Problem 132 - General Chemistry

Question

Ethyl acetate has a characteristic fruity odor and is used as a solvent in paint lacquers and perfumes. An experiment requires \(0.070 \mathrm{~kg}\) of ethyl acetate. What volume is this (in liters)? The density of ethyl acetate is \(0.902 \mathrm{~g} / \mathrm{mL}\).

Step-by-Step Solution

Answer

The volume of ethyl acetate is approximately 0.078 liters.

Step 1: Convert Kilograms to Grams

The problem gives the mass of ethyl acetate as 0.070 kg. Since the density is given in grams per milliliter, we first convert this mass into grams using the conversion factor: 1 kg = 1000 grams. Thus, 0.070 kg = 0.070 * 1000 g = 70 g.

Step 2: Use the Density Formula

Density is defined as mass per unit volume and is given by the formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). Here, the density of ethyl acetate is 0.902 g/mL. We can rearrange the formula to solve for volume: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).

Step 3: Calculate Volume in Milliliters

Substitute the values into the rearranged formula to find the volume: \( \text{Volume} = \frac{70 \text{ g}}{0.902 \text{ g/mL}} \approx 77.59 \text{ mL} \). This gives us the volume of ethyl acetate in milliliters.

Step 4: Convert Milliliters to Liters

Convert the volume from milliliters to liters. Since 1 liter = 1000 milliliters, \( 77.59 \text{ mL} = \frac{77.59}{1000} \text{ L} = 0.07759 \text{ L} \).

Key Concepts

Mass Conversion

Mass conversion is simply turning the mass of a substance from one unit of measurement to another. In many science problems, mass may be provided in kilograms but sometimes you might need to convert it to grams to match the units used for other measurements like density. For example, in the context of the ethyl acetate problem, we began with a mass of 0.070 kilograms. To convert this to grams, you use the conversion factor that 1 kilogram equals 1000 grams.
So you multiply:

• 0.070 kg by 1000.

This gives you 70 grams, which makes it easier to use with the given density in grams per milliliter. Understanding mass conversion is crucial when dealing with different unit systems, especially in chemistry and physics, because it ensures all the measurements are compatible for calculations.

Volume Determination

Finding the volume of a substance becomes straightforward once you have the mass and the density. In scientific terms, density is defined as mass divided by volume: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]To find volume, you rearrange the formula: \[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]This shows volume can be calculated by dividing the mass by the density of the substance. In the ethyl acetate example, with a mass of 70 grams and density of 0.902 grams per milliliter, you substitute the values:

• Mass = 70 g
• Density = 0.902 g/mL

Thus the calculation is:\[ \text{Volume} = \frac{70}{0.902} \approx 77.59 \text{ mL} \]This calculation gives us the volume in milliliters. Knowing how to determine volume is essential for tasks that involve mixing solutions or calculating required quantities of a material.

Unit Conversion

Unit conversion is the process of changing the measurement of a quantity from one unit to another while maintaining the same amount. Often, substances are measured in different units, and you need to convert these to work out problems correctly. For volume, you might need to switch between milliliters and liters.
When working with the ethyl acetate problem, you end up with a volume of 77.59 milliliters. Since some situations prefer liters, knowing that 1 liter equals 1000 milliliters is key:

• Divide 77.59 mL by 1000 to convert it to liters.

This gives you approximately 0.07759 liters. Unit conversion is useful in many scientific disciplines, including chemistry and physics, where understanding and working with different units can affect the precision and success of your calculations.