How Do You Calculate the Kinetic Energy of CO, CO2, and SO3 at 276 K?

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SUMMARY

The kinetic energy (KE) of carbon monoxide (CO), carbon dioxide (CO2), and sulfur trioxide (SO3) at 276 K can be calculated using the equation KE = (3/2) RT, where R is the ideal gas constant (8.314 J/mol-K). However, this equation is applicable primarily to monatomic ideal gases. For polyatomic molecules like CO, CO2, and SO3, it is essential to consider the degrees of freedom to accurately compute their kinetic energy. The discussion highlights the incorrect application of the KE formula for CO and emphasizes the need for a more nuanced approach for polyatomic gases.

PREREQUISITES
  • Understanding of the ideal gas law and kinetic molecular theory
  • Familiarity with the concept of degrees of freedom in molecular physics
  • Knowledge of the ideal gas constant (R) and its units
  • Basic skills in molecular mass calculations
NEXT STEPS
  • Research the concept of degrees of freedom for polyatomic gases
  • Learn how to apply the equipartition theorem to calculate kinetic energy
  • Study the differences in kinetic energy calculations for monatomic vs. polyatomic gases
  • Explore the implications of temperature on molecular motion and energy
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Chemistry students, physics enthusiasts, and educators looking to deepen their understanding of kinetic energy calculations for different types of gases.

SpottedGreen
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Homework Statement



Calculate the kinetic energy of CO, CO2, and SO3 at 276 K .

Homework Equations



KE = (3/2) RT
KE= (1/2)(mass)(velocity)^2

The Attempt at a Solution


[/B]
For CO:
First attempt: KE=(3/2)(RT)=(3/2)(8.314 J/mol-K)(276K) = 3441.996 -- So that's wrong
Second attempt:
Relative Molecular Mass of CO= 28
6.02x10^23 molecules of CO= 28g
1 molecule of CO= 28/6.02x10^23
4.65x10^-23g
4.65x10^-26kg

Kinetic energy of CO= 1/2(4.65x10^-26)(490^2)
= 5.58x10^-21 J -- according to mastering this is also wrong Thank You
 
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SpottedGreen said:
KE = (3/2) RT

I believe this equation applies only to monatomic ideal gases. For molecules, such as CO, CO2, and SO3, you need to calculate the number of degrees of freedom for each of these molecules.
 

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