Q. 13.54 - An Introduction to General, Organic, and Biological Chemistry

Question

The next day. Kate had 1 cup of cereal $(15 g$ carbohydrate) with skim milk$(7 g$ carbohydrate). 1 banana $( 17 g$ carbohydrate). and $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ cup of orange juice ( $12 \mathrm{g}$ carbohydrate) for breakfast.

a. Has Kate remained within the limit of $45$ to $60 \mathrm{g}$of carbohydrate?

b. Using the energy value of $4 kcal/g$ for carbohydrate, calculate the total kilocalories from carbohydrates in Kate's breakfast, rounded to the tens place.

Step-by-Step Solution

Answer

Part a) The limit is $45$ to $60 g$ of carbohydrate, Kate had $51 g$,${\mathrm{kcal}}_{\text{total }}=2.04\times {10}^2\mathrm{kcal}$

Part b) The total kilocalories in Kate's breakfast are $2.04\times {10}^2\mathrm{kcal}$.

Given information (Part-a)

In this problem, we must determine whether Kate has stayed below the carbohydrate allowance for breakfast.

The limit of carbohydrates is $45$ to$60 \mathrm{g}$, and for breakfast she had:

•  1 cup of cereal $=15 \mathrm{g}$ carbohydrate
•  skim milk $=7 \mathrm{g}$ carbohydrate
•  1 banana $=17 \mathrm{g}$carbohydrate
•  $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ cup of orange juice $=12 \mathrm{g}$ carbohydrate.

Explanation (Part-a)

 To figure out if Kate stayed within the carbohydrate limit, simply sum up the carbohydrate mass of everything she ate.

As a result, her total carbohydrate intake is:

                      $$\begin{gathered} m\text{ (carbohydrates })=15 \mathrm{g}+7 \mathrm{g}+17 \mathrm{g}+12 \mathrm{g} \\ m\text{ (carbohydrates) }=51 \mathrm{g} \end{gathered}$$

The limit is $45$ to $60 g$ of carbohydrates, and Kate had $51g$ for breakfast, thus she stayed inside the limit.

Given information (Part-b)

In this problem, we must determine whether Kate has stayed below the carbohydrate allowance for breakfast.
The energy value is $4\mathrm{kcal}/\mathrm{g}$ for carbohydrate, and for breakfast she had:

- 1 cup of cereal $=15 \mathrm{g}$ carbohydrate

- skim milk $=7 \mathrm{g}$ carbohydrate

- 1 banana $=17 \mathrm{g}$ carbohydrate

- $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ cup of orange juice $=12 \mathrm{g}$ carbohydrate.

Explanation (Part-b)

To calculate the energy value first we have to calculate the total mass of carbohydrates she had for breakfast:

                  $$\begin{gathered} m\left(\text{ carbohydrates }\right)=15 \mathrm{g}+7 \mathrm{g}+17 \mathrm{g}+12 \mathrm{g} \\ m\left(\text{ carbohydrates }\right)=51 \mathrm{g} \end{gathered}$$

From the unit of measurement for energy value, we can see that mass and kilocalories are connected in this way:

                                     $\mathrm{kcal}/\mathrm{g}=\frac{\mathrm{kcal}}{\mathrm{g}}$

which means that total kilocalories are equal to

                                    $\mathrm{kcal}=\mathrm{g}\times \mathrm{kcal}/\mathrm{g}$

We can calculate total kilocalories (rounded to the tens place) from total energy and total carbs now that we have the total mass of carbohydrates and the formula.

$$\begin{gathered} {\mathrm{kcal}}_{\text{total }}=51 g\times 4\mathrm{kcal}/\mathrm{g} \\ {\mathrm{kcal}}_{\text{total }}=204\mathrm{kcal}=2.04\times {10}^2\mathrm{kcal} \end{gathered}$$

$\text{ The total kilocalories in Kate's breakfast are }2.04\times {10}^2\text{ kcal. }$