Question

a. The compound \(\mathrm{MgSO}_{4}\) is called Epsom salts. How many grams will you need to prepare a bath containing \(5.00\) moles of Epsom salts? b. In a bottle of soda, there is \(0.25\) mole of \(\mathrm{CO}_{2}\). How many grams of \(\mathrm{CO}_{2}\) are in the bottle?

Short answer

a. 601.83 grams, b. 11.00 grams.

Step-by-step solution

Determine Molar Mass of \(\text{MgSO}_4\)

Find the molar mass by adding the atomic masses of magnesium (Mg), sulfur (S), and oxygen (O). Molar mass of \(\text{MgSO}_4\) = 24.305 + 32.065 + 4(15.999) = 120.366 g/mol.

Calculate Mass for 5.00 Moles of \(\text{MgSO}_4\)

Multiply the molar mass by the number of moles: Mass = 5.00 moles \(\times\) 120.366 g/mol = 601.83 grams.

Determine Molar Mass of \(\text{CO}_2\)

Find the molar mass by adding the atomic masses of carbon (C) and oxygen (O). Molar mass of \(\text{CO}_2\) = 12.011 + 2(15.999) = 44.009 g/mol.

Calculate Mass for 0.25 Moles of \(\text{CO}_2\)

Multiply the molar mass by the number of moles: Mass = 0.25 moles \(\times\) 44.009 g/mol = 11.00 grams.

Key concepts

Molar Mass

The molar mass of a chemical compound is the weight of one mole of that compound. To find the molar mass, you must know the atomic masses of each element in the compound. These atomic masses are usually given in the periodic table and are measured in grams per mole (g/mol).

To calculate the molar mass, add the atomic masses of all the atoms in the compound. For instance, in the compound \(\text{MgSO}_4\), you need the atomic masses of magnesium (Mg), sulfur (S), and oxygen (O).

Simply add them up:
\[ \text{Molar mass of MgSO}_4 = 24.305 \text{ for Mg} + 32.065 \text{ for S} + 4 \times 15.999 \text{ for O} = 120.366 \text{ g/mol} \] Understanding how to calculate the molar mass accurately is crucial for converting moles to grams.

Moles to Grams Conversion

Converting moles to grams is a common task in chemistry. This conversion involves using the concept of molar mass. The general formula for this conversion is:

\[ \text{Mass (grams)} = \text{Moles} \times \text{Molar Mass (g/mol)} \]
For example, to find how many grams are in 5.00 moles of \(\text{MgSO}_4\), use the molar mass you just calculated (120.366 g/mol). Multiply the moles by this molar mass:

\[ \text{Mass of } \text{MgSO}_4 = 5.00 \text{ moles} \times 120.366 \text{ g/mol} = 601.83 \text{ grams} \]

Knowing how to convert moles to grams is essential for preparing solutions and understanding the quantity of reactants needed in a chemical reaction.

Chemical Compounds

Chemical compounds are substances formed when two or more different atoms bond together. These bonds could be covalent (sharing electrons) or ionic (transferring electrons). The formula of a chemical compound tells you the types and numbers of atoms involved. For instance, \(\text{MgSO}_4\) consists of one magnesium (Mg) atom, one sulfur (S) atom, and four oxygen (O) atoms.

Understanding the formula of a compound helps in calculating its molar mass, which in turn is crucial for conversions like moles to grams. Each element in the compound contributes to the overall mass. In real-world scenarios, knowing the molar mass enables you to mix the correct proportions of chemicals for reactions or solutions. For example, when preparing a bath with Epsom salts (\(\text{MgSO}_4\)), knowing its molar mass lets you calculate how many grams are equivalent to a specific number of moles.

By understanding the way chemical compounds are structured and their molar masses, you can master finding the masses required for various chemical applications, whether it is for a simple lab experiment or a real-world industrial process.