MASS-VOLUME RELATIONSHIP
CHEMISTRY
The density of a substance can be calculated using the following formula
Density = mass/volume
This formula indicates that as the mass of a substance increases, its density will increase if the volume remains constant. Similarly, as the volume of a substance increases, its density will decrease if the mass remains constant.
The relationship between mass and volume is important in many areas of chemistry, including analytical chemistry and physical chemistry.
For example, in analytical chemistry, the determination of a substance’s density can be used to identify the substance and determine its purity.
In physical chemistry, the relationship between mass and volume is important in the study of gases, as the density of a gas is directly proportional to its pressure and inversely proportional to its temperature.
Example of a mass-volume calculation
Suppose you have a sample of metal with a mass of 20 grams. You measure the volume of the metal using water displacement and find that it displaces 10 milliliters (mL) of water. What is the density of the metal?
First, we need to convert the volume to liters, since density is typically reported in units of grams per milliliter (g/mL) or grams per cubic centimeter (g/cm^3):
10 mL = 10/1000 L = 0.01 L
Next, we can use the density formula to calculate the density of the metal:
Density = mass/volume = 20 g / 0.01 L = 2000 g/L
So the density of the metal is 2000 g/L. This means that for every liter of the metal, there are 2000 grams of the substance. The mass-volume relationship is demonstrated by the fact that the density of the metal is a result of the relationship between its mass (20 grams) and volume (10 mL or 0.01 L).
The mass-volume relationship in chemistry is defined by the density of a substance, which relates the mass of a substance to its volume. Understanding this relationship is important in many areas of chemistry and can be used to identify substances, determine their purity, and study their physical properties.
The mass-volume relationship in chemistry is a fundamental concept that describes the relationship between the mass and volume of a substance, and it is important in understanding many properties of substances in chemistry.
Sample Problem:
Converting Moles to Mass
Chromium metal is used for decorative electroplating of car bumpers and other surfaces. Find the mass of 0.560 moles of chromium.
Step 1: List the known quantities and plan the problem.
Known
- 0.560 mol Cr
- molar mass of Cr = 52.00 g/mol
Unknown
- 0.560 mol Cr = ? g
The molar mass of chromium will allow us to convert from moles of Cr to grams.
Step 2: Calculate.
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- 0.560 mol Cr×52.00 g Cr1 mol Cr=29.1 g Cr
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Step 3: Think about your result.
Since the desired amount was slightly more than one-half of a mole, the mass should be slightly more than one-half of the molar mass. The answer has three significant figures because the given value (0.560 mol) also has three significant figures.
- Find the masses of the following amounts.
- 2.15 mol of hydrogen sulfide, H2S
- 3.95 × 10−3 mol of lead(II) iodide, PbI2
A similar conversion factor based on molar mass can be used to convert the mass of a known substance to moles. In a laboratory situation, you might perform a reaction and produce a certain amount of a product. It will often be necessary to then determine the number of moles of the product that was formed, but this cannot be measured directly. However, you can use a balance to measure the mass of the product, and the number of moles can be easily calculated. The next Sample Problem illustrates this situation.
Sample Problem 10.5: Converting Mass to Moles
A certain reaction produces 2.81 g of copper(II) hydroxide, Cu(OH)2. Determine the number of moles produced in the reaction.
Step 1: List the known quantities and plan the problem.
Known
- mass of Cu(OH)2 produced = 2.81 g
Unknown
- amount of Cu(OH)2 produced in moles
One conversion factor will allow us to convert from mass to moles.
Step 2: Calculate.
First, it is necessary to calculate the molar mass of Cu(OH)2 from the molar masses of Cu, O, and H. The molar mass is 97.57 g/mol.
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- 2.81 g Cu(OH)2×1 mol Cu(OH)297.57 g Cu(OH)2=0.0288 mol Cu(OH)2
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Step 3: Think about your result.
The molar mass is approximately 100 g/mol, so a quick estimate can be obtained by dividing the original value by 100 (moving the decimal point two places to the left). The relatively small mass of product formed results in a small number of moles.
