Ch.1 - Chemical Tools: Experimentation & Measurement

Problem 113

Chapter 1, Problem 113

Vinaigrette salad dressing consists mainly of oil and vinegar. The density of olive oil is 0.918 g/cm3, the density of vinegar is 1.006 g/cm3, and the two do not mix. If a certain mixture of olive oil and vinegar has a total mass of 397.8 g and a total volume of 422.8 cm3, what is the volume of oil and what is the volume of vinegar in the mixture?

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Let the volume of olive oil be \( V_{\text{oil}} \) and the volume of vinegar be \( V_{\text{vinegar}} \).

We know the total volume is the sum of the volumes of oil and vinegar: \( V_{\text{oil}} + V_{\text{vinegar}} = 422.8 \text{ cm}^3 \).

Using the density formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \), express the mass of olive oil as \( m_{\text{oil}} = 0.918 \times V_{\text{oil}} \).

Express the mass of vinegar as \( m_{\text{vinegar}} = 1.006 \times V_{\text{vinegar}} \).

Since the total mass is the sum of the masses of oil and vinegar, set up the equation: \( 0.918 \times V_{\text{oil}} + 1.006 \times V_{\text{vinegar}} = 397.8 \text{ g} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³). It is a crucial property that helps determine how substances behave when mixed. In this question, the densities of olive oil and vinegar are provided, allowing us to calculate their respective volumes based on their mass in the mixture.

Volume Calculation

Volume calculation involves determining the space occupied by a substance. In this scenario, the total volume of the mixture is given, and we need to find the individual volumes of oil and vinegar. Using the relationship between mass, density, and volume (Volume = Mass/Density), we can derive the volumes of each component in the mixture.

Mixture Properties

A mixture consists of two or more substances that retain their individual properties. In this case, olive oil and vinegar do not mix, which means they will form separate layers based on their densities. Understanding how to analyze the properties of each component in a mixture is essential for solving the problem of finding the volumes of oil and vinegar.

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A bag of Hershey's Kisses contains the following information:

Serving size: 9 pieces = 41 g

Calories per serving: 230

Total fat per serving: 13 g

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A bag of Hershey's Kisses contains the following information:

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Calories per serving: 230

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