Question

\(5.6 \mathrm{~g}\) of carbon monoxide is heated with excess of \(\mathrm{O}_{2}\) to form carbon dioxide. What is the theoretical yield in grams of carbon dioxide \(\left(2 \mathrm{CO}+\mathrm{O}_{2} \longrightarrow 2 \mathrm{CO}_{2}\right) ?\) (1) \(44 \mathrm{~g}\) (2) \(88 \mathrm{~g}\) (3) \(4.4 \mathrm{~g}\) (4) \(8.8 \mathrm{~g}\)

Short answer

8.8 g

Step-by-step solution

Determine the molar mass of CO and CO₂

Find the molar mass of carbon monoxide (CO) and carbon dioxide (CO₂).\[\mathrm{Molar \ mass \ of \ CO} = \mathrm{C (12)} + \mathrm{O (16)} = 28 \mathrm{~g/mol} \] \[\mathrm{Molar \ mass \ of \ CO}_2 = \mathrm{C (12)} + 2 \times \mathrm{O (16)} = 44 \mathrm{~g/mol} \]

Calculate moles of CO

Use the given mass of CO to find the number of moles. \[\mathrm{Moles \ of \ CO} = \frac{\mathrm{Mass \ of \ CO}}{\mathrm{Molar \ mass \ of \ CO}} = \frac{5.6 \mathrm{~g}}{28 \mathrm{~g/mol}} = 0.2 \mathrm{~moles} \]

Use stoichiometry to find moles of CO₂

From the balanced chemical equation, 2 moles of CO produce 2 moles of CO₂. Therefore, \[\text{0.2 moles of CO will produce 0.2 moles of CO}_2 \]

Convert moles of CO₂ to grams

Finally, convert the moles of CO₂ back to grams using its molar mass. \[\mathrm{Mass \ of \ CO}_2 = \mathrm{Moles \ of \ CO}_2 \times \mathrm{Molar \ mass \ of \ CO}_2 = 0.2 \mathrm{~moles} \times 44 \mathrm{~g/mol} = 8.8 \mathrm{~g} \]

Key concepts

molar mass

The concept of molar mass is fundamental in chemistry. Molar mass is the mass of one mole of a substance (an element or a compound). It's usually expressed in grams per mole (g/mol). To find the molar mass of a compound, sum the masses of each element present in one mole of that compound. For example, the molar mass of carbon monoxide (CO) is calculated by adding the atomic mass of carbon (12 g/mol) to the atomic mass of oxygen (16 g/mol), resulting in 28 g/mol. Similarly, carbon dioxide (CO₂) has a molar mass of 44 g/mol, which includes one carbon atom (12 g/mol) and two oxygen atoms (16 g/mol each). Understanding molar mass allows us to convert between grams of a substance and moles, making it easier to understand chemical reactions quantitatively.

stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It's based on the balanced chemical equation and allows us to predict the quantities of substances consumed and produced. For the reaction: 2CO + O₂ → 2CO₂, the stoichiometric coefficients (the numbers in front of the chemical formulas) indicate the mole ratio of the reactants and products. Here, 2 moles of carbon monoxide (CO) react with 1 mole of oxygen (O₂) to produce 2 moles of carbon dioxide (CO₂). These ratios help us determine how much of each reactant is needed and how much product is formed. In the exercise, 0.2 moles of CO produce 0.2 moles of CO₂ based on the 1:1 ratio from the coefficients.

chemical reactions

Chemical reactions describe the process where reactants are transformed into products. In our example, carbon monoxide (CO) reacts with oxygen (O₂) to form carbon dioxide (CO₂). This particular reaction is a type of oxidation-reduction (redox) reaction where CO is oxidized to CO₂. The balanced chemical equation represents the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. Instead, atoms are rearranged to form new compounds. By writing balanced chemical equations, we ensure that the number of each type of atom is conserved throughout the reaction.

mole concept

The mole concept is a way to count particles in chemistry using Avogadro's number (6.022 x 10²³ particles per mole). It's an essential unit for converting between atomic or molecular scale measurements and macroscopic quantities that can be measured in the lab. For instance, when the problem states that 5.6 grams of CO is used, we convert grams to moles by dividing by the molar mass of CO (28 g/mol). This calculation gives us 0.2 moles of CO. Using the mole concept, we can relate this to the number of molecules and use it to determine the ensuing production of CO₂ in grams, given its molar mass (44 g/mol).