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?
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?
Now were to start....
To find the number of liters of SO2 produced when a certain mass of oil burns, we need to use stoichiometry and convert from mass to moles, and then from moles to volume.
Here's how you can calculate it step by step:
Step 1: Calculate the number of moles of sulfur in the oil.
To do this, we need to determine the mass of sulfur in the given mass of oil. Since the oil contains 1.2% sulfur, we can calculate it as follows:
Mass of sulfur = (1.2/100) * Mass of oil
Mass of sulfur = (1.2/100) * 1.00 * 10¬¬¬^-4 kg
Mass of sulfur = 1.20 * 10^-6 kg
Next, we need to calculate the number of moles of sulfur using the molar mass of sulfur (32.06 g/mol):
Number of moles of sulfur = Mass of sulfur / Molar mass of sulfur
Number of moles of sulfur = 1.20 * 10^-6 kg / 32.06 g/mol
Number of moles of sulfur = 3.741 * 10^-8 mol
Step 2: Calculate the number of moles of sulfur dioxide (SO2) produced.
From the balanced equation, we can see that the mole ratio between sulfur and sulfur dioxide is 1:1. Therefore, the number of moles of sulfur dioxide is the same as the number of moles of sulfur:
Number of moles of sulfur dioxide = Number of moles of sulfur
Number of moles of sulfur dioxide = 3.741 * 10^-8 mol
Step 3: Convert the number of moles of sulfur dioxide to liters using its density.
We are given the density of sulfur dioxide, which is 2.60 g/L. To convert moles to liters, we need to use the ideal gas law:
PV = nRT
Where:
P is the pressure (assumed to be constant)
V is the volume
n is the number of moles
R is the ideal gas constant (0.0821 L·atm·K^−1·mol^−1)
T is the temperature (assumed to be constant)
Rearranging the formula to solve for V (volume):
V = nRT / P
Substituting the values into the formula:
V = (3.741 * 10^-8 mol) * (0.0821 L·atm·K^−1·mol^−1) / (2.60 g/L)
V ≈ 1.17 * 10^-7 L
Therefore, approximately 1.17 * 10^-7 liters of SO2 are produced when 1.00 * 10¬¬¬^-4 kg of oil burns at the same temperature and pressure.