A gaseous compound containing carbon and hydrogen was analyzed and found to cons
ist of between
80 and 90 percent carbon by mass. At 145ºC and 1.00 atm, the density of this compound is 2.45 g/L.
What is the molar mass of the compound?
Using Ideal Gas Law
PV = nRT = (mass/f.wt)RT
Solve for f.wt.
f.wt = (mass)RT/PV
= (2.45g)(0.08206L-Atm/mol-K)(418K)/(1-Atm)(1-L)
= 84.04 g/mole
To find the molar mass of the compound, we need to use the density and the percentage of carbon by mass.
First, let's assume we have 100 grams of the gaseous compound.
Since it is given that the compound consists of between 80% and 90% carbon by mass, we can assume that it consists of 80 grams of carbon (the lowest possible value) and 90 grams of carbon (the highest possible value).
Next, we need to convert the mass of carbon to moles. To do this, we divide the mass of carbon by the molar mass of carbon, which is 12.01 g/mol.
For the lowest possible value, the moles of carbon would be 80 g / 12.01 g/mol ≈ 6.66 mol of carbon.
For the highest possible value, the moles of carbon would be 90 g / 12.01 g/mol ≈ 7.49 mol of carbon.
Now, we need to find the total mass of the compound. We can subtract the mass of carbon from the assumed 100 grams:
For the lowest possible value, the total mass of the compound would be 100 g - 80 g = 20 g.
For the highest possible value, the total mass of the compound would be 100 g - 90 g = 10 g.
Finally, we can calculate the molar mass by dividing the total mass of the compound by the moles of carbon:
For the lowest possible value, the molar mass would be 20 g / 6.66 mol ≈ 3.00 g/mol.
For the highest possible value, the molar mass would be 10 g / 7.49 mol ≈ 1.33 g/mol.
Therefore, the molar mass of the compound is between 1.33 g/mol and 3.00 g/mol, depending on the assumed percentage of carbon.
To find the molar mass of the compound, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (1.00 atm)
V = volume (2.45 g/L)
n = number of moles of the compound
R = ideal gas constant (0.08206 L·atm/(mol·K))
T = temperature (145ºC = 145 + 273 = 418 K)
First, let's calculate the number of moles of the compound using the given density:
Density = mass/volume
Rearranging the equation, we get:
Mass = Density * Volume
Mass = 2.45 g/L * 1 L
Mass = 2.45 g
Now, let's calculate the number of moles using the molar mass (M) of the compound:
Moles = Mass/Molar Mass
Substituting the known values:
n = 2.45 g / M
Next, let's rearrange the ideal gas law equation to solve for the molar mass (M):
M = Mass / Moles
Substituting the known values:
M = 2.45 g / n
M = 2.45 g / (2.45 g / M)
M = M
Therefore, the molar mass of the compound is M. The exact molar mass cannot be determined without additional information about the compound.