Why Do We Convert Grams to Kilograms When Calculating RMS Speed in Gases?

So, by converting to kg/mol, you are ensuring that the units will cancel out and give you a velocity in m/s. In summary, to find the rms speed of N2 and O2 at 293K, you must use the formula Vrms=\sqrt{}((3RT)/M), where M is converted to kg/mol. This will give you the correct answer in m/s.
  • #1
ChopChop
6
0

Homework Statement


The atmosphere is composed primarily of nitrogen N2 (78%), and oxygen O2 (21%). Find the rms speed of N2 and O2 at 293K


Homework Equations


Vrms=[tex]\sqrt{}((3RT)/M)[/tex]


The Attempt at a Solution


Vrms, O2=[tex]\sqrt{}((3*8.31J*293K)/(32g/mol))[/tex] =15.11m/s

When I looked at the answer to the book, it was 478 m/s because instead of putting 32g/mol in the denominator, they converted it to 0.032 kg/mol. Can somebody explain to me why the authors of my book decided to do that? Is my first answer still correct? Or do I need to convert to kg every time I have to do a RMS problem?

Thank you for your time
 
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  • #2
It is used in terms of kg because Joules is a unit that involves kg (kg*m^2*s^-2). In order for it to work out, you have to divide by the same units.
 

Related to Why Do We Convert Grams to Kilograms When Calculating RMS Speed in Gases?

1. What is the RMS speed of a gas molecule?

The RMS speed of a gas molecule refers to the root mean square speed, which is the average speed of all the gas molecules in a given sample. It is a measure of the kinetic energy of the molecules.

2. How is the RMS speed of a gas molecule calculated?

The RMS speed of a gas molecule is calculated using the formula: √(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.

3. Why is the RMS speed of a gas molecule important?

The RMS speed of a gas molecule is important because it provides information about the average kinetic energy of the molecules, which is directly related to temperature. It is also used in various equations and formulas to calculate other properties of gases, such as pressure and volume.

4. How does temperature affect the RMS speed of a gas molecule?

According to the formula, the RMS speed of a gas molecule is directly proportional to the square root of the temperature. This means that as the temperature increases, the RMS speed also increases.

5. Can the RMS speed of a gas molecule be measured?

Yes, the RMS speed of a gas molecule can be measured using experimental methods, such as the kinetic theory of gases or the Maxwell-Boltzmann distribution. These methods involve measuring the average speed of a large number of gas molecules and using statistical analysis to determine the RMS speed.

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