Question

Question #67cea

Answer 1

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:

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.