Question

Determine the chemical formula of each compound and refer to the formula to calculate the mass percent composition of each constituent element. (a) nitrogen triiodide (b) xenon tetrafluoride (c) phosphorus trichloride (d) carbon monoxide

Short answer

The mass percent compositions are: (a) Nitrogen in NI3: 3.55%, Iodine in NI3: 96.45%; (b) Xenon in XeF4: 63.35%, Fluorine in XeF4: 36.65%; (c) Phosphorus in PCl3: 22.55%, Chlorine in PCl3: 77.45%; (d) Carbon in CO: 42.88%, Oxygen in CO: 57.12%.

Step-by-step solution

Identify the Chemical Formulas

To calculate mass percent compositions, we need to know the chemical formulas of the compounds. (a) Nitrogen triiodide is NI3, where nitrogen (N) bonds with three iodine (I) atoms. (b) Xenon tetrafluoride is XeF4, where xenon (Xe) bonds with four fluorine (F) atoms. (c) Phosphorus trichloride is PCl3, where phosphorus (P) bonds with three chlorine (Cl) atoms. (d) Carbon monoxide is CO, where carbon (C) bonds with one oxygen (O) atom.

Calculate Molar Mass of Each Compound

Look up the atomic masses on the periodic table for each element in the compounds. Add them up to find the molar mass of each compound. For NI3: (1×N) + (3×I), for XeF4: (1×Xe) + (4×F), for PCl3: (1×P) + (3×Cl), and for CO: (1×C) + (1×O).

Compute Mass Percent Compositions

Divide the total mass of each element within a compound by the total molar mass of the compound and multiply by 100 to find the mass percent composition. Perform this calculation for each element in the compounds NI3, XeF4, PCl3, and CO.

Mass Percent Composition for Nitrogen Triiodide (NI3)

Calculate the molar mass: (1×14.01) + (3×126.90) = 394.71 g/mol. Nitrogen percentage: (14.01/394.71)×100 = 3.55%. Iodine percentage: (3×126.90/394.71)×100 = 96.45%.

Mass Percent Composition for Xenon Tetrafluoride (XeF4)

Calculate the molar mass: (1×131.29) + (4×19.00) = 207.29 g/mol. Xenon percentage: (131.29/207.29)×100 = 63.35%. Fluorine percentage: (4×19.00/207.29)×100 = 36.65%.

Mass Percent Composition for Phosphorus Trichloride (PCl3)

Calculate the molar mass: (1×30.97) + (3×35.45) = 137.32 g/mol. Phosphorus percentage: (30.97/137.32)×100 = 22.55%. Chlorine percentage: (3×35.45/137.32)×100 = 77.45%.

Mass Percent Composition for Carbon Monoxide (CO)

Calculate the molar mass: (1×12.01) + (1×16.00) = 28.01 g/mol. Carbon percentage: (12.01/28.01)×100 = 42.88%. Oxygen percentage: (16.00/28.01)×100 = 57.12%.

Key concepts

Chemical Formula

Understanding the chemical formula of a substance is foundational in chemistry. A chemical formula indicates the types and numbers of atoms that compose a molecule of a substance.
For example, for nitrogen triiodide (NI3), the formula indicates one nitrogen atom (N) and three iodine atoms (I). Similarly, xenon tetrafluoride (XeF4) consists of one xenon atom (Xe) and four fluorine atoms (F).
Getting the formula correct is crucial because it sets the stage for all further calculations, including determining the molar mass and the compound's percent composition.

Molar Mass Calculation

The molar mass of a substance is the weight of 6.022 x 10²³ (Avogadro's number) particles (atoms, molecules, ions) of the substance and is usually expressed in grams per mole (g/mol).
To calculate the molar mass, sum the atomic masses of all atoms within the molecule. The atomic mass of each element is found on the periodic table and reflects the average mass of all the isotopes of that element.

Example Calculation

To illustrate, for carbon monoxide (CO), we take the atomic mass of carbon (12.01 g/mol) and add it to that of oxygen (16.00 g/mol), giving us a molar mass of 28.01 g/mol for CO. It's critical to ensure accuracy during this step since errors here will affect subsequent percent composition calculations.

Percent Composition Calculation

With the correct chemical formula and molar mass, we can calculate the percent composition, which gives us insight into the proportion of each element within the compound.
To perform this calculation, divide the total mass of each element (found by multiplying the atomic mass of the element by the number of atoms of that element in the molecule) by the molar mass of the entire compound, and then multiply by 100 to convert to a percentage.

Application of Percent Composition

This information can be quite useful, for instance, in determining the empirical formula of a compound or in stoichiometric calculations. It is also beneficial for comparing the relative amounts of elements in different compounds.

Stoichiometry

Stoichiometry is a section of chemistry that involves the quantitative relationships of the reactants and products in a chemical reaction. It is grounded on the law of conservation of mass and the concept of the mole.
Through stoichiometry, we can predict the amounts of products formed from a given quantity of reactants or the amounts of reactants needed to form a desired quantity of product.
Understanding percent composition is vital for stoichiometry because it helps us convert between masses of substances and moles, a key step for reacting quantities of reactants or products. As stoichiometry often requires exact quantities, having a firm grasp on all the underlying calculations ensures the best possible accuracy.