Question #67cea

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Answer 1 · 2017-07-14T01:39:27

Here's what I get.

(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 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.