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Calculating Rate Constant using Hard-Sphere Theory

I have a problem I am unable to figure out, I keep using the hard-theory formula for "A" to get the rate constant, however the value I get seems way to small every time I try to do it. Can someone please help me with this problem? I posting the homework set its problem number 5, I keep getting (4.28x10^-29dm3/mol s) as "k" please let me know if one credit is sufficient

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Solution Summary

This solution provides step-wise answer to the given numerical problem. This solution explicitly shows each and every calculation and formula used in it, so that students can grasp the critical aspects involved in it.