What mass of sulfur has to burn to produce 4.5L SO2 at 300°C and 101 kPa in the following reaction?
S(s) + O2(g) -> SO2(g)
A. 3.07 g S
B. 68.8 g S
C. 41.0 g S
D. 13.5 g S
See your post above under Adam. Find n from PV = nRT
To answer this question, we need to use the ideal gas law in order to calculate the number of moles of SO2 produced. We can then use the balanced chemical equation to determine the stoichiometry of the reaction and relate the moles of SO2 to the moles of sulfur. Finally, we can convert the moles of sulfur to grams using the molar mass of sulfur.
Step 1: Calculate the number of moles of SO2
The ideal gas law is expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, convert the temperature from Celsius to Kelvin:
T = 300°C + 273.15 = 573.15 K
Using the ideal gas law, we can rearrange the equation to solve for the number of moles of SO2:
n = PV / RT
Since the pressure is given as 101 kPa and the volume is given as 4.5 L, we can plug in these values along with the gas constant R = 8.3145 J/(mol·K) to find the number of moles of SO2.
n = (101 kPa) * (4.5 L) / (8.3145 J/(mol·K) * 573.15 K)
Step 2: Determine the stoichiometry of the reaction
From the balanced chemical equation, we can see that the balanced equation is:
2 moles of S + 2 moles of O2 -> 2 moles of SO2
This means that for every 2 moles of sulfur, we get 2 moles of SO2.
Step 3: Convert moles of SO2 to moles of Sulfur
Since the stoichiometry of the reaction tells us that for every 2 moles of sulfur, we get 2 moles of SO2, we can use this ratio to determine the number of moles of sulfur.
The moles of sulfur = (2 moles of sulfur / 2 moles of SO2) * the number of moles of SO2
Step 4: Convert moles of Sulfur to grams of Sulfur
Finally, we can convert the number of moles of sulfur to grams using the molar mass of sulfur, which is 32.06 g/mol.
Grams of sulfur = moles of sulfur * molar mass of sulfur
Let's solve for the answer.
n = (101 kPa) * (4.5 L) / (8.3145 J/(mol·K) * 573.15 K)
n ≈ 0.090 moles of SO2
Using the stoichiometry of the reaction, we can determine the number of moles of sulfur:
moles of sulfur = (2 moles of sulfur / 2 moles of SO2) * 0.090 moles of SO2
moles of sulfur = 0.090 moles of sulfur
Now, we can convert the moles of sulfur to grams:
grams of sulfur = 0.090 moles of sulfur * 32.06 g/mol
grams of sulfur ≈ 2.8836 g
Rounding to the appropriate number of significant figures, the mass of sulfur that needs to burn is approximately 2.88 g.
None of the answer choices match this calculated result. Please check the given options again.