Question

Calculate the percent by mass of each element in the following compounds. a. \(\mathrm{ZnO}\) b. \(\mathrm{Na}_{2} \mathrm{~S}\) c. \(\mathrm{Mg}(\mathrm{OH})_{2}\) d. \(\mathrm{H}_{2} \mathrm{O}_{2}\) e. \(\mathrm{CaH}_{2}\) \(\mathrm{f}, \mathrm{K}_{2} \mathrm{O}\)

Short answer

The percent by mass of each element in the given compounds is as follows: a. ZnO: Zn: \(80.31\%\), O: \(19.69\%\) b. Na\(_{2}\)S: Na: \(58.93\%\), S: \(41.07\%\) c. Mg(OH)\(_{2}\): Mg: \(41.66\%\), O: \(54.87\%\), H: \(3.47\%\) d. H\(_{2}\)O\(_{2}\): H: \(5.94\%\), O: \(94.06\%\) e. CaH\(_{2}\): Ca: \(95.25\%\), H: \(4.75\%\) f. K\(_{2}\)O: K: \(83.01\%\), O: \(16.99\%\)

Step-by-step solution

Determine the molar mass of ZnO

The molar mass of ZnO can be found by summing the molar mass of each element in the compound, which is Zinc (Zn) and Oxygen (O): Molar Mass of ZnO = (Molar Mass of Zn) + (Molar Mass of O) = \(65.38 + 16.00 = 81.38 \: g/mol\).

Determine the mass of each element in ZnO

The mass of Zn = Molar Mass of Zn = \(65.38 \: g\). The mass of O = Molar Mass of O = \(16.00 \: g\).

Calculate the percent by mass of each element in ZnO

Percent by mass of Zn = \(\frac{mass\: of\: Zn}{molar\: mass\: of\: ZnO} \times 100 =\frac{65.38}{81.38}\times 100 \approx 80.31\%\). Percent by mass of O = \(\frac{mass\: of\: O}{molar\: mass\: of\: ZnO} \times 100 =\frac{16.00}{81.38}\times 100 \approx 19.69\%\). b. \(\mathrm{Na}_{2} \mathrm{~S}\)

Determine the molar mass of \(\mathrm{Na}_{2} \mathrm{~S}\)

Molar Mass of \(\mathrm{Na}_{2} \mathrm{~S}\) = (2 * Molar Mass of Na) + (Molar Mass of S) = \(2\times 22.99 + 32.06 = 78.04 \: g/mol\).

Determine the mass of each element in \(\mathrm{Na}_{2} \mathrm{~S}\)

The mass of Na = 2 * Molar Mass of Na = \(2 \times 22.99 = 45.98 \: g\). The mass of S = Molar Mass of S = \(32.06 \: g\).

Calculate the percent by mass of each element in \(\mathrm{Na}_{2} \mathrm{~S}\)

Percent by mass of Na = \(\frac{mass\: of\: Na}{molar\: mass\: of\: Na_{2}S} \times 100 =\frac{45.98}{78.04}\times 100 \approx 58.93\%\). Percent by mass of S = \(\frac{mass\: of\: S}{molar\: mass\: of\: Na_{2}S} \times 100 =\frac{32.06}{78.04}\times 100 \approx 41.07\%\). c. \(\mathrm{Mg}(\mathrm{OH})_{2}\)

Determine the molar mass of \(\mathrm{Mg}(\mathrm{OH})_{2}\)

Molar Mass of \(\mathrm{Mg(OH)}_{2}\) = (Molar Mass of Mg) + (2 * Molar Mass of O) + (2 * Molar Mass of H) = \(24.31 + 2\times 16.00 + 2\times 1.01 = 58.33 \: g/mol\).

Determine the mass of each element in \(\mathrm{Mg}(\mathrm{OH})_{2}\)

The mass of Mg = Molar Mass of Mg = \(24.31 \: g\). The mass of O = 2 * Molar Mass of O = \(2\times 16.00=32.00 \: g\). The mass of H = 2 * Molar Mass of H = \(2\times 1.01 = 2.02 \: g\).

Calculate the percent by mass of each element in \(\mathrm{Mg}(\mathrm{OH})_{2}\)

Percent by mass of Mg = \(\frac{mass\: of\: Mg}{molar\: mass\: of\: Mg(OH)_{2}} \times 100 =\frac{24.31}{58.33}\times 100 \approx 41.66\%\). Percent by mass of O = \(\frac{mass\: of\: O}{molar\: mass\: of\: Mg(OH)_{2}} \times 100 =\frac{32.00}{58.33}\times 100 \approx 54.87\%\). Percent by mass of H = \(\frac{mass\: of\: H}{molar\: mass\: of\: Mg(OH)_{2}} \times 100 =\frac{2.02}{58.33}\times 100 \approx 3.47\%\). d. \(\mathrm{H}_{2} \mathrm{O}_{2}\)

Determine the molar mass of \(\mathrm{H}_{2} \mathrm{O}_{2}\)

Molar Mass of \(\mathrm{H}_{2} \mathrm{O}_{2}\) = (2 * Molar Mass of H) + (2 * Molar Mass of O) = \(2\times 1.01 + 2\times 16.00 = 34.02 \: g/mol\).

Determine the mass of each element in \(\mathrm{H}_{2} \mathrm{O}_{2}\)

The mass of H = 2 * Molar Mass of H = \(2\times 1.01 = 2.02 \: g\). The mass of O = 2 * Molar Mass of O = \(2\times 16.00=32.00 \: g\).

