Question

When elemental carbon is burned in the open atmosphere, with plenty of oxygen gas prescnt, the product is carbon dioxide. $$\mathrm{C}(s)+{\mathrm{O}}_2(g)\to {\mathrm{CO}}_2(g)$$ However, when the amount of oxygen present during the burning of the carbon is restricted, carbon monoxide is more likely to result. $$2\mathrm{C}(s)+{\mathrm{O}}_2(g)\to 2\mathrm{CO}(g)$$ What mass of each product is expected when a $5.00-\mathrm{g}$ sample of pure carbon is burned under cach of these conditions?

Short answer

When a 5.00g sample of pure carbon is burned, we can expect 18.3g of CO₂ to be produced in the presence of plenty of oxygen, and 11.6g of CO to be produced when the amount of oxygen is restricted.

Step-by-step solution

Convert the mass of carbon to moles.

Using the molar mass of carbon (C), 12.01g/mol, we can convert the 5.00g sample of pure carbon to moles: moles of C = (mass of C) / (molar mass of C) moles of C = $\frac{5.00g}{12.01g/mol}$= 0.416 moles

Use stoichiometry to find moles of each product.

For each of the conditions, we can relate the moles of carbon reacted to the moles of products formed using stoichiometry. 1. With plenty of oxygen (forming CO₂): According to the balanced equation: C(s) + O₂(g) → CO₂(g) 1 mole of C forms 1 mole of CO₂ So, moles of CO₂ formed = moles of C = 0.416 moles 2. With restricted oxygen (forming CO): According to the balanced equation: 2C(s) + O₂(g) → 2CO(g) 2 moles of C form 2 moles of CO So, moles of CO formed = moles of C = 0.416 moles

Convert moles of products to mass.

Now that we have the moles of each product, we can convert them to mass using the molar mass of the products: 1. Mass of CO₂ formed: molar mass of CO₂ = 12.01g/mol (C) + 2 × 16.00g/mol (O) = 44.01g/mol mass of CO₂ = moles of CO₂ × molar mass of CO₂ mass of CO₂ = 0.416 moles × 44.01g/mol = 18.3g 2. Mass of CO formed: molar mass of CO = 12.01g/mol (C) + 16.00g/mol (O) = 28.01g/mol mass of CO = moles of CO × molar mass of CO mass of CO = 0.416 moles × 28.01g/mol = 11.6g

Summarize the results.

When a 5.00g sample of pure carbon is burned under the two different conditions, we expect the following masses of products: 1. With plenty of oxygen: 18.3g of CO₂ 2. With restricted oxygen: 11.6g of CO

Key concepts

Chemical Reactions

Chemical reactions are processes where reactants transform into products. This change involves making and breaking chemical bonds, leading to new substances with different properties. For example, when carbon burns in oxygen, it primarily produces carbon dioxide (CO₂), but in a limited oxygen environment, carbon monoxide (CO) can form instead. Understanding stoichiometry is essential for predicting the amounts of products formed in these reactions.

In the given exercise, we look at two reactions:

• Burning carbon in excess oxygen: $\mathrm{C}(s)+{\mathrm{O}}_2(g)\to {\mathrm{CO}}_2(g)$
• Burning carbon in restricted oxygen: $2\mathrm{C}(s)+{\mathrm{O}}_2(g)\to 2\mathrm{CO}(g)$

The process of burning, in this context, is a combustion reaction, which is an exothermic process releasing energy, often as heat.

Molar Mass

The molar mass of an element or compound is the mass of one mole of that substance. It is an essential concept in chemistry because it allows us to convert between mass and moles, which is a key step in stoichiometry. The molar mass is expressed in units of grams per mole (g/mol).

For instance, carbon has a molar mass of 12.01 g/mol. A mole is Avogadro's number (approximately $6.02\times {10}^{23}$) of atoms. By knowing the molar mass, we can calculate how many moles are in a given sample. In the example exercise, we begin by converting 5.00 grams of carbon to moles using its molar mass.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions, where the reactant molecules are shown on the left and the products on the right. They must be balanced, meaning the number of atoms for each element must be the same on both sides of the equation.

A balanced chemical equation ensures the law of conservation of mass is upheld. It also provides the stoichiometric coefficients that tell us the ratios of reactants to products. These ratios are fundamental in determining how much product can be formed from given amounts of reactants, as demonstrated in the exercise problem.

Conversion of Moles to Grams

Conversion of moles to grams is a common task in chemistry, and it relies on the molar mass of a substance. Once you have determined the number of moles of a reactant or product, you can then multiply by its molar mass to find the equivalent mass in grams.

In our exercise, after finding the number of moles of carbon dioxide and carbon monoxide produced, the final step is to convert these mole quantities into masses using the molar masses of CO₂ and CO. This process is key to predicting and measuring the actual mass of product that results from a chemical reaction.