Problem 29 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) Write "true" or "false" for each statement. (a) A mole of ducks contain a mole of feathers. (b) A mole of ammonia gas has a mass of \(17.0 \mathrm{~g}\). (c) The mass of 1 ammonia molecule is \(17.0 \mathrm{~g} .\) (d) \(\mathrm{A}\) mole of \(\mathrm{MgSO}_{4}(s)\) contains 4 moles of oxygen atoms.

Step-by-Step Solution

Answer

False, True, False, True

Step 1: Statement (a)

A mole of ducks contain a mole of feathers. This statement is comparing the amount of ducks to the amount of feathers. In chemistry, a mole is defined as 6.022 x 10^23 representative particles of a substance, and it is a way of counting entities like atoms and molecules. Therefore, comparing the moles of ducks to moles of feathers is not correct. The correct answer for this statement is: False

Step 2: Statement (b)

A mole of ammonia gas has a mass of 17.0 g. In order to find out whether this statement is true or false, we need to determine the molar mass of ammonia (NH3). We can find this by adding the molar masses of all the atoms in ammonia: - Nitrogen (N): \(14.01 \mathrm{~g/mol}\) - Hydrogen (H): \(1.01 \mathrm{~g/mol}\) So, the molar mass of ammonia (NH3) is: \((1\times 14.01) + (3\times 1.01) = 17.03 \mathrm{~g/mol}\) Since a mole of ammonia has a mass of 17.03 g, the statement is almost true, and we'll consider it as: True

Step 3: Statement (c)

The mass of 1 ammonia molecule is 17.0 g. This statement is confusing the mass of 1 mole of ammonia (found in statement b) with the mass of a single ammonia molecule. Since we have already determined that a mole of ammonia has a mass of 17.03 g, we can find the mass of 1 ammonia molecule by dividing the mass of 1 mole of ammonia by Avogadro's number (6.022 x 10^23): Mass of 1 ammonia molecule = \(\frac{17.03 \mathrm{~g/mol}}{6.022 \times 10^{23} \mathrm{~molecules/mol}}\) The resulting mass of one ammonia molecule is much smaller than 17.0 g, so this statement is: False

Step 4: Statement (d)

A mole of MgSO4 (s) contains 4 moles of oxygen atoms. To verify this statement, we need to look at the formula of magnesium sulfate (MgSO4) and count the number of oxygen atoms per formula unit. We see that there is one sulfur atom and four oxygen atoms bonded to it in the sulfate ion (SO4^2-), so in one formula unit of MgSO4, there are indeed 4 oxygen atoms. Therefore, 1 mole of MgSO4 contains 4 moles of oxygen atoms, and this statement is: True

Key Concepts

Avogadro's Number

Avogadro's number is a fundamental concept in chemistry that helps us count particles in a mole of substance. Avogadro's number is defined as 6.022 x 10^23, which represents the number of particles, such as atoms, molecules, or ions, present in one mole of any substance.
This large number is incredibly useful because atoms and molecules are extremely small. It would be impractical to count them individually. Instead, chemists use Avogadro's number to convert between the microscopic scale of atoms and molecules to the macroscopic scale we can measure.
For example, when dealing with ammonia ( ext{NH}_3), Avogadro's number allows us to determine how many molecules are in a single mole of ammonia. Specifically, one mole of ext{NH}_3 contains 6.022 x 10^23 ammonia molecules. This number simplifies calculations and communication among chemists worldwide.
Remember, though, that Avogadro's number is constant, but the actual mass of a mole of a given substance depends on its molar mass.

Molar Mass

Molar mass is another essential concept that often pairs with Avogadro's number. It expresses the mass of one mole of any given substance. The units for molar mass are grams per mole (g/mol).
The molar mass of a compound can be calculated by summing the molar masses of the individual elements in that compound. For instance, to find the molar mass of ammonia ( ext{NH}_3), you would add the molar masses of nitrogen ( ext{N}) and hydrogen ( ext{H}):

• Nitrogen: 14.01 g/mol
• Hydrogen: 1.01 g/mol

This results in a total molar mass for ext{NH}_3 of \[(1 \times 14.01) + (3 \times 1.01) = 17.03 \text{ g/mol}.\]With molar mass, we can convert between moles and grams. For example, knowing the molar mass of ammonia, if you have 17.03 grams, you have precisely one mole of ext{NH}_3 molecules.
This understanding is crucial when dealing with chemical reactions, as it ensures you have the correct amount of each substance to fully react with others.

Chemical Formulas

Chemical formulas are shorthand representations of chemical compounds, indicating the elements present in a compound and their relative amounts. For example, ammonia's chemical formula is ext{NH}_3.
The formula gives us specific information:

• ext{N}: One atom of Nitrogen
• ext{H}: Three atoms of Hydrogen

Altogether, this tells us about the ratio of nitrogen to hydrogen in the compound. Chemical formulas are not just for naming substances but help us understand the composition of a compound at a molecular level.
Understanding a chemical formula is essential for interpreting statements about substances. For example, the compound magnesium sulfate is represented by the formula ext{MgSO}_4. This formula indicates one magnesium atom, one sulfur atom, and four oxygen atoms in each unit of magnesium sulfate.
By knowing how to read and interpret chemical formulas, you can determine many facts about a compound, including the types and amounts of atoms in a single mole of the compound. This is especially helpful in exercises where you need to calculate moles of individual atoms based on the compound's chemical formula.