Question

You have a 23 -g sample of ethanol with a density of 0.7893 \(\mathrm{g} / \mathrm{mL}\) . What volume of ethanol do you have?

Short answer

The volume of the 23g sample of ethanol can be calculated using the formula Volume = \( \frac{Mass}{Density} \). By substituting the given values, we get Volume = \( \frac{23 \ \text{g}}{0.7893 \ \text{g/mL}} \) = 29.14 mL. So, the volume of the ethanol sample is approximately 29.14 mL.

Step-by-step solution

1. Write the formula for density

Firstly, we need to write down the formula for density: Density = Mass / Volume

2. Rearrange the formula for Volume

Next, we want to find the volume, so we need to rearrange the formula to make volume the subject. Multiply both sides by volume and then divide both sides by density: Volume = Mass / Density

3. Substitute the given values

Now, substitute the given values into the rearranged formula: Volume = \( \frac{23 \ \text{g}}{0.7893 \ \text{g/mL}} \)

4. Calculate the volume

Finally, divide 23 by 0.7893 to find the volume of ethanol: Volume = \( \frac{23 \ \text{g}}{0.7893 \ \text{g/mL}} \) = 29.14 mL The volume of the 23g sample of ethanol is approximately 29.14 mL.

Key concepts

Ethanol

Ethanol, commonly known as alcohol, is a versatile organic compound frequently used in the production of beverages, thermometers, and even as a fuel. Its chemical formula is C\(_2\)H\(_5\)OH. Ethanol is highly flammable and is considered a polar solvent, making it useful in various chemical reactions and processes.
Its low density compared to water means it can occupy more space per unit of mass, a property that affects how it's measured and used in various applications. The density of ethanol is approximately 0.7893 g/mL at room temperature, significantly impacting calculations and measurements for labs and industrial purposes.

Mass and Volume

When dealing with substances like ethanol, understanding the difference between mass and volume is crucial. Mass is the amount of matter in an object, measured in grams, kilograms, or other units. Volume, on the other hand, refers to the amount of space a substance occupies.
Volume can be measured in liters, milliliters, or cubic meters, depending on the context.

• Mass - measured using scales and balances
• Volume - measured using graduated cylinders or other measurement tools

In calculations, mass and volume are often related through the concept of density, a crucial property in chemistry and physics.

Rearranging Formulas

Rearranging formulas is an important skill, especially when dealing with calculations in chemistry and physics. This involves altering a formula to solve for a different variable. To find the volume of ethanol from its mass, we needed to modify the basic density formula.
The original formula for density is: - Density = Mass / Volume By rearranging, we isolate the volume: - Volume = Mass / Density This is achieved through basic algebra, allowing us to compute the volume once we know the mass and density. Understanding how to rearrange formulas enables the prediction and understanding of different properties of substances based on available data.

Density of Substances

Density is the measure of how much mass is contained within a specific volume of a substance. It's a crucial property in science to determine how substances interact with each other. For substances like ethanol, its density helps predict how it behaves in different environments and conditions.
Density is typically expressed in g/mL or kg/m\(^3\), depending on the context. The formula for calculating density is: - Density = Mass / VolumeKnowing the density of substances allows chemists to convert between mass and volume efficiently. With ethanol having a density of 0.7893 g/mL, it means that each milliliter contains 0.7893 grams of ethanol. This conversion is vital for practical applications such as determining quantities for chemical reactions.