Question

A chemical reaction is used to produce \(3.4 \mathrm{~mol}\) of copper(II) bicarbonate, \(\mathrm{Cu}\left(\mathrm{HCO}_{3}\right)_{2}\). What mass of copper(II) bicarbonate is produced?

Short answer

So, the mass of \(3.4 \mathrm{~mol}\) of copper(II) bicarbonate is \(630.7 \mathrm{~g}\).

Step-by-step solution

Determining atomic masses

Find the atomic masses for the individual elements present in the substance from a Periodic Table. Copper (Cu) has an atomic mass of 63.5 g/mol, Hydrogen (H) is 1 g/mol, Carbon (C) is 12.0 g/mol , and Oxygen (O) is 16.0 g/mol.

Establishing the molar mass formula

Write out the molar mass formula for copper(II) bicarbonate. Notice that there's one atom of Copper, two atoms of Hydrogen, two atoms of Carbon, and six atoms of Oxygen in each molecule.

Calculating the molar mass

Calculate the molar mass by fitting the atomic masses and their quantities into the molar mass formula:\((1 \times 63.5) + (2 \times 1) + (2 \times 12.0) + (6 \times 16.0) = 63.5 + 2 + 24 + 96 = 185.5 \mathrm{~g/mol}\). Thus, the molar mass of copper(II) bicarbonate is \(185.5 \mathrm{~g/mol}\).

Converting moles to grams

To convert numbers of moles to grams, you use the relationship that \(1 \mathrm{~mol}\) of a substance has a mass equal to its molar mass in grams. So, multiply the number of moles of copper(II) bicarbonate by its molar mass: \(3.4 \mathrm{~mol}\) times \(185.5 \mathrm{~g/mol}\) gives \(630.7 \mathrm{~g}\).

Key concepts

Understanding Molar Mass Calculation

In chemistry, the molar mass of a substance is a critical value that connects the microscopic world of atoms and molecules to the macroscopic world we live in. It is defined as the mass of one mole of that substance. To find the molar mass, we sum up the atomic masses of all the atoms in a molecule.

Let's consider copper(II) bicarbonate \(\mathrm{Cu} (\mathrm{HCO}_3)_2\) as an example. A single molecule includes one copper atom, two hydrogen atoms, two carbon atoms, and six oxygen atoms. Using the atomic masses from the periodic table: copper (63.5 g/mol), hydrogen (1 g/mol), carbon (12.0 g/mol), and oxygen (16.0 g/mol). By multiplying each atomic mass by the number of respective atoms in the molecule and adding them together, we can calculate the molar mass: