The average kinetic energy of the molecules in a gas sample depends only on the temperature, T. However, given the same kinetic energies, a lighter molecule will move faster than a heavier molecule, as shown in the equation for rms speed rms speed = rms speed: 3RT where R = 8.314 J/(mol·K) and M is molar mass in kilograms per mole. Note that a joule is the same as a kilogram-meter squared per second squared (kg-m²/s²). What is the rms speed of N₂ molecules at 497 K? V M rms speed: What is the rms speed of He atoms at 497 K? m/s m/s
Thermochemistry
Thermochemistry can be considered as a branch of thermodynamics that deals with the connections between warmth, work, and various types of energy, formed because of different synthetic and actual cycles. Thermochemistry describes the energy changes that occur as a result of reactions or chemical changes in a substance.
Exergonic Reaction
The term exergonic is derived from the Greek word in which ‘ergon’ means work and exergonic means ‘work outside’. Exergonic reactions releases work energy. Exergonic reactions are different from exothermic reactions, the one that releases only heat energy during the course of the reaction. So, exothermic reaction is one type of exergonic reaction. Exergonic reaction releases work energy in different forms like heat, light or sound. For example, a glow stick releases light making that an exergonic reaction and not an exothermic reaction since no heat is released. Even endothermic reactions at very high temperature are exergonic.
![**Understanding the Root Mean Square (RMS) Speed of Gas Molecules**
The average kinetic energy of the molecules in a gas sample depends solely on the temperature, \( T \). However, given the same kinetic energies, a lighter molecule will move faster than a heavier molecule. This concept is illustrated by the equation for RMS speed:
\[
\text{rms speed} = \sqrt{\frac{3RT}{\mathcal{M}}}
\]
Here, \( R = 8.314 \, \text{J/(mol} \cdot \text{K)} \) is the gas constant, and \( \mathcal{M} \) is the molar mass in kilograms per mole. It's important to note that a joule is equivalent to a kilogram-meter squared per second squared (kg·m\(^2\)/s\(^2\)).
### Examples:
1. **What is the RMS speed of \(\text{N}_2\) molecules at 497 K?**
\(\text{rms speed:} \) [ _________ ] m/s
2. **What is the RMS speed of He atoms at 497 K?**
\(\text{rms speed:} \) [ _________ ] m/s
By using this formula, you can calculate the RMS speed for different gases at a specific temperature, understanding how mass and temperature affect molecular speed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc07c092-5f49-4d93-b501-b08294061775%2F37ed86ba-4066-4f04-8d2a-8a43b79f25d9%2F4l0yzfg_processed.png&w=3840&q=75)
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