Question

Using the average atomic masses given inside the front cover of the text, calculate how many moles of each substance the following masses represent. a. \(4.21 \mathrm{g}\) of copper(II) sulfate b. \(7.94 \mathrm{g}\) of barium nitrate c. \(1.24 \mathrm{mg}\) of water d. 9.79 g of tungsten e. 1.45 lb of sulfur f. 4.65 g of ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) g. \(12.01 \mathrm{g}\) of carbon

Short answer

The number of moles for each substance is as follows: a. Copper(II) sulfate (CuSO4): \(n(CuSO_4) = 0.0264\, mol\) b. Barium nitrate (Ba(NO3)2): \(n(Ba(NO_3)_2) = 0.0304\, mol\) c. Water (H2O): \(n(H_2O) = 6.89 \times 10^{-5}\, mol\) For substances d, e, f, and g, follow the same steps as above: find the molar mass and use the formula \(n = \frac{mass}{molar\,mass}\) to calculate the number of moles. Remember to convert the mass units to grams if necessary.

Step-by-step solution

Find molar mass of CuSO4

Look up the molar masses of Cu, S, and O in the periodic table inside the front cover of the text. Cu has a molar mass of 63.5 g/mol, S has a molar mass of 32.1 g/mol, and O has a molar mass of 16.0 g/mol. Calculate the molar mass of CuSO4 as follows: \(M(CuSO_4) = M(Cu) + M(S) + 4 \times M(O) = 63.5 + 32.1 + 4 \times 16.0 = 159.6\, g/mol\)

Calculate the number of moles of CuSO4

Use the formula \(n = \frac{mass}{molar\,mass}\): \(n(CuSO_4) = \frac{4.21\,g}{159.6\,g/mol} = 0.0264\, mol\) #b. Barium nitrate (Ba(NO3)2)#

Find molar mass of Ba(NO3)2

Look up the molar masses of Ba, N, and O in the periodic table. Ba has a molar mass of 137.3 g/mol, N has a molar mass of 14.0 g/mol, and O has a molar mass of 16.0 g/mol. Calculate the molar mass of Ba(NO3)2 as follows: \(M(Ba(NO_3)_2) = M(Ba) + 2(M(N) + 3M(O)) = 137.3 + 2(14.0 + 3 \times 16.0) = 261.3\, g/mol\)

Calculate the number of moles of Ba(NO3)2

Use the formula \(n = \frac{mass}{molar\,mass}\): \(n(Ba(NO_3)_2) = \frac{7.94\,g}{261.3\,g/mol} = 0.0304\, mol\) #c. Water (H2O)#

Convert mass from mg to g

Since the mass of water is given in mg, we need to convert it into grams before using it in the formula. \(1.24\,mg = 1.24 \times 10^{-3}\,g\)

Find molar mass of H2O

Look up the molar masses of H and O in the periodic table. H has a molar mass of 1.0 g/mol and O has a molar mass of 16.0 g/mol. Calculate the molar mass of H2O as follows: \(M(H_2O) = 2 \times M(H) + M(O) = 2 \times 1.0 + 16.0 = 18.0\, g/mol\)

Calculate the number of moles of H2O

Use the formula \(n = \frac{mass}{molar\,mass}\): \(n(H_2O) = \frac{1.24 \times 10^{-3}\,g}{18.0\,g/mol} = 6.89 \times 10^{-5}\, mol\) Continue with the remaining substances (d, e, f, g) following the same steps: find the molar mass and then use the formula to calculate the number of moles. Remember to convert the mass units to grams if necessary.

Key concepts

Molar Mass

Molar mass is a fundamental concept in chemistry that helps us to convert between the mass of a substance and the amount of substance in moles. It is defined as the mass of one mole of a given substance, usually expressed in grams per mole (g/mol). Molar mass is calculated by summing the atomic masses of all the elements present in a molecule. This makes it essential for dictating how much of a particular substance is needed or created in a chemical reaction.

For example, in the compound copper(II) sulfate \((CuSO_4)\), you can determine the molar mass by adding up the atomic masses of copper (Cu), sulfur (S), and oxygen (O). Copper has a molar mass of 63.5 g/mol, sulfur 32.1 g/mol, and each oxygen atom has a molar mass of 16.0 g/mol. Since there are four oxygen atoms in copper(II) sulfate, the total molar mass is calculated as \(M(CuSO_4) = 63.5 + 32.1 + 4 \times 16.0 = 159.6\, g/mol\).

Understanding and calculating molar mass accurately is crucial to performing mole conversions in various chemical calculations.

Periodic Table

The periodic table is an essential tool for chemists because it provides information necessary for calculating molar masses, among many other uses. Every element in the periodic table has an atomic mass, which is based on the weighted average of the naturally occurring isotopes of each element. These atomic masses are typically found underneath the symbol of the element and are listed in atomic mass units (amu). In calculating molar mass, these atomic masses are used to determine the masses of elements in grams per mole.

For instance, when you need to find the molar mass of barium nitrate (\(Ba(NO_3)_2\)), you will turn to the periodic table for the atomic masses of barium (Ba), nitrogen (N), and oxygen (O). Using these atomic masses, you calculate as: \(M(Ba(NO_3)_2) = 137.3 + 2(14.0 + 3 \times 16.0) = 261.3\, g/mol\).

Having a strong understanding of how to extract and utilize atomic masses from the periodic table is vital for accurate molar calculations and chemistry proficiency.

Chemical Calculations

Chemical calculations often involve using molar mass for converting between mass and moles. This allows you to measure how much of a substance you have or need for a reaction, using the chemical unit known as the mole. With the known mass of a compound and its molar mass, you can calculate how many moles of the substance you have using the formula:

• \(n = \frac{\text{mass in grams}}{\text{molar mass in g/mol}}\)

Using this equation helps in determining the exact quantities of reactants and products involved in chemical reactions.

For example, in determining the moles of ethyl alcohol (\(C_2H_5OH\)) given its mass as 4.65 g, you first must find its molar mass using the periodic table. After that, apply the formula to find the moles of ethyl alcohol, ensuring precise chemical calculations for your experiment or theoretical analysis.

Unit Conversion

Unit conversion is a necessary skill in chemistry, particularly when dealing with different mass units. Before you can perform any mole conversion calculation, all given masses must be in grams (g). Many measurements, such as in this exercise, might initially be given in milligrams (mg) or pounds (lb), requiring conversion to grams for consistency.

For instance, in the case of water, which is given as 1.24 mg, you'll have to convert milligrams to grams by recognizing that 1 mg equals 0.001 g. Hence, you convert 1.24 mg to grams by calculating \(1.24 \times 10^{-3}\, g\). Similarly, converting pounds to grams involves recognizing that 1 pound equals approximately 453.59 grams. This conversion is crucial, especially when comparing masses of different substances accurately in chemical problem-solving.

Developing strong unit conversion skills ensures that you are precise in your chemical calculations and avoid errors, which is essential for any serious study of chemistry.