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# Physics/Dimensional Analysis

Question

Problem
Hi,

I'm working on the problem I've attached as an image. The solution is there as it's a worked example from Elementary Principles of Chemical Processes but I cannot figure out how the exponent can have a unit (K) and the equation still be valid.

The unit of k which is (mol/cm^3 . s) doesn't have K in it.

The solution seems fine. All exponents must be dimensionless. In this case,the numerator of the exponent is
20,000cal/mol as given while the temperature in the denominator of the exponent is in kelvins. The units of the numerator of the exponent must be the same as the units of the denominator of the exponent in order for the units to cancel out. in this case:
cal/mol must equal ? * K
Therefore, ? must have units cal/(mol*K)

Physics

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#### James J. Kovalcin

##### Expertise

I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.