Q. 3.97 - An Introduction to General, Organic, and Biological Chemistry

Question

When a $0.66g$ sample of olive oil is burned in a calorimeter, the heat released increases the temperature of $370g$ of water from $22.7^{\circ }\mathrm{C}$ to $38.8^{\circ }\mathrm{C}$. What is the energy value for the olive oil in sample?

Step-by-Step Solution

Answer

The energy value of olive oil are$37.8 KJ/g$ in Kilojoule and$9.03 Kcal/g$ in Kilocalories.

Step 1: Given information

Calories include a certain total energy, indicated by calories burned. It promotes the execution of pharmacological biological functions.

Mass of olive oil$=0.66 g$

Mass of Water$=370 g$

Temperature varies from $22.7^{\circ }C$ to $38.8^{\circ }C$

Step 2: Find Energy in Kilojoule.

The rise in the temperature of  $370g$  of water is  ${22.7}^{\circ }\mathrm{C}$  to ${38.8}^{\circ }\mathrm{C}$ when $0.66g$ of olive oil is heated in calorimeter.

The amount of heat involved in the process in kilojoules is calculated as follows:

$Heat =specific heat\times mass\times ∆T$

On substitution of the respective values we have:

$Heat =specific heat\times mass\times ∆T$

$=4.184\frac{\mathrm{g}}{{\mathrm{g}}^{\circ }\mathrm{C}}\times 370 \mathrm{g}\times \left({38.8}^{\circ }\mathrm{C}-22{.}^{\circ }\mathrm{C}\right)$

$=24,924 J$

$=24.9 KJ$

Thus, the heat added to burn the olive oil is $24.9KJ$, thus, the energy value of the olive oil is calculate as:

Energy value 

$$\begin{gathered} =\frac{24.9 KJ}{0.660 g} \\ =37.9 KJ/g \end{gathered}$$

The energy value of the olive oil is $37.8 KJ/g$

Step 3: Find Energy in Kilocalories.

The amount of heat consume in kcal is calculate as follows:

$Heat specific=heat \times mass$

$=1.00\frac{\text{ cal }}{{\mathrm{g}}^{\circ }\mathrm{C}}\times 370\mathrm{g}\times \left({38.8}^{\circ }\mathrm{C}-{22.7}^{\circ }\mathrm{C}\right)$

$=5,957 cal$

$=5.9 Kcal$

Thus, the heat added to burn the olive oil is $5.9 Kcal$, thus, the energy value of the olive oil is calculated as :

Energy value

$$\begin{gathered} =\frac{5.9 Kcal}{0.660g} \\ =9.03 Kcal/g \end{gathered}$$

The energy value of the olive oil is $9.03 Kcal/g$