Chloroform CHCl3, is a volatile liquid solvent. Caculate the density of cholroform vapor at 98 degrees C and 797 mmHg. Give the answer in grams per liter.
How do I start this out
0.034448
To calculate the density of chloroform vapor, you can start by using the ideal gas law equation, which is given by:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = ideal gas constant = 0.0821 L.atm/mol.K
T = temperature (in Kelvin)
First, let's convert the given temperature of 98 degrees Celsius to Kelvin:
T = 98 + 273.15 = 371.15 K
Next, convert the given pressure of 797 mmHg to atmospheres:
P = 797 mmHg / 760 mmHg/atm = 1.0487 atm
Now, we can rearrange the ideal gas law equation to solve for the number of moles:
n = PV / RT
Substituting the known values:
n = (1.0487 atm) * V / (0.0821 L.atm/mol.K * 371.15 K)
The density is given by the number of moles divided by the volume:
density = n / V
Substituting the previous equation for n:
density = [(1.0487 atm) * V / (0.0821 L.atm/mol.K * 371.15 K)] / V
Simplifying the equation:
density = 1.0487 / (0.0821 * 371.15)
Finally, you can calculate the density of chloroform vapor by evaluating the equation and expressing the answer in grams per liter.
To calculate the density of chloroform vapor at a specific temperature and pressure, you need to use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature (in Kelvin)
To start, we need to convert the given temperature from Celsius to Kelvin. The formula to convert from Celsius to Kelvin is:
K = °C + 273.15
So, converting 98 degrees Celsius to Kelvin:
T = 98 + 273.15
T = 371.15 K
Now, convert the given pressure of 797 mmHg to atm by dividing it by 760 (since 1 atm = 760 mmHg):
P = 797 mmHg / 760
P = 1.04868 atm
Now, we have the temperature T = 371.15 K and pressure P = 1.04868 atm.
To solve for the volume (V), we need to rearrange the ideal gas law equation:
V = (nRT) / P
However, we don't have the number of moles (n) of chloroform vapor. To find that, we need to use the molecular weight of chloroform.
Molecular weight of chloroform (CHCl3) = (1 * atomic mass of C) + (3 * atomic mass of H) + (1 * atomic mass of Cl) = 12.01 + (3 * 1.01) + 35.45 = 119.37 g/mol
Now, we can calculate the number of moles (n) of chloroform vapor using the formula:
n = mass / molecular weight
Since we don't have the mass, we'll assume it to be 1 gram.
n = 1 g / 119.37 g/mol
n ≈ 0.00838 mol
Now we have all the components required to calculate the volume (V).
V = (nRT) / P
Plug in the values:
V = (0.00838 mol * 0.0821 L·atm/mol·K * 371.15 K) / 1.04868 atm
V ≈ 0.2502 L
Finally, to calculate the density (D), we divide the mass of chloroform vapor (1g) by the volume we calculated (0.2502 L):
D = 1 g / 0.2502 L
D ≈ 3.996 g/L
Therefore, the density of chloroform vapor at 98 degrees Celsius and 797 mmHg is approximately 3.996 grams per liter.
PV = nRT
You know P. Assume V = 1 L. You know R and T. Calculate n = mols and that is mols in 1 L.
mols = g/molar mass. you now know mols and you know molar mass. Calculate grams. And that is in 1 L so the answer is g/L. You can do it another way all in one step if you want to redo the equation a little.
PV = nRT
P = (n/V)*RT
but n = g/molar mass so
P = (g/molar mass*V)*RT
But g/V = density = d so
P = (d/molar mass)*RT and solve for d.
d = (P*molar mass)/(RT)