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Chapter 7: Problem 15

Calculate the molar mass for each of the following: a. \(\mathrm{AlF}_{3}\) b. \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}\) c. \(\mathrm{SnF}_{2}\)

Short Answer

Expert verified
a. 83.98 g/mol, b. 98.96 g/mol, c. 156.71 g/mol

Step by step solution

01

Identify Atomic Masses

Gather the atomic masses of the individual elements from the periodic table:- Aluminum (Al): 26.98 g/mol- Fluorine (F): 19.00 g/mol- Carbon (C): 12.01 g/mol- Hydrogen (H): 1.01 g/mol- Chlorine (Cl): 35.45 g/mol- Tin (Sn): 118.71 g/mol
02

Calculate Molar Mass of \(\mathrm{AlF}_3\)

Use the formula to sum the products of each element's atomic mass and its subscript in the compound. For \(\mathrm{AlF}_3\):\[ M(\mathrm{AlF}_3) = 1 \times M(\mathrm{Al}) + 3 \times M(\mathrm{F}) \]\[ = 1 \times 26.98 \text{ g/mol} + 3 \times 19.00 \text{ g/mol} \]\[ = 26.98 + 57.00 \]\[ = 83.98 \text{ g/mol} \]
03

Calculate Molar Mass of \(\mathrm{C}_2 \mathrm{H}_4 \mathrm{Cl}_2\)

Sum the products of each element's atomic mass and its subscript in the compound. For \(\mathrm{C}_2 \mathrm{H}_4 \mathrm{Cl}_2\):\[ M(\mathrm{C}_2 \mathrm{H}_4 \mathrm{Cl}_2) = 2 \times M(\mathrm{C}) + 4 \times M(\mathrm{H}) + 2 \times M(\mathrm{Cl}) \]\[ = 2 \times 12.01 \text{ g/mol} + 4 \times 1.01 \text{ g/mol} + 2 \times 35.45 \text{ g/mol} \]\[ = 24.02 + 4.04 + 70.90 \]\[ = 98.96 \text{ g/mol} \]
04

Calculate Molar Mass of \(\mathrm{SnF}_2\)

Sum the products of each element's atomic mass and its subscript in the compound. For \(\mathrm{SnF}_2\):\[ M(\mathrm{SnF}_2) = 1 \times M(\mathrm{Sn}) + 2 \times M(\mathrm{F}) \]\[ = 1 \times 118.71 \text{ g/mol} + 2 \times 19.00 \text{ g/mol} \]\[ = 118.71 + 38.00 \]\[ = 156.71 \text{ g/mol} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atomic Mass
The atomic mass is the mass of a single atom of a chemical element. It's usually expressed in unified atomic mass units (u) or grams per mole (g/mol). In the periodic table, you can find the atomic mass listed under each element symbol. For instance, aluminum (Al) has an atomic mass of 26.98 g/mol, while fluorine (F) has an atomic mass of 19.00 g/mol.
The atomic mass is an essential concept in chemistry because it allows us to quantify the amount of matter. When calculating the molar mass of a compound, knowing the atomic masses of the comprising elements is the first step.
In our exercise, we gathered the atomic masses for the following elements:
  • Aluminum (Al): 26.98 g/mol
  • Fluorine (F): 19.00 g/mol
  • Carbon (C): 12.01 g/mol
  • Hydrogen (H): 1.01 g/mol
  • Chlorine (Cl): 35.45 g/mol
  • Tin (Sn): 118.71 g/mol
Compound Composition
Understanding a compound's composition means knowing how many atoms of each element are present in the molecule. Each element's amount is usually indicated by a subscript in the chemical formula.
Take the compound \(\mathrm{AlF}_3\) for example:
  • It contains one aluminum (Al) atom.
  • It contains three fluorine (F) atoms.


