A crude oil burned in electrical generating plant contains about 1.2% sulfur by mass. When the oil burns, the sulfur forms sulfur dioxide gas:
S(s) + O2 (g) = SO2 (g)
How many liters of SO2 (d= 2.60 g/L) are produced when 1.00 * 10¬4 kg of oil burns at the same temperature and pressure?
To calculate the number of liters of SO2 produced, we need to determine the mass of sulfur in the given amount of oil and then use the density of SO2 to convert it to volume.
Given:
Mass of oil burned (m) = 1.00 * 10^(-4) kg
Percentage of sulfur in oil = 1.2%
Step 1: Calculate the mass of sulfur in the oil.
Mass of sulfur = Percentage of sulfur * Mass of oil
Mass of sulfur = 1.2% * 1.00 * 10^(-4) kg
Step 2: Balance the chemical equation to determine the mole ratio between sulfur and SO2.
From the balanced equation, we can see that 1 mole of S reacts to produce 1 mole of SO2.
Step 3: Convert the mass of sulfur to moles using the molar mass of sulfur.
Molar mass of sulfur (S) = 32.06 g/mol
Moles of sulfur = Mass of sulfur / Molar mass of sulfur
Step 4: Convert the moles of sulfur to moles of SO2 using the mole ratio.
Moles of SO2 = Moles of sulfur
Step 5: Convert the moles of SO2 to volume using the density of SO2.
Density of SO2 = 2.60 g/L
Volume of SO2 = Moles of SO2 * Density of SO2
Therefore, the number of liters of SO2 produced when 1.00 * 10^(-4) kg of oil burns is Volume of SO2 (in liters).
To find the number of liters of SO2 produced, we need to first calculate the moles of sulfur in the oil, and then use stoichiometry to find the moles of SO2 produced.
Step 1: Calculate the moles of sulfur in the oil.
We know that the oil contains 1.2% sulfur by mass. This means that in 100g of oil, there is 1.2g of sulfur.
To find the moles of sulfur, we need to divide the mass of sulfur by its molar mass.
The molar mass of sulfur (S) is 32.06 g/mol.
Moles of sulfur = (mass of sulfur / molar mass of sulfur)
Moles of sulfur = (1.2g / 32.06 g/mol)
Step 2: Calculate the moles of SO2 produced.
From the balanced equation, we can see that 1 mol of sulfur reacts to produce 1 mol of SO2.
Moles of SO2 = Moles of sulfur
Step 3: Convert moles of SO2 to liters using the given density.
We are given the density of SO2, which is 2.60 g/L.
To convert from moles to grams, we multiply by the molar mass of SO2 (64.06 g/mol), and then divide by the density to get the volume in liters.
Volume (in liters) = (moles of SO2 * molar mass of SO2) / density of SO2
Volume (in liters) = [(moles of sulfur) * (molar mass of SO2)] / (density of SO2)
Volume (in liters) = [(1.2g / 32.06 g/mol) * 64.06 g/mol] / 2.60 g/L
Now, let's plug in the values and calculate the volume:
Volume (in liters) = [(1.2 / 32.06) * 64.06] / 2.60
Volume (in liters) = 1.870 L
Therefore, when 1.00 * 10¬4 kg of oil burns, it produces approximately 1.870 liters of SO2 gas.