Question

Calculate the percent composition by mass of these compounds: (a) \(\mathrm{ZnCl}_{2}\) (d) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) (b) \(\mathrm{NH}_{4} \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) (e) \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) (c) \(\mathrm{MgP}_{2} \mathrm{O}_{7}\) (f) \(\mathrm{ICl}_{3}\)

Short answer

ZnCl2: Zn = 47.98%, Cl = 52.02%. (NH4)2SO4: N = 21.22%, H = 6.12%, S = 24.26%, O = 48.39%. NH4C2H3O2: N = 18.18%, H = 9.18%, C = 31.18%, O = 41.46%. Fe(NO3)3: Fe = 23.10%, N = 17.38%, O = 59.52%. MgP2O7: Mg = 10.94%, P = 27.88%, O = 50.34%. ICl3: I = 54.41%, Cl = 45.59%.

Step-by-step solution

- Calculate Molar Mass

First, find the molar mass of each compound by summing the atomic masses of all atoms in the formula. Use the periodic table for atomic masses.

- Find Mass Percent of Each Element

For each element in the compound, divide the total mass of the element (its atomic mass multiplied by the number of atoms) by the total molar mass of the compound and multiply by 100 to find the percent composition.

- Calculate for \(\text{ZnCl}_2\)

Molar mass: \(\text{Zn} = 65.38\) g/mol, \(\text{Cl} = 35.45\) g/mol \[ \text{Molar mass of ZnCl}_2 = 65.38 + 2(35.45) = 136.28 \text{ g/mol} \] Percent composition: \[ \text{Zn percent} = \frac{65.38}{136.28} \times 100 = 47.98\% \] \[ \text{Cl percent} = \frac{2(35.45)}{136.28} \times 100 = 52.02\% \]

- Calculate for \(\text{(NH}_4\text{)}_2 \text{SO}_4\)

Molar mass: \(\text{N} = 14.01, \text{H} = 1.01, \text{S} = 32.07, \text{O} = 16.00 \) g/mol \[ \text{Molar mass of (NH}_4\text{)}_2 \text{SO}_4 = 2(14.01) + 8(1.01) + 32.07 + 4(16.00) = 132.14 \text{ g/mol} \] Percent composition: \[ \text{N percent} = \frac{2(14.01)}{132.14} \times 100 = 21.22\% \] \[ \text{H percent} = \frac{8(1.01)}{132.14} \times 100 = 6.12\% \] \[ \text{S percent} = \frac{32.07}{132.14} \times 100 = 24.26\%\] \[ \text{O percent} = \frac{4(16.00)}{132.14} \times 100 = 48.39\% \]

- Calculate for \(\text{NH}_4 \text{C}_2 \text{H}_3 \text{O}_2\)

Molar mass: \(\text{N} = 14.01, \text{H} = 1.01, \text{C} = 12.01, \text{O} = 16.00 \) g/mol \[ \text{Molar mass of NH}_4 \text{C}_2\text{H}_3 \text{O}_2 = 14.01 + 7(1.01) + 2(12.01) + 2(16.00) = 77.08 \text{ g/mol}\] Percent composition: \[ \text{N percent} = \frac{14.01}{77.08} \times 100 = 18.18\% \] \[ \text{H percent} = \frac{7(1.01)}{77.08} \times 100 = 9.18\% \] \[ \text{C percent} = \frac{2(12.01)}{77.08} \times 100 = 31.18\% \] \[ \text{O percent} = \frac{2(16.00)}{77.08} \times 100 = 41.46\% \]

- Calculate for \(\text{Fe(NO}_3\text{)}_3\)

Molar mass: \(\text{Fe} = 55.85, \text{N} = 14.01, \text{O} = 16.00 \) g/mol \[ \text{Molar mass of Fe(NO}_3\text{)}_3 = 55.85 + 3(14.01 + 3(16.00)) = 241.86 \text{ g/mol}\] Percent composition: \[ \text{Fe percent} = \frac{55.85}{241.86} \times 100 = 23.10\% \] \[ \text{N percent} = \frac{3(14.01)}{241.86} \times 100 = 17.38\% \] \[ \text{O percent} = \frac{9(16.00)}{241.86} \times 100 = 59.52\% \]

- Calculate for \(\text{MgP}_2\text{O}_7\)

Molar mass: \(\text{Mg} = 24.31, \text{P} = 30.97, \text{O} = 16.00 \) g/mol \[ \text{Molar mass of MgP}_2\text{O}_7 = 24.31 + 2(30.97) + 7(16.00) = 222.22 \text{ g/mol} \] Percent composition: \[ \text{Mg percent} = \frac{24.31}{222.22} \times 100 = 10.94\% \] \[ \text{P percent} = \frac{2(30.97)}{222.22} \times 100 = 27.88\% \] \[ \text{O percent} = \frac{7(16.00)}{222.22} \times 100 = 50.34\% \]

- Calculate for \(\text{ICl}_3\)

Molar mass: \(\text{I} = 126.90, \text{Cl} = 35.45 \) g/mol \[ \text{Molar mass of ICl}_3 = 126.90 + 3(35.45) = 233.25 \text{ g/mol}\] Percent composition: \[ \text{I percent} = \frac{126.90}{233.25} \times 100 = 54.41\% \] \[ \text{Cl percent} = \frac{3(35.45)}{233.25} \times 100 = 45.59\% \]

Key concepts

molar mass calculation

Molar mass is a crucial concept in chemistry that helps us understand the mass of one mole of a given substance, typically measured in grams per mole (g/mol). To calculate the molar mass of a chemical compound, you simply sum the atomic masses of all the atoms present in the molecule based on their proportions. For instance, in \(\text{ZnCl}_2\), we use the atomic mass of Zinc (Zn), which is 65.38 g/mol, and Chlorine (Cl), which is 35.45 g/mol. We then add these values together as shown below:
\[ \text{Molar mass of ZnCl}_2 = 65.38 + 2(35.45) = 136.28 \text{ g/mol} \]
Remember to always refer to the periodic table to find the atomic masses of the elements involved.

chemical compounds

Chemical compounds are substances formed when two or more different types of atoms bind together. They can exist in different forms such as molecular or ionic compounds. For example:

• \(\text{ZnCl}_2\) is a molecular compound consisting of Zinc (Zn) and Chlorine (Cl) atoms.
• \(\text{NH}_4\text{C}_2\text{H}_3\text{O}_2\) is also a molecular compound consisting of Nitrogen (N), Hydrogen (H), Carbon (C), and Oxygen (O) atoms.

Understanding the formula of a compound is fundamental in identifying the elements and their quantities within the molecule. It's crucial to comprehend how these elements combine to form the compound to progress with further calculations such as molar mass and percent composition.

percent composition calculation

The percent composition by mass of a compound indicates the relative amounts of each element in that compound. To find the percent composition, follow these steps:

1. Calculate the molar mass of the compound.
2. For each element, divide the total mass of that element in the formula by the molar mass of the compound.
3. Multiply the result by 100 to get the percentage.

For example, for \(\text{ZnCl}_2\):
\[ \text{Zn percent} = \frac{65.38}{136.28} \times 100 = 47.98\text{%} \]
Percent composition helps in understanding the proportionate presence of each element, which is essential for both practical applications and theoretical studies in chemistry.

atomic masses

Atomic mass is a fundamental property of an element and can be found on the periodic table. It represents the mass of a single atom, usually measured in atomic mass units (amu) or daltons (Da). The precise value is essential in many calculations, such as molar mass and percent composition. For example:

• Zinc (Zn) has an atomic mass of 65.38 g/mol.
• Nitrogen (N) has an atomic mass of 14.01 g/mol.
• Chlorine (Cl) has an atomic mass of 35.45 g/mol.

Using these atomic masses aptly in calculations will ensure correct and precise results, helping in deeper understanding and practical application in chemistry.