Question

Calculate the mass in grams for each of the following liquids. (a) \(250 \mathrm{~mL}\) of gasoline \((d=0.69 \mathrm{~g} / \mathrm{mL})\) (b) \(150 \mathrm{~mL}\) of ethanol \((d=0.79 \mathrm{~g} / \mathrm{mL})\)

Short answer

Gasoline: 172.5 grams; Ethanol: 118.5 grams.

Step-by-step solution

Understanding the Formula

To find the mass of a liquid, use the formula: \( \text{mass} = \text{density} \times \text{volume} \). Here, the volume is given in milliliters (mL), and the density is given in grams per milliliter (g/mL).

Calculate the Mass of Gasoline

For gasoline, the volume \( V = 250 \text{ mL} \) and the density \( d = 0.69 \text{ g/mL} \). Apply the formula: \( \text{mass} = 0.69 \text{ g/mL} \times 250 \text{ mL} = 172.5 \text{ grams} \).

Calculate the Mass of Ethanol

For ethanol, the volume \( V = 150 \text{ mL} \) and the density \( d = 0.79 \text{ g/mL} \). Apply the formula: \( \text{mass} = 0.79 \text{ g/mL} \times 150 \text{ mL} = 118.5 \text{ grams} \).

Key concepts

Density Formula

The density formula is a helpful tool in chemistry that connects three important physical properties: mass, volume, and density. It is expressed as:

• \( ext{mass} = ext{density} \times ext{volume} \)

This simple yet powerful equation lets us calculate the mass of a substance if we know its density and volume.

Density is a measure of how tightly packed the particles within a substance are. It is generally represented as grams per milliliter (g/mL) or grams per cubic centimeter (g/cm\(^3\)).

When using the density formula, it's essential to ensure the units of measurement are consistent. For example, if the volume is in milliliters and the density is in grams per milliliter, the calculated mass will be in grams.

Volume Measurement

Volume measurement is crucial in science, especially in chemistry, where precise measurements are needed for accurate results. Here are some common units of volume in the metric system:

• Milliliters (mL)
• Liters (L)
• Cubic centimeters (cm\(^3\))

For most basic chemistry problems, milliliters or cubic centimeters are preferred due to their small scale and compatibility with lab equipment.

To measure the volume of liquids, tools like graduated cylinders or measuring cups are typically used. It's important to read the level of the liquid at eye level and consider the meniscus — the curve at the surface of the liquid.

Understanding the volume of a liquid allows us to determine how much space it occupies and is essential for tasks like calculating mass using density.

Basic Chemistry Problems

Basic chemistry problems often revolve around the fundamental concepts of density, mass, and volume. Being comfortable with these concepts allows you to solve a variety of everyday chemistry problems.

These tasks usually involve applying known formulas, such as the density formula, and rearranging them as necessary to find the desired quantity. For instance, given the density and volume, you need to find the mass of a substance.

When tackling basic chemistry problems:

• Identify what you are given and what you need to find.
• Choose the appropriate formula to apply.
• Ensure all units are consistent to avoid calculation errors.

By breaking down these problems step by step, they become more manageable and enhance your understanding of essential chemistry concepts.