The density of chloroform at a pressure of 220 mmHg and 25 degrees celsius is 1.42 g/L. Calculate the molar mass of chloroform.
My set up is:
mol*K .289 atm 1 1.42g/L
------------- ------------ ------ ---------
.08206Latm 1 298K
What I am unsure of is if this is the right way to take this since 1.42 is not in liters but grams per liter.
I don't think that will get it. You can modify the ideal gas law of PV = nRT for density as follows:
n = g/M where M is molar mass substitute for n to get
PV = gRT/M or
PVM = gRT.
Then P*M = gRT/v but g/v is density in g/L so
P*M = dRT
and M = dRT/P
M = 1.42*0.08206*298/(220/760)
I wasn't in class when my teacher taught me this, and she did not go over the material well, so how were you able to go from PV=nRT to M=dRT/P?
Go back and re-read my original response. I showed you how I did it; i.e., I didn't just pull it out of the air. I derived the equation for you. I started with PV = nRT, substituted grams/molar mass (g/M) for n, rearranged to get P*M = gRT/v, noted that g/v = density = d and that ends up with P*M = dRT. Then I solve for M = dRT/P.
Oh I see now. I read it as each step you had was just different equations that you combined, not as a series of steps. Thank you!
To calculate the molar mass of chloroform, we need to use the ideal gas law equation, which relates the pressure (P), volume (V), temperature (T), and number of moles (n) of a gas.
The ideal gas law equation is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.08206 L·atm/(mol·K))
T = temperature in Kelvin
In this case, we have the pressure, temperature, and density of chloroform, but we need to convert the density to moles per liter before we can proceed.
To convert the density from grams per liter (g/L) to moles per liter (mol/L), we need to divide the given density (1.42 g/L) by the molar mass of chloroform (M) in grams per mole.
So, rearranging the ideal gas law equation to solve for the molar mass, we have:
M = (PV) / (nRT)
We can rewrite the above equation as:
M = (P / (RT)) * V / n
Now, let's plug in the known values:
P = 220 mmHg (Note: since mmHg is not in the standard units of atm, we need to convert it to atm by dividing by 760 mmHg/atm)
T = 25°C = 298 K
To convert pressure from mmHg to atm, we divide by 760 mmHg/atm:
P = (220 mmHg) / (760 mmHg/atm) ≈ 0.289 atm
With the density of chloroform given as 1.42 g/L, we can use this value to calculate the number of moles (n) corresponding to the given volume of 1 liter.
n = (density / molar mass)
1.42 g/L = (1 L) * (molar mass / 1 mole)
We need to solve for molar mass, so to isolate it:
molar mass = density * 1 mole
Now, plug in the values:
molar mass = 1.42 g/mol
Now we have everything we need to calculate the molar mass of chloroform:
M = (P / (RT)) * V / n
= (0.289 atm) / ((0.08206 L·atm/(mol·K)) * (298 K)) * (1 L) / (1.42 g/mol)
After performing the calculation, the molar mass of chloroform is approximately 119.37 g/mol.