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Acetone (nail polish remover) has a density of \(0.7857 \mathrm{~g} / \mathrm{cm}^{3} .\) a. What is the mass in g of \(28.56 \mathrm{~mL}\) of acetone? b. What is the volume in \(\mathrm{mL}\) of \(6.54 \mathrm{~g}\) of acetone?

Short Answer

Expert verified
a. The mass of 28.56 mL of acetone is 22.434232 g. b. The volume of 6.54 g of acetone is 8.320122 mL.

Step by step solution

01

Calculate the mass of acetone

To calculate the mass of acetone, use the formula: mass (g) = density (g/cm³) × volume (mL). Note that 1 mL is equivalent to 1 cm³. So, multiply the density of acetone by the volume in mL: mass = 0.7857 g/cm³ × 28.56 mL.
02

Perform the multiplication to find the mass

Multiplying the given density by the given volume gives the mass of acetone: mass = 0.7857 g/cm³ × 28.56 cm³ = 22.434232 g.
03

Calculate the volume of acetone

To find the volume, use the formula rearranged from Step 1: volume (mL) = mass (g) / density (g/cm³). Now divide the mass of acetone by its density: volume = 6.54 g / 0.7857 g/cm³.
04

Perform the division to find the volume

Dividing the mass by the density gives the volume of acetone: volume = 6.54 g / 0.7857 g/cm³ = 8.320122 mL.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mass-Volume Relationship
Understanding the mass-volume relationship is critical when you're dealing with the quantity of a substance. This relationship is a direct result of a substance's density, which is defined as its mass per unit volume. In scientific terms, density is often expressed in grams per cubic centimeter (\( g/cm^3 \) or \( g/mL \) for liquids).

To find the mass when you have the volume (like in our acetone example), you simply multiply the volume by the density. Conversely, if you're given the mass and need to find the volume, you divide the mass by the density. A critical step in solving such problems is making sure your units are consistent. Since 1 milliliter (\( mL \)) is equal to 1 cubic centimeter (\( cm^3 \)), there's no need to convert units in this particular instance.
Unit Conversion
Being nimble with unit conversion is an essential skill in chemistry and all other sciences. When solving problems, units might not always match up as conveniently as they did with the acetone example. You should be comfortable converting units such as milliliters to liters or grams to kilograms. To convert units, you can use a conversion factor, which is a fraction that represents the equivalence between two different units.

For example, to convert 28.56 mL to liters, you would use the conversion factor of 1 liter = 1000 mL. This is crucial for reaching an answer with the correct unit, which impacts the interpretation of your result and ensures accuracy in scientific communication.
Chemical Properties of Substances
Each chemical substance has a unique set of properties that dictates how it behaves in different situations. Density is one such property, encapsulating the compactness of a substance's mass in a given volume. It's a fundamental trait that you can use to identify substances or predict how they interact with others.

For instance, knowing the density of acetone can help you predict whether it will float on water (it does because its density is less than that of water). Such properties are intrinsic to the substance and do not change unless the substance itself undergoes a chemical transformation. Understanding the chemical properties of substances, including their densities, is vital in a wide array of scientific and practical applications, from designing an experiment to filling a swimming pool with the right amount of water treatment chemicals.

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Most popular questions from this chapter

Nanotechnology, the field of building ultrasmall structures one atom at a time, has progressed in recent years. One potential application of nanotechnology is the construction of artificial cells. The simplest cells would probably mimic red blood cells, the body's oxygen transporters. Nanocontainers, perhaps constructed of carbon, could be pumped full of oxygen and injected into a person's bloodstream. If the person needed additional oxygen - due to a heart attack perhaps, or for the purpose of space travel- these containers could slowly release oxygen into the blood, allowing tissues that would otherwise die to remain alive. Suppose that the nanocontainers were cubic and had an edge length of \(25 \mathrm{nm}\). a. What is the volume of one nanocontainer? (Ignore the thickness of the nanocontainer's wall.) b. Suppose that each nanocontainer could contain pure oxygen pressurized to a density of \(85 \mathrm{~g} / \mathrm{L}\). How many grams of oxygen could each nanocontainer contain? c. Air typically contains about 0.28 g of oxygen per liter. An average human inhales about \(0.50 \mathrm{~L}\) of air per breath and takes about 20 breaths per minute. How many grams of oxygen does a human inhale per hour? (Assume two significant figures.) d. What is the minimum number of nanocontainers that a person would need in his or her bloodstream to provide 1 hour's worth of oxygen? e. What is the minimum volume occupied by the number of nanocontainers calculated in part d? Is such a volume feasible, given that total blood volume in an adult is about \(5 \mathrm{~L} ?\)

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