Question

Determine the molecular formulas to which the following empirical formulas and molar masses pertain. a. \(\mathrm{SNH}(188.35 \mathrm{~g} / \mathrm{mol})\) b. \(\mathrm{NPCl}_{2}(347.64 \mathrm{~g} / \mathrm{mol})\) c. \(\mathrm{CoC}_{4} \mathrm{O}_{4}(341.94 \mathrm{~g} / \mathrm{mol})\) d. \(\mathrm{SN}(184.32 \mathrm{~g} / \mathrm{mol})\)

Short answer

The molecular formulas for the given empirical formulas and molar masses are: a. \(\mathrm{(SNH)_{4}}\) b. \(\mathrm{(NPCl_{2})_{3}}\) c. \(\mathrm{(CoC}_{4} \mathrm{O}_{4})_{2}\) d. \(\mathrm{(SN)_{4}}\)

Step-by-step solution

Calculate the molar mass of the empirical formula

Calculate the molar mass for the empirical formula \(\mathrm{SNH}\). S: 32.07 g/mol N: 14.01 g/mol H: 1.01 g/mol Molar mass of \(\mathrm{SNH}\) = (32.07 + 14.01 + 1.01) g/mol = 47.09 g/mol.

Determine the integer n

Divide the given molar mass by the empirical formula's molar mass to find n: n = (188.35 g/mol) / (47.09 g/mol) ≈ 4

Calculate the molecular formula

Multiply the empirical formula by the integer n: Molecular formula: \(\mathrm{(SNH)_{4}}\) b. \(\mathrm{NPCl}_{2}(347.64 \mathrm{~g/mol})\)

Calculate the molar mass of the empirical formula

Calculate the molar mass for the empirical formula \(\mathrm{NPCl}_{2}\). N: 14.01 g/mol P: 30.97 g/mol Cl: 35.45 g/mol Molar mass of \(\mathrm{NPCl}_{2}\) = (14.01 + 30.97 + 35.45*2) g/mol = 116.33 g/mol.

Determine the integer n

Divide the given molar mass by the empirical formula's molar mass to find n: n = (347.64 g/mol) / (116.33 g/mol) ≈ 3

Calculate the molecular formula

Multiply the empirical formula by the integer n: Molecular formula: \(\mathrm{(NPCl_{2})_{3}}\) c. \(\mathrm{CoC}_{4}\mathrm{O}_{4}(341.94 \mathrm{~g/mol})\)

Calculate the molar mass of the empirical formula

Calculate the molar mass for the empirical formula \(\mathrm{CoC}_{4} \mathrm{O}_{4}\). Co: 58.93 g/mol C: 12.01 g/mol O: 16.00 g/mol Molar mass of \(\mathrm{CoC}_{4} \mathrm{O}_{4}\) = (58.93 + 12.01*4 + 16.00*4) g/mol = 170.97 g/mol.

Determine the integer n

Divide the given molar mass by the empirical formula's molar mass to find n: n = (341.94 g/mol) / (170.97 g/mol) ≈ 2

Calculate the molecular formula

Multiply the empirical formula by the integer n: Molecular formula: \(\mathrm{(CoC}_{4} \mathrm{O}_{4})_{2}\) d. \(\mathrm{SN}(184.32 \mathrm{~g/mol})\)

Calculate the molar mass of the empirical formula

Calculate the molar mass for the empirical formula \(\mathrm{SN}\). S: 32.07 g/mol N: 14.01 g/mol Molar mass of \(\mathrm{SN}\) = (32.07 + 14.01) g/mol = 46.08 g/mol.

Determine the integer n

Divide the given molar mass by the empirical formula's molar mass to find n: n = (184.32 g/mol) / (46.08 g/mol) ≈ 4

Calculate the molecular formula

Multiply the empirical formula by the integer n: Molecular formula: \(\mathrm{(SN)_{4}}\)

Key concepts

Empirical Formula

The empirical formula of a chemical compound offers us the simplest whole-number ratio of the atoms present. It's like a basic recipe showcasing just the primary proportions of each atom type, without indicating the exact number of each atom as found in reality. The empirical formula is foundational, especially when moving to determine the molecular formula, which provides the detailed number of each type of atom present in a molecule.

Consider the empirical formula

• Example: For SNH, each unit contains one sulfur, one nitrogen, and one hydrogen:
  • S: 32.07 g/mol
  • N: 14.01 g/mol
  • H: 1.01 g/mol

It tells us that these elements are present in a 1:1:1 ratio. However, this formula alone may not be enough to determine how these ratios come together to form the entire compound. The next step is to explore the compound's molar mass to determine its true molecular structure.

Molar Mass

Molar mass is a key player in chemical calculations, as it denotes the mass of one mole of a substance. It is determined by summing up the atomic masses of each element in the compound according to the empirical formula. Molar mass acts like a bridge between the micro world of atoms and the macro world of grams that we measure in the laboratory.

To calculate the molar mass, collect the atomic weights from the periodic table.

• Example: For the empirical formula NPCl₂, each atom’s mass is summed:
  • N: 14.01 g/mol
  • P: 30.97 g/mol
  • Cl: 35.45 g/mol (for two atoms)
  Molar mass = 14.01 + 30.97 + (35.45 * 2) = 116.33 g/mol

The molar mass provides the magic number needed in further calculations to find the molecular formula, offering insight into how many empirical formula units make up the molecule.

Chemical Composition

Chemical composition is the recipe that forms the substance, describing the types and numbers of each atom in a compound. Understanding the composition involves determining which atoms are present and in what ratios they combine. It's akin to figuring out the necessary ingredients and their proportions while baking a cake.

For chemistry enthusiasts, knowing the chemical composition is crucial, as it allows for the determination of how substances react, combine, and interact with one another. Consider a compound's empirical formula as a preliminary step in understanding its composition. While the empirical formula gives a simplified ratio, the molecular formula reveals the actual amounts present in a molecule.

For instance,

• CoC₄ O₄ suggests that cobalt, carbon, and oxygen are in the ratio of 1:4:4, but when scaled correctly using its molar mass, more secretive details about the compound's true chemical structure are unraveled.

Understanding these mixtures is vital for manipulating these substances in real-world applications, from industrial chemistry to biochemistry.

Chemical Calculations

Chemical calculations are essential for chemists to translate the language of chemicals into quantifiable data. They often involve determining the molecular formula from an empirical one, using mathematics to analyze and predict chemical behaviors.

The journey of these calculations starts with the empirical formula and molar mass. By dividing the given molar mass by the calculated empirical formula mass, you can find an integer, often called 'n.' This integer tells you how many times to multiply each element in the empirical formula to get the molecular formula.

• For instance, if the molar mass of SN is given as 184.32 g/mol, with an empirical mass of 46.08 g/mol:
  • n = 184.32 / 46.08 ≈ 4, resulting in a molecular formula of (SN)₄

Chemical calculations allow chemists to explore molecular realities and analyze the implications of chemical creations, thus perfecting formulations for diverse uses.