Given 175 liters of SO3 at 800 torr and 100 degrees C, find the volume at STP, give the mass of the sample and give the number of molecules in the sample.
Can somebody please explain how I figure this out? I'm so lost. :{
I would use
(P1V1/T1) = (P2V2/T2) and solve for V2 at STP.
Then use PV = nRT to solve for n = number of moles of the gas. Since n = grams/molar mass, you know n and molar mass, one can solve for grams.
Finally, you know 1 mole of anything will contain 6.022E23 molecules. Use that piece of information to calculate the number of molecules.
Thank you SOO much~! :D
To solve this problem, you need to use the ideal gas law equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Let's break down the steps to find the volume at STP, the mass of the sample, and the number of molecules in the sample:
Step 1: Convert the given temperature from Celsius to Kelvin.
Since the temperature is given as 100 degrees Celsius, we need to convert it to Kelvin. To do this, add 273.15 to the Celsius temperature:
Kelvin temperature (T) = 100 + 273.15 = 373.15 K
Step 2: Convert the pressure from torr to atm.
The given pressure is in torr, but we need to convert it to atm since the ideal gas constant (R) has units of atm. To do this, divide the torr pressure by 760 (since 1 atm = 760 torr):
Pressure (P) in atm = 800 torr / 760 torr/atm = 1.05 atm
Step 3: Convert the volume to liters at STP.
At STP (standard temperature and pressure), the temperature is 273.15 K and the pressure is 1 atm. To find the volume at STP, we can use the equation:
(V1 / T1) = (V2 / T2), where V1 is the initial volume, T1 is the initial temperature, V2 is the final volume, and T2 is the final temperature.
Rearranging the equation:
V2 = (V1 * T2) / T1
Given V1 = 175 liters, T1 = 373.15 K, T2 = 273.15 K, we can substitute these values into the equation:
V2 = (175 * 273.15) / 373.15
V2 = 127.5 liters (rounded to one decimal place)
Therefore, the volume of the sample at STP is 127.5 liters.
Step 4: Find the number of moles.
To find the number of moles (n), we can use the ideal gas law equation:
PV = nRT
Rearranging the equation:
n = (PV) / RT
Given P = 1.05 atm, V = 127.5 liters, R = 0.0821 L*atm/(mol*K), and T = 273.15 K, we can substitute these values into the equation:
n = (1.05 * 127.5) / (0.0821 * 273.15)
n = 6.369 moles (rounded to three decimal places)
Therefore, the mass of the sample can be found using the molar mass of SO3 (sulfur trioxide) and the number of moles:
Mass = number of moles * molar mass of SO3
The molar mass of SO3 is:
Sulfur (S): 32.07 g/mol
Oxygen (O): 3 * 16.00 g/mol = 48.00 g/mol
Molar mass of SO3 = 32.07 g/mol + 48.00 g/mol = 80.07 g/mol
Mass = 6.369 moles * 80.07 g/mol
Mass = 509.6 grams (rounded to one decimal place)
Therefore, the mass of the sample is 509.6 grams.
Step 5: Find the number of molecules.
To find the number of molecules, we can use Avogadro's number (6.022 x 10^23) and the number of moles. Since 1 mole contains 6.022 x 10^23 molecules, we can multiply the number of moles by Avogadro's number:
Number of molecules = number of moles * Avogadro's number
Given the number of moles as 6.369, we can substitute this value into the equation:
Number of molecules = 6.369 moles * 6.022 x 10^23 molecules/mole
Number of molecules = 3.839 x 10^24 molecules
Therefore, the number of molecules in the sample is approximately 3.839 x 10^24 molecules.
To summarize:
- The volume of the sample at STP is 127.5 liters.
- The mass of the sample is 509.6 grams.
- The number of molecules in the sample is approximately 3.839 x 10^24 molecules.