Calculate the percent by mass of each element in \(\mathrm{H}_{2} \mathrm{O}_{2}\)

Percent by mass of H = \(\frac{mass\: of\: H}{molar\: mass\: of\: H_{2}O_{2}} \times 100 =\frac{2.02}{34.02}\times 100 \approx 5.94\%\). Percent by mass of O = \(\frac{mass\: of\: O}{molar\: mass\: of\: H_{2}O_{2}} \times 100 =\frac{32.00}{34.02}\times 100 \approx 94.06\%\). e. \(\mathrm{CaH}_{2}\)

Determine the molar mass of \(\mathrm{CaH}_{2}\)

Molar Mass of \(\mathrm{CaH}_{2}\) = (Molar Mass of Ca) + (2 * Molar Mass of H) = \(40.08 + 2\times 1.01 = 42.10 \: g/mol\).

Determine the mass of each element in \(\mathrm{CaH}_{2}\)

The mass of Ca = Molar Mass of Ca = \(40.08 \: g\). The mass of H = 2 * Molar Mass of H = \(2\times 1.01 = 2.02 \: g\).

Calculate the percent by mass of each element in \(\mathrm{CaH}_{2}\)

Percent by mass of Ca = \(\frac{mass\: of\: Ca}{molar\: mass\: of\: CaH_{2}} \times 100 =\frac{40.08}{42.10}\times 100 \approx 95.25\%\). Percent by mass of H = \(\frac{mass\: of\: H}{molar\: mass\: of\: CaH_{2}} \times 100 =\frac{2.02}{42.10}\times 100 \approx 4.75\%\). f. \(\mathrm{K}_{2} \mathrm{O}\)

Determine the molar mass of \(\mathrm{K}_{2} \mathrm{O}\)

Molar Mass of \(\mathrm{K}_{2} \mathrm{O}\) = (2 * Molar Mass of K) + (Molar Mass of O) = \(2\times 39.10 + 16.00 = 94.20 \: g/mol\).

Determine the mass of each element in \(\mathrm{K}_{2} \mathrm{O}\)

The mass of K = 2 * Molar Mass of K = \(2\times 39.10 = 78.20 \: g\). The mass of O = Molar Mass of O = \(16.00 \: g\).

Calculate the percent by mass of each element in \(\mathrm{K}_{2} \mathrm{O}\)

Percent by mass of K = \(\frac{mass\: of\: K}{molar\: mass\: of\: K_{2}O} \times 100 =\frac{78.20}{94.20}\times 100 \approx 83.01\%\). Percent by mass of O = \(\frac{mass\: of\: O}{molar\: mass\: of\: K_{2}O} \times 100 =\frac{16.00}{94.20}\times 100 \approx 16.99\%\).

Key concepts

Molar Mass Calculation

Molar mass calculation is a fundamental step in many chemical calculations, including determining the percent by mass of elements in compounds. Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (\[ g/mol \]). To calculate the molar mass, sum up the atomic masses of all atoms present in the molecular formula of a compound. For instance, in zinc oxide (\( \text{ZnO} \)), the molar mass is computed by adding the atomic mass of zinc (\( 65.38 \ g/mol \)) and oxygen (\( 16.00 \ g/mol \)) to get a total of \( 81.38 \ g/mol \).

These values are derived from the periodic table where each element’s atomic mass is listed, often rounding to the nearest hundredth for precision. Molar mass is crucial for converting between grams and moles in stoichiometric calculations.

Chemical Composition

The chemical composition of a substance tells us which elements are present and in what ratio. Understanding this ratio is essential for various calculations, including percent by mass. The chemical formula lets us see the number of each type of atom in a compound.

For instance, in sodium sulfide (\( \text{Na}_{2} ext{S} \)), there are two sodium atoms and one sulfur atom. Knowing the chemical composition helps when determining the mass contribution of each element to the whole compound. This comprises part of the process for deriving percent by mass, important for analyzing how components contribute to a chemical's properties.

Elemental Analysis

Elemental analysis is the quantitative determination of elements within a compound. This process helps in confirming the chemical composition. By performing elemental analysis, chemists can validate the ratio of elements as presented in a compound's formula.

For magnesium hydroxide (\( \text{Mg(OH)}_{2} \)), an elemental analysis would confirm that one magnesium, two oxygen, and two hydrogen atoms are present. Elemental analysis can be a step in quality control, ensuring compounds are synthesized correctly. Understanding and applying elemental analysis is essential to verify empirical and molecular formulas obtained during chemical reactions.

Molecular Structure

The molecular structure refers to the specific arrangement of atoms within a molecule. This structure influences a compound’s physical and chemical properties, such as solubility and reactivity.

When considering hydrogen peroxide (\( \text{H}_{2} ext{O}_{2} \)), the structure with a bent shape enables it to act as an effective oxidizing agent. Structural knowledge assists in theoretical and experimental chemistry, where it's critical to predict behavior. Although determining percent by mass focuses more on quantitative data, recognizing molecular structure helps understand or predict interaction tendencies and reaction outcomes.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It uses the law of conservation of mass, ensuring that matter is neither created nor destroyed in a reaction.

During stoichiometric calculations, such as those required for calcium hydride (\( \text{CaH}_{2} \)), ratios derived from balanced chemical equations guide the transformation of mass from reactants to products. Stoichiometry is crucial for scaling reactions, calculating yields, and planning reactions. By applying stoichiometry, chemists can determine how much of each reactant is needed and predict the amounts of products formed, linking the theoretical to practical lab work.