Question

Calculate the molar mass of the following substances. a. \(\mathrm{H}\) b. Q N \(\mathrm{N}\) c. \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\)

Short answer

The molar masses of the given substances are: a. H: 1 g/mol, b. N: 14 g/mol, and c. (NH4)2Cr2O7: 252 g/mol.

Step-by-step solution

a. Finding the molar mass of H

The given substance only contains hydrogen. To find the molar mass of hydrogen, we can directly check the periodic table. The atomic mass of hydrogen is approximately 1 g/mol. Thus, the molar mass of H is 1 g/mol.

b. Finding the molar mass of N

The given substance only contains nitrogen. To find the molar mass of nitrogen, we can directly check the periodic table. The atomic mass of nitrogen is approximately 14 g/mol. Thus, the molar mass of N is 14 g/mol.

c. Finding the molar mass of (NH4)2Cr2O7

To find the molar mass of (NH4)2Cr2O7, first, identify the elements and their atomic masses from the periodic table: - Hydrogen (H): 1 g/mol - Nitrogen (N): 14 g/mol - Chromium (Cr): 52 g/mol - Oxygen (O): 16 g/mol Now, multiply the atomic mass by the subscript of each element in the substance and add them together: - (NH4)2 has 4 hydrogen atoms and 2 nitrogen atoms, so the mass contribution is (2 x 14) + (8 x 1) = 28 + 8 = 36 g/mol. - Cr2 has 2 chromium atoms, so the mass contribution is (2 x 52) = 104 g/mol. - O7 has 7 oxygen atoms, so the mass contribution is (7 x 16) = 112 g/mol. Now, add the mass contributions of all elements: 36 (for NH4) + 104 (for Cr2) + 112 (for O7) = 252 g/mol. Thus, the molar mass of (NH4)2Cr2O7 is 252 g/mol.

Key concepts

Understanding the Periodic Table

The periodic table isn't just a colorful wall chart found in every chemistry classroom; it's a crucial tool for scientists and students alike in understanding the basics of chemistry. It organizes all known elements in a tabular arrangement based on their atomic number, electron configurations, and recurring chemical properties.

Elements are ordered from left to right and top to bottom in order of increasing atomic number. This arrangement places elements with similar properties in the same column (groups). For instance, the noble gases which are inert, or non-reactive, are all found in the far right-hand column.

When it comes to molar mass calculations, the periodic table provides the essential information on atomic masses, sometimes referred to as atomic weights, which are typically given in atomic mass units (u) or grams per mole (g/mol). These values are an average of the masses of all the isotopes of an element, weighted by their natural abundance.

Atomic Mass: The Building Block of Molar Mass

Atomic mass, also known as atomic weight, is a fundamental concept when calculating molar mass. To put it simply, atomic mass represents the weight of a single atom of an element and is measured in atomic mass units (u) or grams per mole (g/mol) when referring to the amount of substance.

This value is crucial in molar mass calculation as it essentially tells you how much one mole of that element weighs. One mole of any substance, whether it's an atom, molecule or ion, contains exactly 6.022 x 10^23 (Avogadro's number) representative particles.

To find the atomic mass of an element, you’ll refer to the periodic table, where each element is listed along with its atomic mass. For example, hydrogen has an atomic mass of about 1 g/mol, meaning one mole of hydrogen atoms weighs 1 gram. This number is instrumental when we're piecing together the total molar mass of a compound.

Deciphering the Molecular Formula

A molecular formula serves as a shorthand representation of a substance's composition. It indicates the types and numbers of atoms present in a molecule. For example, water's molecular formula is H2O, telling us that each molecule consists of two hydrogen (H) atoms and one oxygen (O) atom.

If you’re dealing with a more complex compound like ammonium dichromate (NH4)2Cr2O7, the molecular formula breaks down into its constituent elements: nitrogen (N), hydrogen (H), chromium (Cr), and oxygen (O). The subscript numbers tell you how many atoms of each element are in one molecule. In this case, there are 8 hydrogen, 2 nitrogen, 2 chromium, and 7 oxygen atoms.

To find the molar mass using the molecular formula, simply multiply the atomic mass of each element by the number of times the element appears in the molecule (indicated by the subscripts), and then add all of these values together. The result is the total molar mass of the compound, which indicates how much one mole of this compound weighs.