Problem 47 - General Chemistry: Principles and Modern Applications

Question

A 2.18 L sample of butyric acid, a substance present in rancid butter, has a mass of 2088 g. What is the density of butyric acid in grams per milliliter?

Step-by-Step Solution

Answer

The density of butyric acid is 0.959 g/mL.

Step 1: Convert Liters to Milliliters

Start by converting the volume from liters to milliliters. Use the conversion factor 1 L = 1000 mL. Therefore, multiply 2.18 L by 1000 to get the volume in milliliters.

Step 2: Calculate the Density

Now, calculate the density of butyric acid by dividing its mass by its volume. The formula to calculate density (\(d\)) is \(d= \frac{mass}{volume}\),where the mass is 2088 g and the volume is the result from Step 1.

Step 3: Present the Density in grams per milliliter

Finally, present the result from Step 2 as the density of butyric acid in grams per milliliter.

Key Concepts

Conversion Factors

When dealing with measurements, conversion factors are key for making units compatible. In the problem of calculating the density of butyric acid, you need to convert the given volume from liters to milliliters. This is because density is typically expressed in grams per milliliter (g/mL). The conversion factor that relates these two units of volume is:

• 1 liter = 1000 milliliters

This means that for every liter, there are 1000 milliliters. Thus, to convert 2.18 liters to milliliters, you multiply by the conversion factor:

• 2.18 liters × 1000 = 2180 milliliters

This simple multiplication makes the volume suitable for further calculations. Keep in mind that understanding how to use conversion factors effectively allows you to move seamlessly between different units of measurement.

Density Formula

The density formula is a crucial aspect of understanding how to find the density of a substance. Density (\(d\)) is defined as the mass (\(m\)) of an object divided by its volume (\(V\)). Mathematically, it is expressed as:\[ d = \frac{m}{V} \]In our problem, we're trying to find the density of butyric acid in grams per milliliter. We have a mass of 2088 grams and a volume of 2180 milliliters. Substitute these values into the equation:\[ d = \frac{2088 \, \text{grams}}{2180 \, \text{milliliters}} \]The calculation yields a density of approximately 0.958 grams per milliliter. This density indicates how much mass is contained in a given volume, and it is a characteristic property of butyric acid which can be used to identify it.

Butyric Acid

Butyric acid, known for its presence in rancid butter, is an organic acid with a distinct, pungent smell. It is a four-carbon chain fatty acid with the chemical formula CH₃CH₂CH₂COOH. This small, simple carboxylic acid is not only notable for its odor but also plays various roles in biochemical processes:

• It occurs naturally in dairy products and is a byproduct of anaerobic fermentation.
• It is a precursor to other substances used in flavorings and fragrances.
• Butyric acid is also significant in animal nutrition and health.

In the context of this exercise, understanding the density of butyric acid provides insight into its composition and behavior in different environments. Recognizing its physical properties, such as density, is essential for applications in chemistry and biology. While often associated with an unpleasant smell, butyric acid is a valuable compound in various industrial and research settings.