Calculate RMS Speed of Nitrogen at 227°C

[Kill.Me.No]

Hiya,

Im having trouble answering this question.


If the density of nitrogen at STP (1.01 X 10^5 Pa and 0 degrees celsius) is 1.25kgm^-3, calculate the RMS speed of nitrogen at 227 degrees celsius.

Could someone please point me in the right direction?

Thank you.
__________________

 

[hage567]

What have you tried? Can you think of any equations that might be useful?

 

[m2003]

Hello,

To calculate the RMS (root-mean-square) speed of nitrogen at 227°C, we will need to use the ideal gas law and the formula for RMS speed.

First, let's convert 227°C to Kelvin by adding 273.15 (since Kelvin is measured from absolute zero). This gives us a temperature of 500.15 K.

Next, we can use the ideal gas law, PV = nRT, to calculate the number of moles of nitrogen present at STP. Since we know the pressure (1.01 X 10^5 Pa), volume (1 m^3), and temperature (273.15 K), we can solve for n (number of moles). This gives us a value of 44.8 moles of nitrogen.

Now, we can use the formula for RMS speed, v = √(3RT/M), to calculate the RMS speed of nitrogen at 227°C. We will use the molar mass of nitrogen (28.02 g/mol) as the value for M. Plugging in our values, we get:

v = √(3 * 8.314 J/mol*K * 500.15 K / 0.0448 kg/mol)

Solving this equation gives us an RMS speed of 516.6 m/s.

I hope this helps! Let me know if you have any further questions.