Calculate the density of sulfur trioxide gas at 35 degrees celsius and 715 torr pressure.
I know that d=m/v = PM/RT. Im not sure how to set this up. I know the molar mass of sulfur trioxide is 80.0642 but im not sure if I need to use that.
I got 2.98g/L. Is this correct?
P = 715 torr x (1 atm/760 torr) = ? atm
M = you have
R = 0.08206 L*atm/mol*K
T = (273 + 35) kelvin.
Well, let me shed some light on this for you. First, let's determine the values we need:
Given:
Temperature (T) = 35 degrees Celsius
Pressure (P) = 715 torr
Now, we know that density (d) equals mass (m) divided by volume (v). The ideal gas law equation can be used to solve for density:
d = (PM) / (RT)
where:
P = pressure (in atm)
M = molar mass (in g/mol)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
To calculate density, we need to convert the temperature from Celsius to Kelvin, and the pressure from torr to atm:
T = 35 + 273.15 = 308.15 K
P = 715 torr * (1 atm / 760 torr) ≈ 0.940 atm
Since you mentioned that the molar mass of sulfur trioxide (SO3) is 80.0642 g/mol, we'll need that too.
Now we can plug in the values into the density equation:
d = (P * M) / (R * T)
= (0.940 atm * 80.0642 g/mol) / (0.0821 L·atm/(mol·K) * 308.15 K)
Now, let me do the math to calculate the density for you:
d ≈ 2.873 g/L
So, the density of sulfur trioxide gas at 35 degrees Celsius and 715 torr pressure is approximately 2.873 g/L.
Now, whether you found this explanation clear or not, I hope I didn't "sulfur" through it!
To calculate the density of sulfur trioxide gas at a given temperature and pressure, you can use the ideal gas law equation: 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, you need to convert the temperature from Celsius to Kelvin. The conversion formula is K = °C + 273.15. So, for a temperature of 35 degrees Celsius, the temperature in Kelvin would be:
T = 35 + 273.15 = 308.15 K
Next, you need to convert the pressure from torr to atmospheres (atm). Since the ideal gas constant, R, is typically given in atm, you need to use consistent units. The conversion factor is 1 atm = 760 torr. So, for a pressure of 715 torr, the pressure in atmospheres would be:
P = 715 torr / 760 torr = 0.93947 atm
Now, you can rearrange the ideal gas law equation to solve for the density (d). The rearranged equation is: d = PM/RT.
Given that the molar mass (M) of sulfur trioxide is 80.0642 g/mol, you have all the necessary values to calculate the density.
Plug in the values into the equation:
d = (P * M) / (R * T)
d = (0.93947 atm * 80.0642 g/mol) / (0.0821 atm·L/mol·K * 308.15 K)
Simplifying the equation:
d = 6.908 g/L
So, the density of sulfur trioxide gas at 35 degrees Celsius and 715 torr pressure is approximately 6.908 g/L.
To calculate the density of sulfur trioxide gas at a given temperature and pressure, you can use the ideal gas law equation, which you have correctly identified as:
d = (PM) / (RT)
where:
- d represents the density of the gas
- P is the pressure of the gas (in this case, given as 715 torr)
- M is the molar mass of the gas (in this case, sulfur trioxide with a molar mass of 80.0642 g/mol)
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature of the gas (in this case, 35 degrees Celsius, which needs to be converted to Kelvin)
Now, let's set up the calculation:
1) Convert the temperature from Celsius to Kelvin:
- K = °C + 273.15
- T = 35°C + 273.15 = 308.15 K
2) Plug in the given values into the equation:
- P = 715 torr
- M = 80.0642 g/mol
- R = 0.0821 L·atm/(mol·K)
- T = 308.15 K
d = (P * M) / (R * T)
3) Calculate the density:
- Make sure to use consistent units. Converting torr to atm and grams to kilograms will give us the answer in kg/L.
- P = 715 torr * (1 atm / 760 torr) = 0.940 atm
- M = 80.0642 g/mol * (1 kg / 1000 g) = 0.0800642 kg/mol
d = (0.940 atm * 0.0800642 kg/mol) / (0.0821 L·atm/(mol·K) * 308.15 K)
4) Calculate the final result:
- Using the units provided above, the density will be in kg/L.
d = 0.02310 kg/L
Therefore, the density of sulfur trioxide gas at 35 degrees Celsius and 715 torr pressure is approximately 0.02310 kg/L.