Problem 69 - Chemistry A Molecular Approach

Question

Ethylene glycol (antifreeze) has a density of \(1.11 \mathrm{~g} / \mathrm{cm}^{3}\) MISSED THIS? Read Section 1.6; Watch \(\mathrm{KCV} 1.6,\) IWE 1.10 a. What is the mass in g of \(417 \mathrm{~mL}\) of ethylene glycol? b. What is the volume in \(\mathrm{L}\) of \(4.1 \mathrm{~kg}\) of ethylene glycol?

Step-by-Step Solution

Answer

The mass of 417 mL of ethylene glycol is 462.87 g. The volume of 4.1 kg of ethylene glycol is 3.69369 L.

Step 1: Calculate Mass Using Density

To calculate the mass of ethylene glycol, use the formula mass = density × volume. Density of ethylene glycol is given as 1.11 g/cm³. To use this density in the formula, the volume should be in cubic centimeters (cm³). Convert 417 mL to cm³ by recognizing that 1 mL = 1 cm³. Now calculate the mass as 417 cm³ × 1.11 g/cm³.

Step 2: Convert Mass to Grams

Perform the multiplication from the previous step to find the mass. The mass is 417 cm³ × 1.11 g/cm³ = 462.87 g.

Step 3: Calculate Volume Using Density for 4.1 kg

Volume can be found using the formula volume = mass / density. First, convert the mass from kilograms to grams, because the density is given in grams per cubic centimeter. Convert 4.1 kg to grams: 4.1 kg = 4100 g.

Step 4: Convert Volume to Liters

Now calculate the volume using the density, and then convert this volume to liters. The formula will be: volume in cm³ = 4100 g / (1.11 g/cm³). Then, convert cm³ to liters by using the conversion factor 1 L = 1000 cm³.

Step 5: Perform the Calculation

Performing the division for volume, 4100 g / 1.11 g/cm³ = 3693.69 cm³. Convert the volume to liters: 3693.69 cm³ ÷ 1000 cm³/L = 3.69369 L.

Key Concepts

Mass and Volume Conversion

Understanding the relationship between mass and volume is fundamental in science to grasp many concepts, including density. To convert between the two, it's crucial to know the unit of measurement and the substance being measured. In many scientific problems, like calculating the mass of a liquid such as ethylene glycol, one must often convert milliliters (mL) to cubic centimeters (cm³). Thankfully, for liquid substances at standard conditions, the conversion is straightforward: 1 mL is equal to 1 cm³.

In the given step-by-step solution, this conversion is used to find the mass of 417 mL of ethylene glycol. By recognizing that mass is the product of volume and density, the calculation becomes simple multiplication. This principle is a common technique used in chemistry and physics whenever you are working with fluids and their properties.

Density Formula

The density of a substance is a measure of its mass per unit volume. The formula to calculate density is \( density = \frac{mass}{volume} \). In practical terms, density helps us understand how much substance is packed into a given space. For instance, the density of ethylene glycol is given as 1.11 g/cm³, meaning each cubic centimeter of ethylene glycol has a mass of 1.11 grams.

When solving problems related to density, it's essential to ensure that the mass and volume units are compatible. Here, we find the mass by rearranging the density formula to \( mass = density \times volume \) and then by inserting the known values. Similarly, to find the volume given the mass, you would rearrange to \( volume = \frac{mass}{density} \). By managing these equations appropriately, you can navigate through many practical and theoretical applications involving density.

Units of Measurement Conversion

Converting units of measurement is a necessary skill in many scientific exercises, as encountered with both mass and volume in our example problem. The density problem provided requires a series of conversions: kilograms to grams for mass, and cubic centimeters to liters for volume.

To make these conversions, one must know the appropriate conversion factors, such as 1 kg equals 1000 grams or 1 L equals 1000 cm³. These factors are based on the International System of Units (SI) which simplifies scientific communication globally. Here's a tip: always ensure that your final units correspond to the question being asked. For instance, when you are asked to find the volume in liters, make sure to convert your volume from cubic centimeters to liters by dividing by 1000, allowing for accurate and relevant results.