Chapter U4.74, Problem 4E

(a)

Interpretation Introduction

Interpretation:

The milligrams of ethanol that would be lethal to a 132 lb adult given that LD50 for ethanol is 7060 mg/kg needs to be calculated.

Concept Introduction:

Lethal dose of a substance is given by LD₅₀which is the amount of substance the kills 50% of a target sample.

Answer to Problem 4E

Amount of ethanol that would be lethal is 423,600 mg.

Explanation of Solution

Given:

LD₅₀ for ethanol = 7060 mg/kg

Weight of adult = 132 lb

Calculation:

Step 1: Convert 132 lb to kg

1 kg = 2.2 lb

  $\text{Weight of adult in kg = }\frac{132\text{ lb}\times \text{1 kg}}{2.2\text{ lb}}=60\text{ kg}$

Step 2: Calculate the mg of ethanol

  $\begin{array}{l}\text{Ethanol lethal dose = }\frac{7060\text{ mg}\times \text{60 kg}}{1\text{ kg}}\\ =423,600\text{ mg}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The number of glasses containing 13000 mg of ethanol that would be lethal to a 22lb child needs to be calculated.

Concept Introduction:

Lethal dose of a substance is given by LD₅₀which is the amount of substance the kills 50% of a target sample.

Answer to Problem 4E

Number of glasses = 5

Explanation of Solution

Given:

Weight of child = 22 lb

Amount of ethanol per glass = 13000 mg

Calculation:

Step 1: Convert 22 lb to kg

1 kg = 2.2 lb

  $\text{Weight of child in kg = }\frac{22\text{ lb}\times \text{1 kg}}{2.2\text{ lb}}=10\text{ kg}$

Step 2: Calculate the ethanol lethal dose

  $\begin{array}{l}\text{Ethanol lethal dose = }\frac{7060\text{ mg}\times 1\text{0 kg}}{1\text{ kg}}\\ =70,600\text{ mg}\end{array}$

Step 3: Calculate the number of glasses

  $\begin{array}{l}\text{Number of glasses = }\frac{70600\text{ mg}}{13000\text{ mg/glass}}\\ =5.4\simeq 5\text{ glasses}\end{array}$