Q.2.61 - An Introduction to General, Organic, and Biological Chemistry

Question

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

a. A container holds 0.500 qt of liquid. How many milliliters of lemonade will it hold? 

b. What is the mass, in kilograms, of a person who weighs 175 lb? 

c. An athlete has 15% body fat by mass. What is the weight of fat, in pounds, of a 74-kg athlete? 

d. A plant fertilizer contains 15% nitrogen (N) by mass. In a container of soluble plant food, there are 10.0 oz of fertilizer. How many grams of nitrogen are in the container? 

Step-by-Step Solution

Answer

a. 473 mL

b. 79.5 Kg

c. 24 lb

d. 43 g

Step 1: Part (a) Given Information

A container holds 0.500 qt of liquid. 

Step 2: Part (a) Explanation

A container holds 0.500 qt of liquid. In order to determine the holding capacity of lemonade in milliliters, we will follow the unit conversion method.

$$\begin{gathered} 1 qt=946 mL \\ Or \\ 1 mL=\frac{1}{946}qt \end{gathered}$$

So,

$0.500 qt\times \frac{946 mL}{1 qt}=473 mL$

Thus, It will hold 473 mL of milliliters of lemonade.

Step 1: Part (b) Given Information

A person who weighs 175 lb.

Step 2: Part (b) Explanation

A person who weighs 175 lb. In order to determine the person's mass in kg, we will follow the unit conversion method.

$$\begin{gathered} 1 Kg=2.20 lb \\ or \\ 1 lb=\frac{1}{2.20}Kg \end{gathered}$$

So,

$175 lb\times \frac{1 Kg}{2.20 lb}=79.5 Kg$

Thus, the person's weight in kilograms is 79.5.

Step 1: Part (c) Given Information

An athlete has 15% body fat by mass and the weight of an athlete is 74 Kg.

Step 2: Part (c) Explanation

The weight of fat can be determined by using the unit conversion method.

$$\begin{gathered} 1 \mathrm{Kg} \mathrm{of} \mathrm{body} \mathrm{mass}=2.20 \mathrm{lb} \mathrm{of} \mathrm{body} \mathrm{weight} \\ \frac{2.20 \mathrm{lb} \mathrm{of} \mathrm{body} \mathrm{weight}}{1 \mathrm{Kg} \mathrm{of} \mathrm{body} \mathrm{mass}}\mathrm{and} \frac{1 \mathrm{Kg} \mathrm{of} \mathrm{body} \mathrm{mass}}{2.20 \mathrm{lb} \mathrm{of} \mathrm{body} \mathrm{weight}} \\ 15 \mathrm{lb} \mathrm{of} \mathrm{body} \mathrm{fat}=100 \mathrm{lb} \mathrm{of} \mathrm{body} \mathrm{mass} \\ \frac{15 \mathrm{lb} \mathrm{of} \mathrm{body} \mathrm{fat}}{100 \mathrm{lb} \mathrm{of} \mathrm{body} \mathrm{mass}}=\frac{100 \mathrm{lb} \mathrm{of} \mathrm{body} \mathrm{mass}}{15 \mathrm{lb} \mathrm{of} \mathrm{body} \mathrm{fat}} \end{gathered}$$

Calculating the final answer:

$$\begin{gathered} 74 \mathrm{Kg} \mathrm{of} \mathrm{body} \mathrm{weight}\times \frac{2.20 \mathrm{lb} \mathrm{of} \mathrm{body} \mathrm{mass}}{1 \mathrm{Kg} \mathrm{of} \mathrm{body} \mathrm{weight}}\times \frac{15 \mathrm{lb} \mathrm{of} \mathrm{body} \mathrm{fat}}{100 \mathrm{lb} \mathrm{of} \mathrm{body} \mathrm{mass}} \\ =24.42 \mathrm{lb} \mathrm{of} \mathrm{body} \mathrm{fat} \end{gathered}$$

Step 1: Part (d) Given Information

A plant fertilizer contains 15% nitrogen (N) by mass. In a container of soluble plant food, there are 10.0 oz of fertilizer.  

Step 2: Part (d) Explanation

A plant fertilizer contains 15% nitrogen (N) by mass. In a container of soluble plant food, there are 10.0 oz of fertilizer.  The unit conversion will be as follows:

$$\begin{gathered} 1 oz=29 g \\ or \\ 1 g=\frac{1}{29}oz \end{gathered}$$

And, $15 \mathrm{g} \mathrm{of} \mathrm{Nitrogen} \mathrm{mass}=100 \mathrm{g} \mathrm{of} \mathrm{plant} \mathrm{mass}$

Calculating final answer:

$10 oz\times \frac{29 g}{1 oz}\times \frac{15 g}{100 g}=43 g$

Thus, the grams of nitrogen in a container is 43 grams.