Question

Hydrogen gas reacts with each of the halogen elements to form the hydrogen halides (\(\mathrm{HF}, \mathrm{HCl}, \mathrm{HBr}, \mathrm{HI}\) ). Calculate the percent by mass of hydrogen in each of these compounds.

Short answer

The percent by mass of hydrogen in each hydrogen halide compound is: HF - 5% HCl - 2.74% HBr - 1.23% HI - 0.78%

Step-by-step solution

Calculate the molar mass of hydrogen

Calculate the molar mass of hydrogen (H), which is approximately 1 g/mol.

Calculate the molar mass of each halogen element

Determine the molar mass of each halogen element (F, Cl, Br, I) using the periodic table: F - 19 g/mol Cl - 35.5 g/mol Br - 80 g/mol I - 127 g/mol

Calculate the molar mass of each hydrogen halide compound

For each hydrogen halide compound, we will add the molar mass of hydrogen to the molar mass of the corresponding halogen element: HF - 1 g/mol (H) + 19 g/mol (F) = 20 g/mol HCl - 1 g/mol (H) + 35.5 g/mol (Cl) = 36.5 g/mol HBr - 1 g/mol (H) + 80 g/mol (Br) = 81 g/mol HI - 1 g/mol (H) + 127 g/mol (I) = 128 g/mol

Calculate the percent by mass of hydrogen in each compound

Divide the molar mass of hydrogen by the molar mass of each hydrogen halide compound and multiply by 100 to obtain the percentage: For HF: \(\frac{1 g/mol (H)}{20 g/mol (HF)} \times 100 = 5\%\) hydrogen by mass For HCl: \(\frac{1 g/mol (H)}{36.5 g/mol (HCl)} \times 100 \approx 2.74\%\) hydrogen by mass For HBr: \(\frac{1 g/mol (H)}{81 g/mol (HBr)} \times 100 \approx 1.23\%\) hydrogen by mass For HI: \(\frac{1 g/mol (H)}{128 g/mol (HI)} \times 100 \approx 0.78\%\) hydrogen by mass So, the percent by mass of hydrogen in each hydrogen halide compound is as follows: HF - 5% HCl - 2.74% HBr - 1.23% HI - 0.78%

Key concepts

Chemical Reactions

Chemical reactions are processes that result in the transformation of one set of chemical substances to another. These changes involve making or breaking of bonds between atoms. A key point to remember is that during a chemical reaction, the mass of the products equals the mass of the reactants. This is known as the Law of Conservation of Mass.

In the exercise, we are discussing a specific type of chemical reaction where hydrogen gas reacts with halogen elements to produce hydrogen halides. Hydrogen halides are binary compounds of hydrogen with halogens. These reactions are critical because they are broadly used in the chemical industry for synthesising various important compounds.

Molar Mass

Molar mass is a fundamental concept in chemistry, defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is equivalent to the atomic or molecular weight of a substance taken in grams. The molar mass provides a bridge between the mass of material and the amount of material (number of atoms, molecules, or ions).

To calculate the molar mass, the individual atomic masses of each atom in a compound must be considered, as seen in the exercise where the molar mass of hydrogen and the respective halogen were added together to form the molar mass of each hydrogen halide.

Stoichiometry

Stoichiometry is the part of chemistry which deals with the quantitative relationships that the reactants and products in a chemical reaction follow. It is based on the balanced chemical equation for any given reaction.

In this exercise, stoichiometry comes into play when determining the percent composition by mass. The main idea is to calculate the mass of each element in a compound and express it as a percentage of the total mass of the compound. Stoichiometry uses the concept of molar mass to convert between mass and moles, facilitating the calculation of the percent by mass of an element in a compound.

Hydrogen Halides

Hydrogen halides are a group of diatomic molecules formed by a covalent bond between hydrogen and a halogen atom — fluorine, chlorine, bromine, or iodine. Each of these molecules (HF, HCl, HBr, HI) possesses distinct physical and chemical properties which are widely utilized in various chemical reactions and applications.

When calculating the percent by mass of hydrogen in hydrogen halides, it's essential to recognize the different molar masses of the halogens contribute significantly to the overall molar mass of the compound, and thereby affect the percentage content of hydrogen. Although hydrogen's molar mass is quite small, its percentage by mass can vary widely depending on the heavier halogen to which it is bonded.