Question 67cea

Jul 14, 2017

Here's what I get.

Explanation:

(a) Exponential decay model

The rate law for a first-order reaction is

${\left[\text{A"]_t = ["A}\right]}_{0} {\left(\frac{1}{2}\right)}^{n}$

where

${\left[\text{A}\right]}_{t}$ and ${\left[\text{A}\right]}_{0}$ are the concentrations of component $\text{A}$ 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,

$\text{A}$ is the blood alcohol concentration $\text{BAC}$,

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

${t}_{2} = \text{1.5 h}$.

So, your exponential expression is

${\left[\text{BAC}\right]}_{t} = 0.3 {\left(\frac{1}{2}\right)}^{\frac{t}{1.5}}$

(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.