Question #67cea

1 Answer
Jul 14, 2017

Answer:

Here's what I get.

Explanation:

(a) Exponential decay model

The rate law for a first-order reaction is

#["A"]_t = ["A"]_0(1/2)^n#

where

#["A"]_t# and #["A"]_0# are the concentrations of component #"A"# at time #t# and at the start of the experiment (#t = 0#)

#n =# the number of half-lives

Now, #n= t/t_½#, so

#["A"]_t = ["A"]_0(1/2)^(t/(t_2)#

(I had to write the half-life as #t_2# to get the expression to display properly)

In this problem,

#"A"# is the blood alcohol concentration #"BAC"#,

#["BAC"]_0 = "0.3 mg/mL"#, and

#t_2 = "1.5 h"#.

So, your exponential expression is

#["BAC"]_t = 0.3(1/2)^(t/1.5)#

(b) Graph

I plotted the graph in Excel:

Graph

It looks like BAC = 0.075 mg/mol at 3.0 h.

I would guess that BAC = 0.08 mg/mL at 2.9 h.

You can drive home at about 02:55.