Question

Calculate the volume in milliliters for each of the following liquids. (a) \(25.0 \mathrm{~g}\) of ether \((d=0.714 \mathrm{~g} / \mathrm{mL})\) (b) \(15.0 \mathrm{~g}\) of acetone \((d=0.792 \mathrm{~g} / \mathrm{mL})\)

Short answer

Ether: 35.0 mL, Acetone: 18.9 mL.

Step-by-step solution

Identify the Given Data for Ether

We have 25.0 grams of ether and its density is given as 0.714 grams per milliliter. Density is the mass per unit volume given by the formula \( d = \frac{m}{V} \).

Apply the Density Formula to Ether

Using the formula \( d = \frac{m}{V} \), rearrange to solve for volume \( V = \frac{m}{d} \). Substitute 25.0 g for mass \( m \) and 0.714 g/mL for density \( d \).

Calculate the Volume for Ether

Calculate the volume: \( V = \frac{25.0 \, \text{g}}{0.714 \, \text{g/mL}} \approx 35.0 \, \text{mL} \). The volume of ether is 35.0 mL.

Identify the Given Data for Acetone

For acetone, we have 15.0 grams with a density given as 0.792 grams per milliliter. Again, we'll use the formula \( d = \frac{m}{V} \) to find the volume.

Apply the Density Formula to Acetone

Using the same rearranged formula \( V = \frac{m}{d} \), substitute 15.0 g for \( m \) and 0.792 g/mL for \( d \).

Calculate the Volume for Acetone

Calculate the volume: \( V = \frac{15.0 \, \text{g}}{0.792 \, \text{g/mL}} \approx 18.9 \, \text{mL} \). The volume of acetone is approximately 18.9 mL.

Key concepts

Volume Calculation

Calculating volume is an essential part of solving problems related to density. When you know the mass of a substance and its density, you can easily find its volume using the formula:

1. Density formula: \( d = \frac{m}{V} \)
2. Volume formula: \( V = \frac{m}{d} \)

To calculate volume:

• Find the mass (\( m \)), which is usually given in grams.
• Identify the density (\( d \)) provided, in grams per milliliter (g/mL).
• Rearrange the formula to solve for volume (\( V \)).
• Substitute the known values into the formula and solve for \( V \).

For example, with ether given as 25.0 g and a density of 0.714 g/mL, the volume calculation is straightforward: \( V = \frac{25.0 \, \text{g}}{0.714 \, \text{g/mL}} \approx 35.0 \, \text{mL} \). This tells us it takes about 35 milliliters to contain 25 grams of ether.

Mass-Volume Relationship

The relationship between mass and volume is a key component of understanding density. Density, often symbolized as \( d \), is a measure of how much mass (\( m \)) is contained within a certain volume (\( V \)).

• It describes how tightly packed the particles in a substance are.
• The higher the density, the more mass is held within a specific volume.

This relationship can help us determine how substances will behave under different volumes or masses.
For instance, in the case of acetone, knowing it has a mass of 15.0 g and a density of 0.792 g/mL, you can find how much space its mass will occupy: \( V = \frac{15.0 \, \text{g}}{0.792 \, \text{g/mL}} \approx 18.9 \, \text{mL} \). Here, 15 grams of acetone results in a volume of about 18.9 milliliters.

Unit Conversion in Chemistry

Unit conversion is vital in chemistry to ensure consistent, accurate, and understandable results. When dealing with measurements, you often need to convert units such as grams, milliliters, or even liters to make meaningful comparisons or calculations.

• Volume and density calculations often use units like grams (g) and milliliters (mL). These are common in chemistry as they make equations manageable and relate directly to laboratory measurements.
• Converting between units might appear in metrics, like changing liters to milliliters by multiplying by 1000 (since 1 liter = 1000 mL).

When you understand how to convert units, you can confidently tackle problems requiring different measurements. For example, converting the given density of a liquid to match the units of mass can streamline solving for the volume, such as using grams and milliliters to calculate the volume of ether based on its density and mass.