RMS speed of nitrogen molecule

In summary, the task was to compute the rms speed of a nitrogen molecule at a temperature of 35.0 degrees Celsius using the equation V(rms) = sqrt((3RT)/M). The attempt at a solution involved plugging in the values of 8.31 for R, 308 K for T, and 14.0 g/mol for M, resulting in a solution of 23.4 m/s. However, this answer was marked incorrect in online homework. After correctly using this value for parts b and c of the question, it was discovered that the problem was due to not converting from grams to kilograms. Additional questions to consider were also discussed, including the molar mass of nitrogen molecules and the mass of a
  • #1
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Homework Statement



Compute the rms speed of a nitrogen molecule of 35.0 celcius.

Homework Equations



V(rms) = sqrt((3RT)/M)

The Attempt at a Solution



I plugged in 8.31 for R and 308 K for T and 14.0 g/mol for M. I arrived at a solution of 23.4 m/s but this answer came back as incorrect in online homework. However, I used this value to complete parts b and c to this question and correctly completed them. What gives?
 
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  • #2
Did you change g to Kg?
 
  • #3
A couple of questions to ponder:

(a) If 1 mole of nitrogen atoms has a mass of 14.0 g, then a mole of nitrogen molecules has a mass of ____?

(b) If 1 mole of nitrogen molecules has a mass of (insert answer to a here), then a single nitrogen molecule has a mass of ____?

Also, as Dadface said, convert from g to kg.
 
  • #4
Nitrogen is a diatomic molecule. Thanks for the reminder...all is well.
 

Related to RMS speed of nitrogen molecule

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

The root mean square (RMS) speed of a nitrogen molecule is approximately 515 meters per second at room temperature (25 degrees Celsius).

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

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

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

The RMS speed of a gas molecule is important because it helps to determine the average kinetic energy of the molecules, which is related to the temperature of the gas. This information is useful in understanding the behavior of gases in various conditions.

4. Does the RMS speed of a nitrogen molecule change with temperature?

Yes, the RMS speed of a nitrogen molecule increases with an increase in temperature. This is because as the temperature increases, the average kinetic energy of the molecules also increases, resulting in higher RMS speeds.

5. How does the RMS speed of a nitrogen molecule compare to other gases?

The RMS speed of a nitrogen molecule is similar to the RMS speed of other gases at the same temperature. However, it may vary based on the molar mass of the gas. For example, at the same temperature, lighter gases such as hydrogen and helium will have higher RMS speeds compared to heavier gases like nitrogen.

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