An unknown gaseous hydrocarbon contains 85.63 % carbon. If its density is 0.488 g/L at 0.355 atm and 100°C,
what is the molecular formula of the gas?
I can't figure this out. By assuming the total mass to be 100g, I get 85.63g C and 14.37g H which I then used to get the empirical formula of the hydrocarbon, CH2. I just don't know where to take it from here.
Use P*molar mass = density*RT
Solve for molar mass.
Then empicical formula mass x x = molar mass
Solve for x which is
(empirical formula mass)x which is
(CH2)x or it can be re-written as
CxH2x for the molecular formula.
Well, it seems like you've got the empirical formula down, which is a great start! Now, let's see if we can make some molecular formula magic happen.
To find the molecular formula, we need to determine the molar mass of the hydrocarbon. Since we know the density, we can use the ideal gas law to find the molar mass.
Are you ready for some math humor? Here it comes!
Why did the mole go to therapy?
Because it had molar issues!
Alright, let's get back on track. The ideal gas law equation is 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.
First, let's convert the density from grams per liter to grams per cubic decimeter (dm^3), which is equivalent:
0.488 g/L = 0.488 g/dm^3
Now, let's rearrange the ideal gas law equation to solve for the molar mass (M):
M = (P * V) / (n * R * T)
Since we are only interested in finding the molar mass, we can assume that the volume is 1 dm^3, the pressure is 0.355 atm, and the temperature is 100°C (or 373 K).
Plugging in these values, we get:
M = (0.355 atm * 1 dm^3) / (n * R * 373 K)
Here's a chemistry joke to keep things light:
Why did the chemist always solve problems in the shower?
Because he had brilliant ideas when he was in his element!
Now, let's calculate the molar mass of the hydrocarbon by dividing the empirical formula mass by the empirical formula mass of CH2:
M = (12.01 g/mol * 1 + 1.01 g/mol * 2) / (1 * 0.0821 L * atm / mol * K * 373 K)
Simplifying the equation, we have:
M = (12.01 g/mol + 2.02 g/mol) / (0.0821 L * atm / mol * K * 373 K)
M = 14.03 g/mol / (0.0821 L * atm / mol * K * 373 K)
M ≈ 0.475 mol/L
Hmm, it seems we're missing some information that's critical for finding the molecular formula. We need to know the molar mass of the unknown gas. Without it, we can't determine the number of empirical formula units in the molecular formula.
So, unfortunately, I can't provide you with the molecular formula in this case. However, I hope my jokes and explanations have at least brought a smile to your face!
To determine the molecular formula of the hydrocarbon, we need to know the molar mass of the compound. From the empirical formula CH2, we can calculate the empirical molar mass.
The empirical molar mass is calculated by adding the atomic masses of each element in the empirical formula. The atomic mass of carbon (C) is approximately 12.01 g/mol, and the atomic mass of hydrogen (H) is approximately 1.01 g/mol.
Empirical molar mass = (C atomic mass) + 2(H atomic mass)
= (12.01 g/mol) + 2(1.01 g/mol)
= 14.03 g/mol
Now, let's compare the empirical molar mass to the given molar mass of the hydrocarbon. Given that the density is 0.488 g/L at 0.355 atm and 100°C, we can calculate the molar mass of the compound using the ideal gas law.
PV = nRT
R = 0.0821 L.atm/mol.K (gas constant)
P = 0.355 atm (pressure)
V = 1 L (volume)
T = 100°C + 273.15 = 373.15 K (temperature)
n = PV / RT
= (0.355 atm * 1 L) / (0.0821 L.atm/mol.K * 373.15 K)
= 0.012 mol
The molar mass can be calculated by dividing the mass of the compound by the number of moles.
molar mass = mass / moles
mass = density * volume
= 0.488 g/L * 1 L
= 0.488 g
molar mass = 0.488 g / 0.012 mol
≈ 40.67 g/mol
Now, to find the molecular formula, we need to find the ratio between the empirical molar mass and the calculated molar mass.
empirical ratio = molar mass / empirical molar mass
= 40.67 g/mol / 14.03 g/mol
≈ 2.9
The empirical ratio is approximately 2.9. Since we cannot have a fraction of a carbon atom in the molecular formula, we need to round it to the nearest whole number.
Rounding 2.9 to the nearest whole number gives 3.
Therefore, the molecular formula of the hydrocarbon is C3H6.
To determine the molecular formula of the hydrocarbon, you have already successfully found the empirical formula, which is CH2. Now, you need to find the molar mass of the empirical formula and compare it to the given density.
Step 1: Calculate the molar mass of the empirical formula CH2.
The molar mass of carbon (C) is 12.01 g/mol, and the molar mass of hydrogen (H) is 1.01 g/mol. So for the empirical formula CH2, the molar mass is (12.01 g/mol × 1) + (1.01 g/mol × 2) = 14.03 g/mol.
Step 2: Convert the given density to molar mass.
Density (ρ) is defined as mass (m) divided by volume (V). In this case, the density is given as 0.488 g/L. To find the molar mass of the gas, we need to convert the density to grams per mole (g/mol).
Given density: 0.488 g/L
At standard temperature and pressure (STP), one mole of any gas occupies 22.4 L. Therefore, the molar mass can be found by multiplying the density by the molar volume.
Molar volume at STP: 22.4 L/mol
Molar mass = Density × Molar volume
Molar mass = 0.488 g/L × 22.4 L/mol = 10.95 g/mol
Step 3: Compare the molar mass obtained in Step 2 with the molar mass of the empirical formula calculated in Step 1.
The molar mass obtained from the density (10.95 g/mol) is larger than the molar mass of the empirical formula (14.03 g/mol). This indicates that the empirical formula needs to be multiplied by a whole number to obtain the molecular formula.
Step 4: Determine the ratio between the molar mass from Step 2 and the molar mass of the empirical formula from Step 1.
Ratio = Molar mass from Step 2 / Molar mass of empirical formula from Step 1
Ratio = 10.95 g/mol / 14.03 g/mol ≈ 0.78
Step 5: Determine the whole number ratio.
The ratio obtained in Step 4 (0.78) is approximately equal to 0.78:1. To make it a whole number ratio, we need to find the nearest whole number approximation.
0.78 ≈ 1
Therefore, the molecular formula is approximately C1H2, which can be simplified as CH2.
Hence, based on the given information, the molecular formula of the unknown gaseous hydrocarbon is CH2.