# Simple RMS velocity question, what's wrong with my answer?

• couchpotato
In summary, Simple RMS velocity is a measure of the average speed of particles in a gas or liquid, calculated by taking the square root of the sum of the squared velocities of all the particles in a sample divided by the total number of particles. It is significant in understanding the overall movement and energy of particles and is different from average velocity as it takes into account the magnitude and direction of each particle's velocity. Common mistakes when calculating Simple RMS velocity include forgetting to square the velocities and not including the direction of the velocities in the calculation.
couchpotato
Thread moved from the technical forums, so no Homework Template is shown
Find the rms speed for an argon atom if 1.5 mol of the gas is confined to a 5.6 liter container at a pressure of 5.5 atm.

PV = nRT
RT = PV/n
v_RMS = \sqrt (3RT/M)

= \sqrt (3PV/nM)

= \sqrt ((3 * (5.5atm * 101.325kPA/atm) * (5.6 * 10^-3 m^3) / (1.5 mol * 39.948 * 10^-3)

= 12.5 m/s

However this is apparently wrong. Can someone please tell me what I went wrong?

Thanks

Your substitutions are correct, but you've slipped a factor of 1000 (possibly the k in kPa) in your working out. This becomes a factor of sqrt (1000).

Thank you!

## 1. What is Simple RMS velocity?

Simple RMS velocity is a measure of the average speed of particles in a gas or liquid. It takes into account the velocities of all the particles in a sample and calculates the root mean squared (RMS) value.

## 2. How is Simple RMS velocity calculated?

The Simple RMS velocity is calculated by taking the square root of the sum of the squared velocities of all the particles in a sample, divided by the total number of particles. This calculation is represented by the equation: v(rms) = √(v1² + v2² + ... + vn²)/n, where v(rms) is the Simple RMS velocity, v1-vn are the velocities of each particle, and n is the total number of particles.

## 3. What is the significance of Simple RMS velocity?

Simple RMS velocity is significant because it provides insight into the overall movement and energy of particles in a gas or liquid. It is also used to calculate other important properties such as temperature and pressure in thermodynamics.

## 4. Is Simple RMS velocity the same as average velocity?

No, Simple RMS velocity and average velocity are not the same. Average velocity only takes into account the average speed of particles, while Simple RMS velocity takes into account the magnitude and direction of each particle's velocity. In other words, Simple RMS velocity is a more comprehensive measure of the overall movement of particles in a sample.

## 5. What are some common mistakes when calculating Simple RMS velocity?

One common mistake is forgetting to square the velocities before summing them, which would result in a lower value for Simple RMS velocity. Another mistake is not including the direction of the velocities in the calculation, which would result in an incorrect value. It is important to carefully follow the equation and include all necessary components to accurately calculate Simple RMS velocity.

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