How to Calculate Translational Kinetic Energy of a Gas Using Ideal Gas Law

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To calculate the total translational kinetic energy of 0.5 L of oxygen gas at 0°C and 1.3 atm, the ideal gas law (PV=nRT) is used to determine the number of moles of gas. The translational kinetic energy can be expressed as K = (3/2)nRT, which simplifies the calculation. Substituting the values for pressure and volume into the ideal gas law allows for the determination of moles, which can then be plugged into the kinetic energy equation. This approach clarifies the relationship between the ideal gas law and translational kinetic energy. Understanding these connections simplifies the problem-solving process.
KsonGV
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1.Find the total translational kinetic energy of 0.5 L of oxygen gas held at a temperature of 0°C and a pressure of 1.3 atm.


2.
R = 8.314

PV=nRT
PV=NkT

K=(.5*m*v^2)

Translational Kinetic Energy = T=(2/3)(1/k)[(.5)mv^2]


3.
The problem says to express the total translational kinetic energy of the oxygen gas by combining the expression for the translational kinetic energy and the ideal-gas law to obtain an expression for K in terms of the pressure and volume of the gas.
I tried subsitituting T= PV/nR to T=(2/3)(1/k)[(.5)mv^2] but I am not sure if I am on the right track.
 
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You can use PV = nRT to find the mols of oxygen gas you have. Then, you can use the translational kinetic energy equation for gasses, K = (3/2)nRT, to find K.
 
Oh. So i need to find the moles using the ideal gas law then plug it into the K equation. I was over thinking the whole problem.
 

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