Problem 64 - Chemistry: An Atoms-Focused Approach

Question

What is the mass of \(65.0 \mathrm{mL}\) of ethanol? (Its density at room temperature is \(0.789 \mathrm{g} / \mathrm{mL} .\) )

Step-by-Step Solution

Answer

Answer: The mass of 65.0 mL of ethanol at room temperature is approximately 51.29 g.

Step 1: Write the formula for mass, volume, and density

Use the formula \(m = ρ × V\), where \(m\) is the mass, \(ρ\) is the density, and \(V\) is the volume.

Step 2: Identify given information

The volume of ethanol is \(65.0\: \mathrm{mL}\) and the density is \(0.789\: \frac{\mathrm{g}}{\mathrm{mL}}\).

Step 3: Calculate the mass of ethanol

Using the formula from Step 1 and the given information from Step 2, plug in the values and calculate the mass: $$ m = ρ × V = 0.789\: \frac{\mathrm{g}}{\mathrm{mL}} × 65.0\: \mathrm{mL} $$

Step 4: Solve for mass

Carry out the calculation: $$ m = \left(0.789\: \frac{\mathrm{g}}{\mathrm{mL}} \right) \times 65.0\: \mathrm{mL} = 51.285 \: \mathrm{g} $$

Step 5: Provide the answer

The mass of \(65.0 \: \mathrm{mL}\) of ethanol at room temperature is approximately \(51.29 \: \mathrm{g}\).

Key Concepts

Understanding Mass in Density Calculations

In density calculations, mass refers to the amount of matter present in a substance. It is usually measured in grams (g) for simplicity in everyday calculations. Knowing the mass of a substance allows you to understand how much of that substance exists. To find mass using density, you need the formula:

• \( m = \rho \times V \)

Here:

• \( m \) represents mass,
• \( \rho \) is density,
• \( V \) is volume.

This formula tells us that mass is the product of density and volume. In our ethanol problem, we used this formula to determine how much 65.0 mL of ethanol weighs by multiplying its density (0.789 g/mL) by its volume.

The Role of Volume in Density Calculations

Volume is a basic concept in understanding density and mass relationships. It refers to the amount of space that a substance occupies. Volume is measured in units like milliliters (mL), liters (L), or cubic centimeters (cc). In density calculations, volume is crucial because it helps determine mass when combined with density. By knowing the volume, you can multiply it with the density to find the mass of a substance.
For instance, in our exercise, we started with a known volume of ethanol, 65.0 mL. This means ethanol takes up that much space. Using this volume, along with the known density, we calculated the mass to understand how much ethanol is present.

Understanding Ethanol and Its Properties

Ethanol is a common type of alcohol found in spirits and is used in various industrial applications. It is a clear, volatile, and flammable liquid at room temperature. When working with ethanol in calculations, its density is a vital property. Density indicates how tightly the substance's molecules are packed. For ethanol, the density at room temperature is 0.789 g/mL. This value being less than water's density (1 g/mL) explains why ethanol floats when combined with water.
In practical terms, knowing the density of ethanol helps in a variety of scenarios, including determining the mass of a given volume, like our problem with 65.0 mL of ethanol. Knowing the density, we were able to accurately calculate its mass, illustrating the importance of understanding ethanol’s properties in scientific calculations.