Pressure of Gas given Root Mean Square Speed and Volume Calculator

Pressure of Gas Formula:

\[ P_{gas} = \frac{(C_{RMS})^2 \times M_{molar}}{3 \times V_{gas}} \]

Pressure of Gas (Pa):

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1. What is Pressure of Gas given RMS Speed and Volume?

Definition: This calculator determines the pressure exerted by a gas based on its root mean square speed, molar mass, and volume.

Purpose: It helps in understanding the kinetic theory of gases and calculating gas pressure under specific conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_{gas} = \frac{(C_{RMS})^2 \times M_{molar}}{3 \times V_{gas}} \]

Where:

\( P_{gas} \) — Pressure of gas (Pascals)
\( C_{RMS} \) — Root mean square speed (m/s)
\( M_{molar} \) — Molar mass (kg/mol)
\( V_{gas} \) — Volume of gas (m³)

Explanation: The formula relates gas pressure to the average kinetic energy of gas molecules and the space they occupy.

3. Importance of Gas Pressure Calculation

Details: Understanding gas pressure is crucial in thermodynamics, chemical engineering, and various industrial applications involving gases.

4. Using the Calculator

Tips: Enter the root mean square speed in m/s, molar mass in kg/mol, and gas volume in m³. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is root mean square speed?
A: It's the square root of the average of the squares of the individual velocities of gas molecules.

Q2: How do I find molar mass?
A: Molar mass can be found by summing the atomic masses of all atoms in a molecule of the gas.

Q3: What units should I use?
A: Use SI units: m/s for speed, kg/mol for molar mass, and m³ for volume to get pressure in Pascals.

Q4: Does this work for ideal gases only?
A: This formula is derived from kinetic theory and works best for ideal gases under normal conditions.

Q5: How does temperature affect the result?
A: Temperature affects the root mean square speed (CRMS increases with temperature), which in turn affects pressure.