Calculate the volume of carbon dioxide produced when 0.5 tonnes of iron are produced. When iron oxide is heated with carbon monoxide, pure iron and carbon dioxide are formed. Ans: 500000g/112g/mol= 13392.9L
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To calculate the volume of carbon dioxide produced when 0.5 tonnes of iron are produced, we need to determine the amount of iron in moles and then use the balanced chemical equation to find the amount of carbon dioxide in moles. Finally, we can convert the amount of carbon dioxide from moles to liters using the ideal gas law.
Step 1: Convert the mass of iron from tonnes to grams
0.5 tonnes = 500,000 grams
Step 2: Convert the mass of iron from grams to moles
The molar mass of iron (Fe) is 55.845 g/mol.
Moles of iron = mass of iron / molar mass of iron
Moles of iron = 500,000 g / 55.845 g/mol ≈ 8,948.32 mol
Step 3: Use the balanced chemical equation to find the moles of carbon dioxide
The balanced chemical equation for the reaction is:
Fe2O3 + 3CO -> 2Fe + 3CO2
From the equation, we see that for every 2 moles of iron produced, 3 moles of carbon dioxide are produced.
Moles of CO2 = (moles of iron / 2) * 3
Moles of CO2 = (8,948.32 mol / 2) * 3 ≈ 13,422.48 mol
Step 4: Convert the moles of carbon dioxide to liters
To convert moles to liters, we can use the ideal gas law, which states:
V = nRT/P
Where:
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
P = pressure in atmospheres
Assuming standard temperature and pressure (273 K and 1 atm), we can plug in the values:
V = (13,422.48 mol * 0.0821 L·atm/(mol·K) * 273 K) / 1 atm
V ≈ 367,899 L
Therefore, the volume of carbon dioxide produced when 0.5 tonnes of iron are produced is approximately 367,899 liters.