A container with volume 1.83 L is initially evacuated. Then it is filled with 0.246 g of N2. Assume that the pressure of the gas is low enough for the gas to obey the ideal-gas law to a high degree of accuracy. If the root-mean-square speed of the gas molecules is 192 m/s, what is the pressure of the gas?

The  pressure is  

Explanation:

From the question we are told that

    The  volume of the container is  

     The mass of   is  

     The root-mean-square velocity is  

The  root -mean square velocity is mathematically represented as

Now the ideal gas law is mathematically represented as

=>  

Where n is the number of moles which is mathematically represented as

Where  M  is the molar mass of  

So  

=>    

=>    

=>  

substituting values

    =>    

=>        

the area between the graph and the t axis

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