I need this in detail and step by step!! I need to fully understand this for my

Question

I need this in detail and step by step!! I need to fully understand this for my test. Please be detailed and clear
Equations provided: A.J t A A 14. The reaction that occurs in a Breathalyzer, a device used to determine the alcohol level in a person's bloodstream, is given below. If the rate of appearance of Cr (SO4), is 1.64 mol/min at a particular moment, what is the rate of disappearance of C,HO at that moment? 2K,cro, + 8H,so, + 3C,l 1,0 2Cr(so,), + 2K,so, + 1 111,0 A) 0. 547 mol/min B) 109 mol/min C) 2.46 mol/min D) 4.92 mol/min E) 1.64 mol/min

Explanation / Answer

Answer is option (B) 1.09 mol/min.

2K2Cr2O7 + 8H2SO4 + 3C2H6O ---> 2Cr2(SO4)3 + 2K2SO4 + 11H2O

The rate of the reaction is to be expressed in terms of fall in concentration of a reactant per mole or increase in concentration of a product per mole. And is expressed as

r = -(1/2) d[K2Cr2O7]/dt = -(1/8) d[H2SO4]/dt = -(1/3) d[C2H6O]/dt = +(1/2) d[2Cr2(SO4)3]/dt = +(1/2) d[K2SO4]/dt = +(1/11) d[H2O]/dt

Here, the negative sign and positive represents fall in concentration of reactants per mole and increase in concentration of products per mole.

So, r = -(1/3) d[C2H6O]/dt = +(1/2) d[2Cr2(SO4)3]/dt
or, -(1/3) d[C2H6O]/dt = +(1/2) d[2Cr2(SO4)3]/dt
or, -(2/3) d[C2H6O]/dt = d[2Cr2(SO4)3]/dt -------------------(1)

Since, rate of apperance of Cr2(SO4)3 = +(1/2) d[2Cr2(SO4)3]/dt = 1.64 mol/min

So, the rate od disapperance of C2H6O = (2/3) x 1.64 mol/min = 1.09 mol/min

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