Q. 2.118 - An Introduction to General, Organic, and Biological Chemistry

Question

A sunscreen preparation contains $2.50\sqrt{x}$ benzyl  salicylate by mass. If a tube contains $4.0$ ox of sunscreen, how many kilograms of benzyl salicylate are needed to manufacture $325$ tubes of sunscreen? (2.6)

Step-by-Step Solution

Answer

The number of kilograms of benzyl salicylate needed to manufacture is determined as $0.92 kg$

Step 1 : Given Information

The given is the information about the preparation of sunscreen with benzyl salicylate.

The objective is to determine how many kilograms are needed to manufacture mass amount of tubes.

The sunscreen consists of  $2.50\sqrt{x}$benzyl  salicylate.

Step 2 : Explanation

A sunscreen preparation contains $2.50\%$ by mass benzyl salicylate.

Since, 1 tube contains $4.0 oz$ of sunscreen, thus, $325$ tubes of sunscreen will contain

$325\text{ tube }\times \frac{4.0\mathrm{oz}}{1\text{ tube }}=1,300 \mathrm{oz}$

Thus, $325$ tubes of sunscreen will contain $1,300 \mathrm{oz}$ of sunscreen.

Step 3 : Explanation

Since,

$1 \mathrm{kg}=35.2 \mathrm{oz}$

So, $1,300 \mathrm{oz}$ of sunscreen is converted to $\mathrm{kg}$ as follows:

$1,300\backslash \mathrm{not}\delta \mathrm{z}\times \frac{1 \mathrm{kg}}{35.2\backslash \mathrm{notz}}=36.93 \mathrm{kg}$

Hence, $325$ tubes of sunscreen will contain $36.93 \mathrm{kg}$ of sunscreen. Since, a sunscreen preparation contains $2.50\%$ by mass benzyl salicylate, thus $\frac{2.50}{100}\times 36.93 \mathrm{kg}=0.92 \mathrm{kg}$

So, $0.92 \mathrm{kg}$ of benzyl salicylate is needed to manufacture $325$ tubes of sunscreen.