Pure carbon was burnt in excess of oxygen the gaseous products are 60 mole % CO2, 15 mole %CO and 25 mole % O2 calculate moles of O2 taken is initially 30 mole of carbon are taken

To solve the problem of how many moles of O2 were initially taken when 30 moles of carbon are burned in excess oxygen, we need to analyze the combustion reactions and the resulting gaseous products. Let's break it down step by step.

Understanding the Combustion of Carbon

When carbon burns in oxygen, it can produce two main products: carbon dioxide (CO2) and carbon monoxide (CO). The reactions can be represented as follows:

• C + O2 → CO2 (complete combustion)
• 2C + O2 → 2CO (incomplete combustion)

In this scenario, we are given the mole percentages of the products formed after burning 30 moles of carbon:

• 60 mole % CO2
• 15 mole % CO
• 25 mole % O2

Calculating Total Moles of Gas Products

First, we need to determine the total number of moles of gas produced. Since we know the mole percentages, we can express the total moles of gas (let's call it T) in terms of the moles of each gas:

• CO2: 0.60T
• CO: 0.15T
• O2: 0.25T

Since the total moles of carbon burned is 30, we can relate this to the moles of CO2 and CO produced. The moles of carbon consumed in producing CO2 and CO can be expressed as:

• From CO2: 30 moles of C produce 30 moles of CO2.
• From CO: 15 moles of C produce 15 moles of CO.

Setting Up the Equations

Let’s denote the moles of CO2 produced as x and the moles of CO produced as y. From the mole percentages, we have:

• x = 0.60T
• y = 0.15T

Since each mole of CO2 produced consumes 1 mole of carbon, and each mole of CO produced consumes 2 moles of carbon, we can write:

30 = x + 0.5y

Substituting Values

Substituting the expressions for x and y into the equation gives:

30 = 0.60T + 0.5(0.15T)

Now, simplifying this:

30 = 0.60T + 0.075T

30 = 0.675T

Finding Total Moles of Gas

Now, we can solve for T:

T = 30 / 0.675 ≈ 44.44 moles

Calculating Moles of O2 Consumed

Next, we can find the moles of O2 produced. Since we know that 25% of the total moles of gas are O2, we can calculate:

O2 = 0.25T = 0.25 × 44.44 ≈ 11.11 moles

Now, to find the moles of O2 initially taken, we need to consider that O2 is consumed during the combustion process. The total moles of O2 consumed can be calculated as:

Initial O2 = O2 consumed + O2 remaining

O2 consumed = (moles of C burned) + (moles of CO produced) = 30 + 15 = 45 moles

Thus, the initial moles of O2 taken can be calculated as:

Initial O2 = 45 + 11.11 ≈ 56.11 moles

Final Answer

Therefore, the initial moles of O2 taken when 30 moles of carbon were burned is approximately 56.11 moles.