Q. 2.109 - An Introduction to General, Organic, and Biological Chemistry

Question

The following nutrition information is listed on a box of crackers: (2.6)

Serving size $0.50$ ) 02 ( 6 crackers)

Fat $4$ g per serving; Sodium $140 mg$ per serving

a. If the box has a net weight (contents only) of $8.000$, about how many crackers are in the box?

b. If you ate $10$ crackers, how many ounces of fat did you consume?

c. How many servings of crackers in part a would it take to obtain the Daily Value (DV) for sodium, which is $2.4 \mathrm{g}$ ?

Step-by-Step Solution

Answer

a) The number of crackers in the box is determined as $96$ crackers

b) The number of ounces of fat consumed is determined as $0.2 oz$

c) The number of servings of crackers would take to obtain the daily value is determined as $16$ servings

Step 1 : Information (part a)

The given is the nutrition information on the box of crackers.

The objective is to find the number of crackers, ounces of fat consumed and number of servings.

There are 4 g of Fat per serving and 140 mg Sodium per serving. 

Step 2 : Explanation (part a)

a.

The equality from the serving size $0.50\mathrm{oz}$ ( 6 crackers) is as follows:

$0.50\mathrm{oz}=6$ crackers

As a result, the conversion factors will be:

$\frac{0.50\mathrm{oz}}{6\text{ crackers }}$and $\frac{6\text{ crackers }}{0.50\mathrm{oz}}$

The conversion factor that should be used is as follows:

$\frac{6\text{ crackers }}{0.50\mathrm{oz}}$

Calculate the number of crackers from the specified conversion factor $8.0\mathrm{oz}$.

$8.0\backslash \mathrm{not}z\times \frac{6\text{ crackers }}{0.50\backslash \mathrm{not}z}=96$ crackers

Thus, box has $96$ crackers

Step 3 : Introduction (part b)

The objective is to find the ounces of fat consumed

Step 4 : Explanation (part b)

b.

Use the following equalities and derive the desired conversion factors to determine the ounce O Z of fat. The following are the conversion factors that should be used:

$\frac{1\text{ serving }}{6\text{ crackers }},\frac{4 \mathrm{gfat}}{1\mathrm{serving}},\left\{\frac{1\mathrm{lb}}{454 \mathrm{g}}\right.$ and $\frac{16\mathrm{oz}}{1\mathrm{lb}}$

$10 crakers \times \frac{1 serving}{6 crakers}\times \frac{4 g fat}{1 serving }\times \frac{1 lb fat}{454 g fat}\times \frac{16 oz fat}{1 lb fat}=0.2 oz$

fat Hence, the consumed fat will be $0.20 z$ 

Step 5 : Introduction (part c)

The objective is to find the number of servings.

Step 6 : Explanation (part c)

C.

The equality from the information $140\mathrm{mg}$ sodium per serving is as follows:

$140\mathrm{mg}$ sodium $=1$ serving

As a result, the conversion factors will be:

$\frac{140\mathrm{mg}\text{ sodium }}{1\text{ serving }}$ and $\frac{1\text{ serving }}{140\mathrm{mg}\text{ sodium }}$

The conversion factor that should be used is as follows:

1 serving

140mg sodium

To calculate the number of servings from $2300\mathrm{mg}$ sodium, use the selected conversion factor.

Sodium: $2300\mathrm{mg}\times \frac{1\text{ serving }}{140\mathrm{mg}\text{ sodium }}=16$ servings

As a result, $16$ servings will be consumed to meet the daily sodium requirement.