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?
V= 9.19 x 10^4 L
To find the volume of SO2 produced, we need to follow these steps:
Step 1: Calculate the number of moles of sulfur in the oil.
Step 2: Calculate the number of moles of SO2 produced.
Step 3: Use the ideal gas equation to calculate the volume of SO2.
Let's start with step 1:
Step 1: Calculate the number of moles of sulfur in the oil.
- We are given that the oil contains 1.2% sulfur by mass.
- Mass percent can be converted to mass by dividing the percentage by 100 and multiplying by the mass of the oil.
- So, the mass of sulfur in the oil = (1.2/100) * (1.00 * 10^-4 kg) = 1.2 * 10^-6 kg.
To calculate the number of moles, we need to divide the mass of sulfur by the molar mass of sulfur (32.07 g/mol).
Molar mass of sulfur = 32.07 g/mol
Mass of sulfur = 1.2 * 10^-6 kg
Convert mass to grams:
1.2 * 10^-6 kg * (1000 g/kg) = 1.2 * 10^-3 g
Number of moles of sulfur = (1.2 * 10^-3 g) / (32.07 g/mol) = 3.74 * 10^-5 mol
Now let's move on to step 2:
Step 2: Calculate the number of moles of SO2 produced.
According to the balanced chemical equation, 1 mole of S reacts to produce 1 mole of SO2.
Therefore, the number of moles of SO2 produced is also 3.74 * 10^-5 mol.
Finally, let's proceed to step 3:
Step 3: Use the ideal gas equation to calculate the volume of SO2.
The ideal gas equation is given by:
PV = nRT
Where:
P = pressure (given)
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (given)
Rearranging the equation to solve for V:
V = (nRT) / P
Given:
Pressure (P) = not provided
Density (d) = 2.60 g/L (Note that density can be related to molar mass and molar volume by d = molar mass / molar volume)
Molar mass of SO2 = 32.07 g/mol + 2 * 16.00 g/mol = 64.07 g/mol
Since density is related to molar volume, we can calculate the volume (V) using the equation:
d = molar mass / molar volume
Therefore, molar volume (V) = molar mass / density
Molar volume (V) = 64.07 g/mol / 2.60 g/L = 24.64 L/mol
Now we can use this value to calculate the volume of SO2 produced:
V = (3.74 * 10^-5 mol) * (24.64 L/mol) = 9.21 * 10^-4 L
Therefore, when 1.00 * 10^-4 kg of oil burns, it produces approximately 9.21 * 10^-4 liters (or 0.000921 liters) of SO2.