Question

What mass of \(\mathrm{SO}_{2}\) is present in \(26.8 \mathrm{~L}\) of \(1.22 \mathrm{M} \mathrm{SO}_{2}\) solution?

Short answer

2096 g of \(\mathrm{SO}_2\) is present.

Step-by-step solution

Understand Molarity

Molarity (M) is defined as moles of solute per liter of solution. This means a 1.22 M solution of \(\mathrm{SO}_2\) has 1.22 moles of \(\mathrm{SO}_2\) in every liter of solution.

Calculate Moles of \(\mathrm{SO}_2\)

The volume of the solution is given as 26.8 L. To find the moles of \(\mathrm{SO}_2\), multiply the molarity of the solution by its volume.\[\text{Moles of } \mathrm{SO}_{2} = \text{Molarity} \times \text{Volume} = 1.22 \, \mathrm{mol/L} \times 26.8 \, \mathrm{L}\] \[\text{Moles of } \mathrm{SO}_{2} = 32.696 \, \text{mol}\]

Find Molecular Mass of \(\mathrm{SO}_2\)

To find the mass, we need the molecular mass of \(\mathrm{SO}_2\). The molecular mass is the sum of the atomic masses of its elements: \(\mathrm{S}\) (32.07 g/mol) and two \(\mathrm{O}\) (16.00 g/mol each).\[\text{Molecular Mass of } \mathrm{SO}_2 = 32.07 \, \mathrm{g/mol} + 2 \times 16.00 \, \mathrm{g/mol} = 64.07 \, \mathrm{g/mol}\]

Calculate Mass of \(\mathrm{SO}_2\)

Using the moles of \(\mathrm{SO}_2\) calculated earlier and the molecular mass, we can find the mass:\[\text{Mass of } \mathrm{SO}_2 = \text{Moles} \times \text{Molecular Mass} = 32.696 \, \text{mol} \times 64.07 \, \text{g/mol}\]\[\text{Mass of } \mathrm{SO}_2 = 2095.81472 \, \text{g}\]Rounding to appropriate significant figures, the mass is approximately 2096 g.

Key concepts

Chemical Calculations

Chemical calculations are crucial for understanding how different substances interact in a chemical reaction. These calculations help predict the outcomes of reactions and determine the needed quantities of reactants. In the concept of molarity, a common unit in chemical calculations, you measure the concentration of a solution. Molarity is defined as the number of moles of solute per liter of solution. This allows chemists to easily scale reactions.

• A higher molarity means a more concentrated solution.
• A lower molarity means a more diluted solution.

To calculate the moles of a solute in a solution, use the formula:
\[\text{Moles of solute} = \text{Molarity} \times \text{Volume}\]This formula is fundamental in chemical calculations as it connects volume, moles, and molarity. Knowing any two of these values allows you to calculate the third, which is essential when preparing solutions and performing experiments.

Stoichiometry

Stoichiometry is the arithmetic of chemical reactions. It involves the calculation of reactants and products in chemical processes. This concept is central to chemistry because it helps you plan and predict the results of experiments and efficiently use resources.
To understand stoichiometry, one must first grasp the chemical equation that represents the reaction. A balanced chemical equation shows the proportional relationships between reactants and products. These relationships, expressed in moles, allow for conversion between amounts of different substances in the reaction.
When you calculate the moles of a substance using its volume and molarity, you can then use stoichiometry to determine how much of another substance is needed or produced. This ensures the reactants are mixed in the correct ratios, preventing waste or incomplete reactions. In our exercise, knowing the amount of \(\text{SO}_2\) in moles is crucial for further stoichiometric calculations.

Molecular Mass

Molecular mass is a key concept for converting moles into grams, which is vital in practical chemistry. The molecular mass of a compound is the sum of the atomic masses of the atoms in a molecule. This allows chemists to understand how much of a substance is present, not just in terms of moles, but in terms of mass, which is often more practical for experiments.
For instance, the molecular mass of \(\text{SO}_2\) can be determined as follows:

• The atomic mass of sulfur (\(\text{S}\)) is 32.07 g/mol.
• The atomic mass of oxygen (\(\text{O}\)) is 16.00 g/mol, and there are two oxygen atoms in \(\text{SO}_2\).

Thus, the molecular mass of \(\text{SO}_2\) is:\[32.07 \, \text{g/mol} + 2 \times 16.00 \, \text{g/mol} = 64.07 \, \text{g/mol}\]Knowing the molecular mass, one can convert moles of a compound to its mass:
\[\text{Mass} = \text{Moles} \times \text{Molecular Mass}\]This conversion is vital for determining how much chemical is needed or has been produced, ensuring precision and accuracy in laboratory work and industrial applications.