Question

The reaction \(2 \mathrm{C}+\mathrm{O}_{2} \longrightarrow 2 \mathrm{CO}\) is carried out by taking \(24 \mathrm{~g}\) of carbon and \(96 \mathrm{~g}\) of \(\mathrm{O}_{2}\). Which one is the limiting reagent? (1) \(\mathrm{C}\) (2) \(\mathrm{O}_{2}\) (3) \(\mathrm{CO}_{2}\) (4) Nonc

Short answer

Limitating regaent is C. Because we have too much O2.

Step-by-step solution

- Write the balanced chemical equation

The balanced chemical equation for the reaction is:y C + 1 O2 -> 2 CO.

- Calculate the molar masses

Find the molar masses of the reactants.Molar mass of C = 12 g/molMolar mass of O2 = 32 g/mol

- Convert mass to moles

Convert the given masses of the reactants to moles using their molar masses.For C: n = 24 g / 12 g/mol = 2 moles C For O2: n = 96 g / 32 g/mol = 3 moles O2

- Determine the mole ratio

From the balanced chemical equation, the mole ratio of C to O2 is 2:1. This means 2 moles of C react with 1 mole of O2.However, we have 2 moles of C and 3 moles of O2.

- Identify the limiting reagent

According to the mole ratio, 2 moles of C require 1 mole of O2. Since we have more than enough O2 (3 moles) for 2 moles of C, the limiting reagent is C.

Key concepts

balanced chemical equation

Understanding a balanced chemical equation is crucial when solving problems related to limiting reagents. A balanced chemical equation shows the relationship between the reactants and the products in a chemical reaction. In our given reaction, \( 2 \mathrm{C} + \mathrm{O}_2 \longrightarrow 2 \mathrm{CO} \), this equation tells us that 2 atoms of carbon (C) react with 1 molecule of oxygen (O2) to produce 2 molecules of carbon monoxide (CO).
To balance the equation, we ensure that the number of atoms of each element on the reactant side equals the number of atoms on the product side. This balance is essential because it follows the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction.
In this case, we can see:

• 2 atoms of carbon (C) on the reactant side become 2 atoms of carbon on the product side (in 2 molecules of CO).
• 1 molecule of oxygen (O2) supplies 2 atoms of oxygen, which are needed in 2 molecules of CO.

Keeping the chemical equation balanced allows us to accurately determine the quantities of reactants needed and the products formed.

molar masses

Molar mass is the mass of one mole of a substance, usually measured in grams per mole (g/mol). Knowing the molar masses of reactants is essential for converting between masses of substances and moles, which allows us to work with the stoichiometric relationships in our balanced equation.
For our reaction, the molar mass of carbon (C) is:

• 12 g/mol

While for oxygen (O2), the molar mass comes from adding the atomic masses of two oxygen atoms:

• 32 g/mol

By converting the given masses of the reactants to moles, using the formula:
\( n = \frac{mass}{molar mass} \)
we can determine the number of moles involved in the reaction. For example:

• For carbon (C): \( n_C = \frac{24 \text{ g}}{12 \text{ g/mol}} = 2 \text{ moles} \)
• For oxygen (O2): \( n_{O_2} = \frac{96 \text{ g}}{32 \text{ g/mol}} = 3 \text{ moles} \)

This conversion is essential for comparing the quantities of reactants precisely based on their amounts in moles.

mole ratio

The mole ratio derives directly from the balanced chemical equation and shows the proportional relationship between the quantities of reactants and products.
In our reaction: \( 2 \mathrm{C} + \mathrm{O}_2 \longrightarrow 2 \mathrm{CO} \),
the mole ratio of carbon (C) to oxygen (O2) is 2:1, meaning:

• 2 moles of C react with 1 mole of O2 to produce 2 moles of CO.

This ratio indicates how much of each reactant is needed or produced. It also helps to identify the limiting reagent, which is the reactant that runs out first and thus limits the amount of product formed.
To determine the limiting reagent, we compare the actual mole ratios of the given reactants to the required mole ratios from the balanced equation. Here, the given amounts are 2 moles of C and 3 moles of O2.
According to the balanced equation, 2 moles of C completely react with only 1 mole of O2. Since we have more moles of O2 than required (3 moles), C is the limiting reagent.

chemical reaction

A chemical reaction involves the transformation of reactants into products through a process that rearranges atoms, preserving the total number and types of atoms per the law of conservation of mass.
In our example: \(2 \mathrm{C} + \mathrm{O}_2 \longrightarrow 2 \mathrm{CO}\), carbon and oxygen undergo a reaction to form carbon monoxide. Here are some key points about chemical reactions:

• Reactants: The starting substances (in this case, carbon and oxygen).
• Products: The substances formed (carbon monoxide).
• Conservation: The number of each type of atom remains the same before and after the reaction.

Chemical reactions occur due to the breaking and forming of chemical bonds, resulting in new substances with different properties from the reactants. Understanding these fundamental principles helps in predicting and calculating the outcomes of reactions, including identifying limiting reagents and product yields.