Question

How many grams are in a mole of each of the following substances? (a) \(\mathrm{Ti}\) (c) \(\mathrm{Hg}\) (b) \(\mathrm{Br}_{2}\) (d) \(\mathrm{H}_{2} \mathrm{O}\)

Short answer

(a) Ti: 47.87 g/mol, (b) Hg: 200.59 g/mol, (c) Br2: 159.80 g/mol, (d) H2O: 18.02 g/mol.

Step-by-step solution

Understanding Molar Mass

To find out how many grams are in a mole of a substance, we need to know its molar mass. This value corresponds to the atomic or molecular weight of the substance in grams per mole (g/mol). The molar mass can be directly obtained from the periodic table for elements and by summing the atomic masses for compounds.

Finding Molar Mass of Titanium (Ti)

Titanium ( Ti ) is a chemical element. From the periodic table, the atomic mass of Ti is approximately 47.87 g/mol. Therefore, the molar mass of Ti is 47.87 grams per mole.

Finding Molar Mass of Mercury (Hg)

Mercury ( Hg ) is also a chemical element. Its atomic mass given on the periodic table is about 200.59 g/mol, which means the molar mass of Hg is 200.59 grams per mole.

Finding Molar Mass of Bromine (Br extsubscript{2})

Bromine exists as a diatomic molecule, Br_2 . The atomic mass of Br is approximately 79.90 g/mol. Thus, the molar mass of Br_2 is calculated as follows: 2 imes 79.90 = 159.80 , so Br_2 has a molar mass of 159.80 grams per mole.

Finding Molar Mass of Water ( H extsubscript{2} O)

Water ( H_2O ) is composed of two hydrogen atoms and one oxygen atom. The atomic mass of hydrogen ( H ) is approximately 1.01 g/mol and for oxygen ( O ) it is about 16.00 g/mol. Thus, the molar mass is calculated by: 2 imes 1.01 + 16.00 = 18.02 . Hence, H_2O has a molar mass of 18.02 grams per mole.

Key concepts

Atomic Mass

When we talk about atomic mass, we refer to the mass of a single atom of an element, usually expressed in atomic mass units (amu). This number indicates the combined total of protons and neutrons in the atom's nucleus, with electrons having a negligible mass. To be more precise, one atomic mass unit is defined as one-twelfth of the mass of a carbon-12 atom.

In practical terms, atomic mass helps us understand how much one mole of an element weighs when calculated in grams, which is reflected on the periodic table. Molar mass, which is often synonymous with molecular weight, combines the individual atomic masses of all atoms in a molecule to understand how much a mole of that compound weighs.

Understanding atomic mass is crucial for comparing the different masses of elements and their isotopes, which can slightly vary due to differences in neutron numbers.

• Atomic mass is key for calculating the molar mass of elements and compounds.
• It helps in understanding chemical reactions, as reactants are often measured in terms of moles.

Periodic Table

The periodic table is a critical tool in chemistry that organizes all known chemical elements in a systematic and informative array. Each element included in the periodic table is organized based on its atomic number, which is the number of protons in its nucleus, and this, directly relates to its atomic mass.

Every entry on the periodic table provides essential information, including the element's chemical symbol, atomic number, and atomic mass. The periodic table also gives insights into the element's properties, such as its metal, metalloid, or non-metal classification, and its typical reactive nature corresponding to its group and period placement.

The periodic table is crucial for anyone working with chemical calculations, as it provides quick access to atomic masses needed for calculating molar masses and thus, the amount of an element or compound contained in a mole.

• Elements are arranged by increasing atomic number, revealing patterns in their properties.
• Quick reference to atomic masses aids in calculating how many grams per mole for reactions.

Grams per Mole

Grams per mole, often denoted as g/mol, is a unit of measurement that describes the mass of one mole of a substance. This is crucial when it comes to calculations that involve converting between the number of particles and the amount of substance characterized as weight in a laboratory setting.

Converting grams to moles is done by using the molar mass of a substance, which is usually found using the periodic table. For instance, if you know the mass of a chemical sample in grams, knowing its molar mass lets you calculate exactly how many moles of the chemical you have. This is extremely useful in stoichiometry, the calculation of reactants and products in chemical reactions.

This concept emphasizes how knowing the molar mass allows chemists to scale the reactions up or down depending on the quantities of reactants or products required.

• Allows conversion between weight and amount for various elements and compounds.
• Central to stoichiometry in balancing chemical equations and scale-up reactions.