50 cm³ of gasoline are mixed with 50 cm³ of water. What is the average density of the mixture?

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Step 1: Recall the formula for density, which is \( \text{density} = \frac{\text{mass}}{\text{volume}} \). To find the average density of the mixture, we need the total mass and the total volume of the mixture.

Step 2: Determine the mass of each component. Use the formula \( \text{mass} = \text{density} \times \text{volume} \). Look up the densities of gasoline and water (e.g., \( \rho_{\text{gasoline}} \approx 0.7 \ \text{g/cm}^3 \) and \( \rho_{\text{water}} = 1.0 \ \text{g/cm}^3 \)). Then calculate the mass of gasoline and water using their respective volumes (50 cm³ each).

Step 3: Add the masses of gasoline and water to find the total mass of the mixture: \( \text{total mass} = \text{mass of gasoline} + \text{mass of water} \).

Step 4: Add the volumes of gasoline and water to find the total volume of the mixture: \( \text{total volume} = \text{volume of gasoline} + \text{volume of water} \).

Step 5: Calculate the average density of the mixture using the formula \( \text{average density} = \frac{\text{total mass}}{\text{total volume}} \). Substitute the total mass and total volume values obtained in the previous steps to find the result.

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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) or kilograms per cubic meter (kg/m³). It is a fundamental property of materials that indicates how much mass is contained in a given volume. Understanding density is crucial for calculating the average density of a mixture, as it helps determine how different substances interact when combined.

Mixture

A mixture is a combination of two or more substances where each retains its own properties. In this case, gasoline and water are mixed, but they do not chemically react. The average density of the mixture can be calculated by considering the individual densities and volumes of the components, which is essential for solving the problem presented.

Volume and Mass Relationship

The relationship between volume and mass is critical in density calculations. When mixing substances, the total volume of the mixture is the sum of the individual volumes, while the total mass is the sum of the individual masses. This relationship allows for the determination of the average density of the mixture by using the formula: average density = total mass / total volume.