Q. 2.62 - An Introduction to General, Organic, and Biological Chemistry

Question

Solve each of the following problems using one or more conversion factors: 

a. Wine is $12\%$ alcohol by volume. How many milliliters of alcohol are in a $0.750-\mathrm{L}$ bottle of wine?

b. Blueberry high-fiber muffins contain $51\%$ dietary fiber by mass. If a package with a net weight of $12 \mathrm{oz}$ contains six muffins, how many grams of fiber are in each muffin?

c. A jar of crunchy peanut butter contains $1.43 \mathrm{kg}$ of peanut butter. If you use $8.0\%$ of the peanut butter for a sandwich, how many ounces of peanut butter did you take out of the container?

d. In a candy factory, the nutty chocolate bars contain $22.0\%$ pecans by mass. If $5.0 \mathrm{kg}$ of pecans were used for candy last Tuesday, how many pounds of nutty chocolate bars were made?

Step-by-Step Solution

Answer

(a) The $90 \mathrm{mL}$ of alcohol are in bottle of wine

(b) The  $29 \mathrm{g}$ fibre are there in each muffin

(c) The $4 \mathrm{oz}$ of peanut butter did you take out of the container

(d) The $50 \mathrm{lb}$ of nutty chocolate bar were made

Part (a) Step 1: Given information

We need to find the millimeters of alcohols in bottle of wine 

Part (a) Step 2: Explanation

We know that

$12\%$of  alcohol means $\frac{12 \cancel{\mathrm{mL}}}{100 \cancel{\mathrm{mL}}}$

And $1000 \mathrm{mL}=1 \mathrm{L}$

Therefore, required amount of alcohol is,

$\frac{12 \cancel{\mathrm{mL}}}{100 \cancel{\mathrm{mL}}}\times \frac{1000 \mathrm{mL}}{1 \cancel{\mathrm{L}}}\times 0.750 \cancel{\mathrm{L}}=90 \mathrm{mL}$

Part (b) Step 1: Given informnation

We need to find the grams of fiber in each muffin

Part (b) Step 2: Explanation

We know that 

$\frac{1 \mathrm{lb}}{16 \mathrm{coz}}, \frac{6 \mathrm{muffins}}{1 \mathrm{package}}, \frac{100 \mathrm{g}}{2.2 \mathrm{lb}}, \frac{51 \mathrm{g}}{100 \mathrm{g} \mathrm{muffins}}$

Therefore, grams of fiber in each muffin is,

$12 \cancel{\mathrm{oz}}\times \frac{1 \mathrm{package}}{6 \cancel{\mathrm{muffins}}}\times \frac{1\cancel{ \mathrm{lb}}}{16 \cancel{\mathrm{oz}}}\times \frac{1000 \mathrm{g}}{2.20 \cancel{\mathrm{lb}}}\times \frac{51 \cancel{\mathrm{g} \mathrm{muffins} }}{100 \cancel{\mathrm{g}} }=29 \mathrm{g}$

Part (c) Step 1: Given information

We need to find the no. of ounces of peanut butter did you take out of the container 

Part (c) Step 2: Explanation

We know that

$\frac{8 \mathrm{g}}{100 \mathrm{g}}, \frac{1 \mathrm{kg}}{2.20 \mathrm{lb}}, \frac{1 \mathrm{lb}}{16 \mathrm{oz}}$

Therefore, 

Ounces of peanut butter did you take out of the container,

$1.43 \cancel{\mathrm{kg}}\times \frac{8 \cancel{\mathrm{kg}}}{100 \cancel{\mathrm{kg}}}\times \frac{2.20 \cancel{\mathrm{lb}}}{1 \cancel{\mathrm{kg}}}\times \frac{16 \mathrm{oz}}{1 \cancel{\mathrm{lb}}}=4 \mathrm{oz}$

Part (d) Step 1: Given information

We need to find the pounds of nutty chocolate bars that were made 

Part (d) Step 2: Explanation

We know that

$1 \mathrm{kg}=2.20 \mathrm{lb}$

The $22 \mathrm{kg}$ of pecans $=100 \mathrm{kg}$ of nutty chocolate

Therefore, pounds of nutty chocolate bars were made 

$5 \cancel{\mathrm{kg} \mathrm{pecans}}\times \frac{2.20 \mathrm{lb}}{1 \cancel{\mathrm{kg}}}\times \frac{100 \cancel{\mathrm{kg}} \mathrm{nutty} \mathrm{chocolate}}{22 \cancel{\mathrm{kg} \mathrm{pecans}}}=50 \mathrm{lb} \mathrm{nutty} \mathrm{chocolate}$