If 24 grams of carbon are completely burnt in excess oxygen to form carbon dioxide (CO2), how many moles of CO2 are produced?

Introduction / Context:
Stoichiometry questions that connect mass, moles and balanced equations are central to basic chemistry. This problem asks how many moles of carbon dioxide are produced when a known mass of carbon is completely burnt in oxygen. It tests your understanding of molar mass, mole calculations and the simple one to one mole ratio in the combustion of carbon to carbon dioxide. Mastering this type of calculation is essential for more advanced topics such as limiting reagents and yield.

Given Data / Assumptions:

• Mass of carbon burned: 24 g.
• Carbon is completely burnt in excess oxygen, so oxygen is not limiting.
• The main reaction is C + O2 → CO2.
• The molar mass of carbon is approximately 12 g/mol.
• The question asks for moles of CO2 formed, not its mass.

Concept / Approach:
The balanced chemical equation for complete combustion of carbon is C + O2 → CO2. This equation shows that one mole of carbon reacts with one mole of oxygen to form one mole of carbon dioxide. Therefore, the mole ratio between carbon and carbon dioxide is 1:1. First, you calculate how many moles of carbon are present in 24 g. Then, using the 1:1 ratio, you conclude that the same number of moles of CO2 is produced. This method uses the basic formula moles = mass / molar mass.

Step-by-Step Solution:
Step 1: Write the balanced equation for complete combustion of carbon: C + O2 → CO2.Step 2: Determine the molar mass of carbon. The atomic mass of carbon is about 12 g/mol.Step 3: Calculate the number of moles of carbon in 24 g using n = mass / molar mass.Step 4: n(C) = 24 g / 12 g/mol = 2 mol of carbon.Step 5: From the balanced equation, 1 mol of carbon gives 1 mol of CO2, so the mole ratio C:CO2 is 1:1.Step 6: Therefore, 2 mol of carbon will produce 2 mol of CO2 when combustion is complete and oxygen is in excess.Step 7: Conclude that the number of moles of CO2 formed is 2 mol.

Verification / Alternative check:
As a quick check, you can consider a smaller amount. If 12 g of carbon (1 mol) produces 1 mol of CO2, then doubling the mass of carbon to 24 g should double the amount of CO2 formed. That gives 2 mol of CO2, which matches the calculated result. You could also compute the mass of CO2 produced: 2 mol of CO2 have a mass of about 2 * 44 = 88 g, consistent with mass balance when you consider the addition of oxygen mass from the air.

Why Other Options Are Wrong:
Option a, 0.5 mol, would correspond to only 6 g of carbon reacting, which is much less than the given 24 g. Option b, 1 mol, would be correct for 12 g of carbon, not for 24 g. Option d, 0.25 mol, is even smaller and does not match the given mass. Option e, 4 mol, would require 48 g of carbon, which is double the provided mass. None of these match the 1:1 stoichiometric relationship and the correct mole calculation for 24 g of carbon.

Common Pitfalls:
A frequent error is to forget to divide the mass by molar mass and instead treat grams as if they were moles. Another common mistake is to misinterpret the mole ratio, for example thinking that one mole of carbon produces two moles of CO2, which is not supported by the balanced equation. To avoid these, always start by writing the balanced equation, then carefully convert mass to moles, and then apply the mole ratio step by step.

Final Answer:
When 24 g of carbon is completely burnt in excess oxygen, it produces 2 mol of CO2.