When 10L of isobutane is burnt at 27°c and 1 bar pressure, calculate thr 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 (C4H10) at different conditions, we can use the ideal gas law and stoichiometry. Let's break this down step by step.

Combustion Reaction of Isobutane

The balanced chemical equation for the complete combustion of isobutane is:

• C4H10 + 6.5 O2 → 4 CO2 + 5 H2O

This equation tells us that one mole of isobutane produces four moles of carbon dioxide. Therefore, for every 10 liters of isobutane, we can calculate the volume of CO2 produced.

Step 1: Calculate Moles of Isobutane

Using the ideal gas law, we can find the number of moles of isobutane in 10 liters at 27°C and 1 bar. The ideal gas law is given by:

• PV = nRT

Where:

• P = pressure (in bar)
• V = volume (in liters)
• n = number of moles
• R = ideal gas constant (0.08314 L·bar/(K·mol))
• T = temperature (in Kelvin)

First, convert the temperature from Celsius to Kelvin:

• T(K) = 27 + 273.15 = 300.15 K

Now, substituting the values into the ideal gas law:

• n = PV / RT
• n = (1 bar) * (10 L) / (0.08314 L·bar/(K·mol) * 300.15 K)
• n ≈ 0.404 moles of isobutane

Step 2: Calculate 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 0.404 moles of isobutane is:

• Moles of CO2 = 0.404 moles of isobutane * 4 = 1.616 moles of CO2

Step 3: Calculate Volume of CO2 at New Conditions

Next, 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:

Convert the temperature to Kelvin:

• T(K) = 80 + 273.15 = 353.15 K

Now, we can calculate the volume of CO2 using the ideal gas law rearranged to solve for V:

• V = nRT / P
• V = (1.616 moles) * (0.08314 L·bar/(K·mol)) * (353.15 K) / (1.5 bar)
• V ≈ 31.8 L

Final Result

Thus, the volume of carbon dioxide produced from the combustion of 10 liters of isobutane at 80°C and 1.5 bar pressure is approximately 31.8 liters. This calculation illustrates how gas behavior changes with temperature and pressure, adhering to the principles of the ideal gas law.