To find the compound's molar mass, we multiply the atomic mass of each element by the number of atoms present in the formula.
For \(\mathrm{AlF}_3\): \[ M(\mathrm{AlF}_3) = 1 \times 26.98 \text{ g/mol} + 3 \times 19.00 \text{ g/mol} = 83.98 \text{ g/mol} \]

Similarly, for \(\mathrm{C}_2 \mathrm{H}_4 \mathrm{Cl}_2\), breaking down the formula shows:
  • 2 carbon (C) atoms.
  • 4 hydrogen (H) atoms.
  • 2 chlorine (Cl) atoms.
Molecular Weight Determination
Molecular weight, also known as molar mass, is the sum of all the atomic masses in a molecule. It is critical in stoichiometry, which is the calculation of reactants and products in chemical reactions. To calculate the molar mass, follow these steps:

  • Identify the compound's chemical formula.
  • Find the atomic masses of all elements in the compound (use the periodic table).
  • Multiply the atomic mass of each element by its subscript in the chemical formula.
  • Sum the results to get the compound's total molar mass.

For example, to find the molecular weight of \(\mathrm{SnF}_2\):
First, we note it contains:
  • 1 tin (Sn) atom.
  • 2 fluorine (F) atoms.

Then use the given atomic masses:
\[ M(\mathrm{SnF}_2) = 1 \times 118.71 \text{ g/mol} + 2 \times 19.00 \text{ g/mol} = 156.71 \text{ g/mol} \]

Understanding how to determine molecular weight is fundamental for solving chemistry problems related to stoichiometry and chemical composition.

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Most popular questions from this chapter

Calculate the mass percent composition for each of the following compounds: (7.4) a. \(\mathrm{K}_{2} \mathrm{CrO}_{4}\) b. \(\mathrm{Al}\left(\mathrm{HCO}_{3}\right)_{3}\) c. \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\)

Calculate the empirical formula for each of the following compounds: (7.4) a. \(2.20 \mathrm{~g}\) of \(\mathrm{S}\) and \(7.81 \mathrm{~g}\) of \(\mathrm{F}\) b. \(6.35 \mathrm{~g}\) of \(\mathrm{Ag}, 0.825 \mathrm{~g}\) of \(\mathrm{N}\), and \(2.83 \mathrm{~g}\) of \(\mathrm{O}\) c. \(43.6 \% \mathrm{P}\) and \(56.4 \% \mathrm{O}\) d. \(22.1 \% \mathrm{Al}, 25.4 \% \mathrm{P}\), and \(52.5 \% \mathrm{O}\)

Caffeine has an empirical formula of \(\mathrm{C}_{4} \mathrm{H}_{5} \mathrm{~N}_{2} \mathrm{O} .\) If it has an experimental molar mass of \(194 \mathrm{~g}\), what is the molecular formula of caffeine?

Calculate the empirical formula for each of the following: a. \(2.90 \mathrm{~g}\) of \(\mathrm{Ag}\) and \(0.430 \mathrm{~g}\) of \(\mathrm{S}\) b. \(2.22 \mathrm{~g}\) of \(\mathrm{Na}\) and \(0.774 \mathrm{~g}\) of \(\mathrm{O}\) c. \(2.11 \mathrm{~g}\) of \(\mathrm{Na}, 0.0900 \mathrm{~g}\) of \(\mathrm{H}, 2.94 \mathrm{~g}\) of \(\mathrm{S}\), and \(5.86 \mathrm{~g}\) of \(\mathrm{O}\) d. \(5.52 \mathrm{~g}\) of \(\mathrm{K}, 1.45 \mathrm{~g}\) of \(\mathrm{P}\), and \(3.00 \mathrm{~g}\) of \(\mathrm{O}\)

Calculate the molar mass for each of the following: a. \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{4}\) b. \(\mathrm{Ga}_{2}\left(\mathrm{CO}_{3}\right)_{3}\) c. \(\mathrm{KBrO}_{4}\)
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