Question

When elemental carbon is burned in the open atmosphere, with plenty of oxygen gas present, the product is carbon dioxide. $$\mathrm{C}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)$$ However, when the amount of oxygen present during the burning of the carbon is restricted, carbon monoxide is more likely to result. $$2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{CO}(g)$$What mass of each product is expected when a \(5.00-\mathrm{g}\) sample of pure carbon is burned under each of these conditions?

Short answer

In conclusion, when a \(5.00\text{-g}\) sample of pure carbon is burned in the open atmosphere with plenty of oxygen gas present, \(18.31\text{ g}\) of carbon dioxide is expected. Whereas, when the amount of oxygen is restricted during burning, \(23.32\text{ g}\) of carbon monoxide is likely to result.

Step-by-step solution

Balance the equations if needed

Both equations are already balanced: 1. \(C(s) + O_{2}(g) \rightarrow CO_{2}(g)\) 2. \(2C(s) + O_{2}(g) \rightarrow 2CO(g)\)

List the molecular weights (g/mol) of each element

To convert from grams of carbon to moles of carbon in our sample, we need the molecular weights of each element: 1. Carbon (C): 12.01 g/mol 2. Oxygen (O): 16.00 g/mol

Calculate the moles of Carbon in the sample

Using the molecular weight of carbon, we can determine the moles of carbon in our 5.00 g sample: moles of carbon = (5.00 g) / (12.01 g/mol) = 0.4163 moles (rounded to four decimal places)

Determine the moles of each product under each condition

Now, using the balanced equations, we can calculate the moles of products in each condition. 1. For the carbon dioxide (CO₂) according to the first equation: moles of CO₂ = moles of C = 0.4163 moles 2. For the carbon monoxide (CO) according to the second equation: moles of CO₂ = 2 × moles of C = 2 × 0.4163 moles = 0.8326 moles

Calculate the mass of each product

Lastly, we need to convert the moles of each product back into grams using their molecular weights: 1. For carbon dioxide (CO₂): mass of CO₂ = (0.4163 moles) × (12.01 g/mol (C) + 2 × 16.00 g/mol (O)) = (0.4163 moles) × (44.01 g/mol) = 18.31 g (rounded to two decimal places) 2. For carbon monoxide (CO): mass of CO = (0.8326 moles) × (12.01 g/mol (C) + 16.00 g/mol (O)) = (0.8326 moles) × (28.01 g/mol) = 23.32 g (rounded to two decimal places) In conclusion, when the 5.00-g sample of pure carbon is burned in the open atmosphere with plenty of oxygen gas present, 18.31 g of carbon dioxide is expected. Whereas, when the amount of oxygen is restricted during burning, 23.32 g of carbon monoxide is likely to result.

Key concepts

Chemical Reactions

Understanding chemical reactions is fundamental in the field of chemistry, and it involves studying how substances change into different substances through the breaking and forming of chemical bonds. When elemental carbon is burned, one of two reactions can occur, depending on the presence of oxygen. If oxygen is abundant, carbon reacts with oxygen gas to form carbon dioxide (CO₂). However, under limited oxygen supply, carbon monoxide (CO) is formed instead.

Chemicals react according to a fixed ratio, dictated by the balanced chemical equation. For instance, one mole of carbon will react with one mole of oxygen to yield one mole of CO₂. The understanding of stoichiometry is essential, as it is the method used to calculate the quantities of reactants and products involved in a chemical reaction. In this problem, we first identify the balanced chemical equations and then use stoichiometry to predict the masses of the products formed from a given mass of carbon.

Molecular Weight

Molecular weight, sometimes referred to as molecular mass, is the sum of the atomic masses of the atoms in a molecule. It's expressed in atomic mass units (amu) or grams per mole (g/mol). This property is fundamental when converting between moles and grams in stoichiometry, as it helps us know precisely how much one mole of a given substance weighs.

Take carbon (C) for example, with a molecular weight of 12.01 g/mol, and oxygen (O), with a molecular weight of 16.00 g/mol. We can also calculate the molecular weight of compounds like CO₂ and CO by adding the atomic masses of the respective atoms within each molecule. Knowing the molecular weight allows us to convert moles of a substance to grams and vice versa, enabling us to measure out precise amounts for chemical reactions.

Moles to Grams Calculation

The mole is a fundamental unit in chemistry that denotes an exact number of particles, such as atoms or molecules. Converting moles to grams is a crucial step in many chemical calculations. The formula for this conversion is quite straightforward:
\[ \text{mass (g)} = \text{moles} \times \text{molecular weight (g/mol)} \]
Applying this to our problem, if we want to convert 0.4163 moles of carbon, with a molecular weight of 12.01 g/mol, to grams, we multiply the two values getting approximately 5.00 g - which was our starting sample's mass. This calculation is equally important when determining the mass of the products as it allows us to predict the outcomes of a reaction in a real-world scenario, like how much CO₂ will result when burning carbon in ample oxygen or how much CO forms in a limited oxygen environment.