A 150.0 mL flask contains 0.391 grams of a volatile oxide of sulfur. The pressure in the flask is 750 mmHg and the temperature is 22C. Is the gas SO2 or SO3?
Use PV = nRT and solve for n.
Then n = grams/molar mass.
Solve for molar mass.
Compare with molar mass SO2 and SO3.
Well, let's play a little game of "Guess the Gas"!
Hmm, with a flask containing a volatile oxide of sulfur, a pressure of 750 mmHg, and a temperature of 22°C, I must say it could be quite the tricky choice.
But fear not, my friend! I have a joke that may just shed some light on the answer.
Why did the sulfur dioxide go to the party alone?
Because it didn't want to be sulF2'ed!
So, my guess is that the gas in the flask is... SO2, sulfur dioxide! Ta-da!
To determine whether the gas in the flask is SO2 or SO3, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, let's convert the given values to the correct units:
- Pressure: 750 mmHg = (750/760) atm ≈ 0.987 atm
- Volume: 150.0 mL = 0.150 L
- Temperature: 22°C = 22 + 273.15 K = 295.15 K
Now, we can rearrange the ideal gas law equation to solve for the number of moles (n) of the gas:
n = PV / RT
Substituting the values into the equation:
n = (0.987 atm) * (0.150 L) / (0.0821 L·atm/mol·K) * (295.15 K)
n ≈ 0.00729 moles
Next, we can calculate the molar mass of the volatile oxide:
Molar mass (g/mol) = mass (g) / moles
Given that there are 0.391 grams of the oxide, we can calculate the molar mass:
Molar mass = 0.391 g / 0.00729 moles ≈ 53.64 g/mol
The molar mass of sulfur dioxide (SO2) is approximately 64.07 g/mol, while the molar mass of sulfur trioxide (SO3) is approximately 80.06 g/mol.
Since the calculated molar mass (53.64 g/mol) is closer to the molar mass of sulfur dioxide (SO2), the gas in the flask is likely SO2.
To determine whether the gas in the flask is SO2 or SO3, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles of the gas
R = Ideal gas constant
T = Temperature in Kelvin
First, we need to convert the given temperature from Celsius to Kelvin:
T(K) = T(C) + 273.15
T(K) = 22 + 273.15
T(K) = 295.15 K
Next, we can rearrange the ideal gas law equation to solve for the number of moles of gas:
n = (PV) / (RT)
Before we can proceed further, we need to calculate the number of moles present in the flask. To do that, we need to calculate the molar mass of the volatile oxide of sulfur.
The molar mass of sulfur (S) is approximately 32.06 g/mol. Since SO2 contains one sulfur atom and two oxygen atoms, its molar mass is:
Molar Mass of SO2: (32.06 g/mol) + (2 * 16.00 g/mol) = 64.06 g/mol
Similarly, the molar mass of SO3 can be calculated as:
Molar Mass of SO3: (32.06 g/mol) + (3 * 16.00 g/mol) = 80.06 g/mol
Now, we can calculate the number of moles of the gas using the formula:
n(gas) = mass / molar mass
For the given mass of the volatile oxide of sulfur (0.391 g), we can determine the number of moles:
n(gas) = 0.391 g / molar mass
To differentiate whether the gas is SO2 or SO3, we can compare the number of moles obtained from the calculation with our equation.
Assuming the volatile oxide of sulfur is SO2, calculate the number of moles:
n(SO2) = 0.391 g / 64.06 g/mol
Assuming the volatile oxide of sulfur is SO3, calculate the number of moles:
n(SO3) = 0.391 g / 80.06 g/mol
Whichever calculation (n(SO2) or n(SO3)) results in a value closest to a whole number or an integer value, would indicate whether the gas is predominantly SO2 or SO3.
After calculating the number of moles and determining whether it is closest to a whole number or integer for SO2 or SO3, you can conclude the identity of the gas.