocket propellant consists of a fuel and an oxidizer that react to release energy and form exhaust gases. For example:

• **Hydrogen and Oxygen (H₂ + O₂)** - This mix is popular due to its high specific impulse and clean combustion, resulting in water vapor (H₂O) as a by-product.
• **Hydrogen and Fluorine (H₂ + F₂)** - Although dangerous and corrosive, this combination produces extremely high specific impulse, making it suitable for advanced missions needing significant thrust.
• **Ammonia and Fluorine (NH₃ + F₂), Alcohol and Oxygen** - These are alternative propellant options, but they typically offer lower specific impulse compared to hydrogen-based systems.

The choice of a particular propellant pair is influenced by desired mission parameters, such as thrust, safety, and environmental concerns. Selecting propellants that offer the necessary balance of performance attributes is vital for ensuring the mission's success and safety.