Ethylene glycol (antifreeze) has a density of 1.11 g/cm 3 . a. What is the mass in g of 417 mL of ethylene glycol? b. What is the volume in L of 4.1 kg of ethylene glycol?

Hello everyone. Today we have the following problem. Ethylene Glycol also known as Antifreeze has a density of 1.1 g per centimeter cubed. A what is the mass in grams of 243 mL of Ethylene Glycol? And B what is the volume in liters of 2.7 kg of Ethylene Glycol? So for this problem, we need to determine the mass. So we can, we can essentially arrange the equation that density is equal to mass divided by volume such that mass now is equal to the density multiplied by the volume. And so we have our density which is the 1.11 g per cubed. And for our volume, we have 243 milliliters. However, we must convert this from milliliters to centimeters cubed to match the units for a density. And we can multiply the volume by the ratio or the conversion factor that 1 mL is equal to one centimeter cubed. Once our units for milliliters and centimeters cubed cancel out, we are left with a mass of 2.70 times 10 to the second grams. Moving on to our second part of the question finding the volume in leaders, we need to determine the volume. So we rearrange the equation once again. But this time stating that volume is equal to mass divided by density. The other mass that we solve for in part A which is 2.70 times 10 to the second grams. And we divide that by our density which is one 0.11 g per centimeter qed. However, we need to multiply by some conversion factors. For example, we need to multiply our grams. So we started with kilograms of ethylene Glycol part B. So we need to multiply by the conversion factor, that 1 kg is equal to 10 to the third grams. And then lastly, since we need to convert from centimeters cubed to liters, we can use the conversion factor at one milliliter is equal to one centimeter cubed. And then multiply that by 1 mL is equal to 10 to the negative third liters. So our units of kilograms will cancel out as will our units of centimeters cubed and milliliters and grams such that we are left with a volume, a final volume of 2.4 L. So if we look at our answer choices, we see that answer choice d best reflects these answers. And with that, we have solved the problem overall, I hope this helped. And until next time

Ch.1 - Matter, Measurement & Problem Solving

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Ch.1 - Matter, Measurement & Problem Solving

Problem 69b

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Chapter 1, Problem 69b

Ethylene glycol (antifreeze) has a density of 1.11 g/cm³. a. What is the mass in g of 417 mL of ethylene glycol? b. What is the volume in L of 4.1 kg of ethylene glycol?

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Step 1: Understand the relationship between mass, volume, and density. The formula to use is: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \).

Step 2: For part (a), rearrange the formula to find mass: \( \text{Mass} = \text{Density} \times \text{Volume} \).

Step 3: Convert the volume from mL to cm³ for part (a), knowing that 1 mL = 1 cm³. Therefore, 417 mL = 417 cm³.

Step 4: Substitute the given values into the formula for part (a): \( \text{Mass} = 1.11 \text{ g/cm}^3 \times 417 \text{ cm}^3 \).

Step 5: For part (b), rearrange the formula to find volume: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \). Convert the mass from kg to g, knowing that 1 kg = 1000 g, so 4.1 kg = 4100 g. Then, substitute the values into the formula: \( \text{Volume} = \frac{4100 \text{ g}}{1.11 \text{ g/cm}^3} \). Convert the result from cm³ to L, knowing that 1000 cm³ = 1 L.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density

Density is defined as the mass of a substance per unit volume, typically expressed in grams per cubic centimeter (g/cm³) or kilograms per liter (kg/L). It is a crucial property that helps in determining how much mass is contained in a given volume of a substance. In this question, the density of ethylene glycol is used to calculate the mass from volume and vice versa.

Mass-Volume Relationship

The mass-volume relationship is a fundamental concept in chemistry that describes how mass and volume are interrelated through density. The formula used is mass = density × volume. This relationship allows for the conversion between mass and volume when the density of a substance is known, which is essential for solving the parts of the question regarding ethylene glycol.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this question, it is necessary to convert between milliliters (mL) and liters (L) as well as between grams (g) and kilograms (kg). Understanding how to perform these conversions is vital for accurately answering the question and ensuring that all measurements are in compatible units.