Problem 72 - General Chemistry

Question

The reaction of oxygen and hydrogen is used to propel rockets. Liquid oxygen has a boiling point of \(-222.7^{\circ} \mathrm{C}\). What is this temperature in degrees Fahrenheit?

Step-by-Step Solution

Answer

The temperature is \(-368.86^{\circ} \mathrm{F}\).

Step 1: Understanding the Conversion Formula

To convert temperatures from Celsius to Fahrenheit, we use the formula: \( F = \frac{9}{5}C + 32 \), where \( C \) is the temperature in Celsius and \( F \) is the temperature in Fahrenheit.

Step 2: Substitute the Celsius Temperature

Given the boiling point of liquid oxygen is \(-222.7^{\circ} \mathrm{C}\), substitute this value into our formula: \( F = \frac{9}{5}(-222.7) + 32 \).

Step 3: Calculate the Product

First, calculate \( \frac{9}{5} \times (-222.7) \). This gives us \(-400.86\).

Step 4: Add 32 to the Product

Now, add 32 to the product from the previous step: \(-400.86 + 32 \). This results in \(-368.86\).

Step 5: Conclusion

The temperature \(-222.7^{\circ} \mathrm{C}\) is equivalent to \(-368.86^{\circ} \mathrm{F}\).

Key Concepts

Celsius to Fahrenheit Conversion

In order to transform a temperature reading from Celsius to Fahrenheit, a specific formula is employed which is: \[ F = \frac{9}{5}C + 32 \] Here, \( F \) symbolizes the temperature in Fahrenheit whereas \( C \) denotes the temperature in Celsius. This calculation involves two main steps:

• First, multiply the Celsius temperature by \( \frac{9}{5} \).
• Second, add 32 to that result.

This formula accounts for the different starting points and intervals of the two scales. The Celsius scale is based on the freezing and boiling points of water at 0°C and 100°C, while the Fahrenheit scale assigns these to 32°F and 212°F, respectively. Such conversion is crucial in scientific contexts where temperature readings might determine experimental results.

Boiling Point

The boiling point of a substance is the temperature at which it turns from a liquid phase into a gas. For liquid oxygen, this occurs at a chilling \(-222.7^{\circ}~\mathrm{C}\).Boiling points vary significantly among different substances and depend on factors such as atmospheric pressure. Under increased atmospheric pressure, boiling points also tend to rise due to the additional energy required for the transition of molecules from liquid to gas. In contrast, at lower pressures, substances boil at lower temperatures. Recognizing the boiling points of different liquids is fundamental in chemistry and engineering, especially for applications like cryogenics and aerospace technologies where precise temperature control is essential.

Liquid Oxygen Properties

Liquid oxygen (LOX) is oxygen in its liquid state, achieved at extremely low temperatures. Apart from its characteristic pale blue color, liquid oxygen is classified as a cryogenic liquid. Some unique properties include:

• High density, allowing for compact storage of oxygen gas.
• It's paramagnetic, meaning it is attracted to magnetic fields.
• It spontaneously ignites when it comes into contact with fuels like hydrocarbons.

Because of these features, LOX is extensively used in industrial processes and medical therapies. However, handling it requires strict protocols due to its cryogenic nature and reactivity with combustible materials. Understanding these properties is vital for safely utilizing liquid oxygen in various applications.

Rocket Propulsion Reactions

Rocket propulsion operates fundamentally on the principles of Newton’s third law of motion: "For every action, there is an equal and opposite reaction." In this context, the action is the expulsion of high-speed gas from the rocket engine, leading to the opposite reaction of the rocket moving forward. Combining liquid oxygen with fuels like hydrogen creates a powerful oxidizer for propellant reactions. The ensuing chemical reaction releases vast amounts of energy and produces water vapor as a byproduct, exerting a backward force through rapid expulsion and thus propelling the rocket forward. Key considerations in rocket propulsion include:

• The specific impulse, which measures the efficiency of the rocket engine.
• Thrust-to-weight ratio, which is crucial for ensuring liftoff.
• Engine temperature management to prevent overheating.

Through harnessing these reactions, rockets achieve the enormous velocities necessary for space travel, making liquid oxygen an indispensable component in the aerospace industry.