When 10L of isobutane is burnt at 27°c and 1 bar pressure, calculate the volume of co2 produced at 80°c and 1.5 bar pressure

To determine the volume of carbon dioxide (CO2) produced from the combustion of 10 liters of isobutane at different conditions, we can use the ideal gas law and stoichiometry. Let's break this down step by step.

Understanding the Combustion Reaction

The combustion of isobutane (C4H10) can be represented by the following balanced chemical equation:

• C4H10 + 6.5 O2 → 4 CO2 + 5 H2O

This equation shows that one mole of isobutane produces four moles of carbon dioxide. Therefore, for every 10 liters of isobutane burned, we can calculate the volume of CO2 produced based on the stoichiometry of the reaction.

Calculating Moles of Isobutane

First, we need to find the number of moles of isobutane in 10 liters at the given conditions (27°C and 1 bar). Using the ideal gas law, we can express this as:

• PV = nRT

Where:

• P = pressure (1 bar = 100 kPa)
• V = volume (10 L = 0.01 m³)
• n = number of moles
• R = ideal gas constant (8.314 J/(mol·K))
• T = temperature in Kelvin (27°C = 300 K)

Rearranging the formula to solve for n gives:

• n = PV / RT

Substituting the values:

• n = (100 kPa) * (0.01 m³) / (8.314 J/(mol·K) * 300 K)

Calculating this yields:

• n ≈ 0.40 moles of isobutane

Determining Moles of CO2 Produced

From the balanced equation, we know that 1 mole of isobutane produces 4 moles of CO2. Therefore, the moles of CO2 produced from 0.40 moles of isobutane is:

• 0.40 moles C4H10 * 4 moles CO2/mole C4H10 = 1.60 moles CO2

Calculating Volume of CO2 at New Conditions

Now, we need to find the volume of CO2 produced at the new conditions of 80°C and 1.5 bar. Again, we will use the ideal gas law:

• PV = nRT

We need to convert the temperature to Kelvin (80°C = 353 K) and the pressure to kPa (1.5 bar = 150 kPa). Rearranging for volume (V) gives:

• V = nRT / P

Substituting the values for CO2:

• V = (1.60 moles) * (8.314 J/(mol·K)) * (353 K) / (150 kPa)

Calculating this results in:

• V ≈ 31.6 liters of CO2

Final Result

Thus, when 10 liters of isobutane is burned at 27°C and 1 bar, approximately 31.6 liters of CO2 are produced at 80°C and 1.5 bar pressure. This calculation illustrates the relationship between gas volumes and the conditions under which they are measured, highlighting the principles of gas behavior under varying temperatures and pressures.