# Root mean square speed and ideal gases

• tigerlili
In summary, the problem involves finding the root mean square speed and molar mass of a gas at a given temperature and pressure. The equations used are vrms= sqrt (3RT/M) and pV=nRT, with additional relationships pM=dRT and pV=(m/M)RT. The main issue is determining the correct units for density and pressure to yield a final speed in m/s.
tigerlili

## Homework Statement

At 318 K and 1.04 x 10-2 atm, the density of a gas is 1.75 x 10-5 g/cm3. (a) Find vrms for the gas molecules. (b) Find the molar mass of the gas.

## Homework Equations

vrms= sqrt (3RT/M)
pV=nRT
pM=dRT
pV=(m/M)RT

## The Attempt at a Solution

the main problem i am having here is units, and i am getting really frustrated, because i am a chem major, and this is chemistry!

in order to solve for the root mean square speed, i said, based on the above relationships, RT/M = p/d

so i plugged into vrms= sqrt (3p/d) BUT i don't know what units the density and pressure should be into yield m/s for the final speed- i have no idea to even apply unit analysis here

thanks!

i think p - N/m^2 because: P/D = (N/m^2) / (kg/m^3) = m.N / kg. According to N's 2nd law: F = ma => N/kg = m/s^2 => m.N / kg = m.m/s^2 = m^2/s^2.

okay, thanks for your help :)

## What is the root mean square speed of gas particles?

The root mean square speed of gas particles is the average speed of all the individual particles in a gas sample. It takes into account both the direction and magnitude of the particles' velocities.

## How is root mean square speed related to temperature?

According to the kinetic theory of gases, the root mean square speed of gas particles is directly proportional to the square root of the temperature. This means that as the temperature increases, the average speed of gas particles also increases.

## What is the ideal gas law?

The ideal gas law, also known as the universal gas law, is a mathematical relationship between pressure, volume, temperature, and the number of moles of gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

## How does the ideal gas law relate to root mean square speed?

The ideal gas law can be used to calculate the root mean square speed of gas particles. By rearranging the equation to solve for the root mean square speed (v), we get v = √(3RT/M), where R is the gas constant and M is the molar mass of the gas.

## Can the root mean square speed of gas particles ever be equal to zero?

No, the root mean square speed of gas particles can never be equal to zero. According to the kinetic theory of gases, gas particles are in constant motion and therefore always have a non-zero velocity. However, at extremely low temperatures, the root mean square speed can approach zero.

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