Cyclohexane is composed of 85.6 % C and 14.4% H. when it is mixed in the proper ratio with oxygen, it can be used as an anesthetic. At 755 mmHg, and 25 degrees Celcius, it has a density of 2.05 g/L.
what is the molar mass of cyclohexane and its molecular formula?
Will you check the problem. It appears to me that the density is almost 1/2 what it should be. If you confirm that 2.05 g/L is correct, I will show you how to work it with those numbers but we won't come out with C6H12.
The way i posted it the first time is correct..please help! im stuck
If we take 100 g sample, we will have 85.6 g C and 14.4 g H.
mols C = 85.6/12 = about 7
mols H = 14.4/1 = about 14
ratio is 1:2; therefore, the simplest empirical formula is CH2. We are ok to here.
1 L of gas at 755 mm Hg pressure and 298 K will have a volume of ?? at STP. Use P1V1/T1 = P2V2/T2. I found 0.91 L.
So 2.05g/L (at non-standard conditions) will be 2.05/0.91 L at STP = 2.25 g/L.
We know that 1 mol of cyclohexane has a volume of 22.4 L at STP; therefore, 2.25 g/L x 22.4L = about 50 g and this is where we get into trouble because the molar mass of C6H12 is about 84. But we will go with the flow here.
The simplest empirical formula is CH2 (from above) and that has a molar mass of 12 + 2 = 14. So how many times will 14 go into 50.4. That is 50.4/14 = 3.6. We can round the 3.6 to 4 (it must be an even number in almost all cases) so the molecular formula would then be (CH2)4 or C4H8 and that doesn't look like cyclohexane (because hex is 6). If we round down to 3 we have C3H6. The density at STP should be about 3.75. Check my thinking. Check my work. I may have made an error.
To find the molar mass and molecular formula of cyclohexane, we start by calculating the number of moles of carbon (C) and hydrogen (H) in a 100g sample of cyclohexane.
Number of moles of C = mass of C / atomic mass of C
= 85.6g / 12g/mol ≈ 7 moles
Number of moles of H = mass of H / atomic mass of H
= 14.4g / 1g/mol ≈ 14 moles
The ratio of C to H is 1:2, so the simplest empirical formula is CH2.
Next, we need to calculate the volume of the gas at standard temperature and pressure (STP, 0 degrees Celsius and 1 atmosphere pressure) using the given conditions of 755 mmHg and 25 degrees Celsius. We can use the ideal gas law equation P1V1/T1 = P2V2/T2.
Given:
P1 = 755 mmHg
V1 = 1 L (since it is given as density)
T1 = 25 degrees Celsius = 298 K
P2 = 1 atm (STP)
T2 = 0 degrees Celsius = 273 K (STP)
Using the equation P1V1/T1 = P2V2/T2:
V2 = (P1 * V1 * T2) / (P2 * T1)
= (755 mmHg * 1 L * 273 K) / (1 atm * 298 K)
≈ 0.91 L
Now, we can calculate the density at STP using the given density of 2.05 g/L at non-standard conditions.
Density at STP = (density at non-standard conditions * V2) / V1
= (2.05 g/L * 0.91 L) / 1 L
≈ 1.87 g/L
Since we know that 1 mole of a gas occupies 22.4 L at STP, we can calculate the molar mass by dividing the density at STP by the molar volume at STP.
Molar mass of cyclohexane = density at STP / molar volume at STP
= 1.87 g/L / 22.4 L/mol
≈ 0.0835 g/mol
However, this molar mass (0.0835 g/mol) is significantly lower than the actual molar mass of cyclohexane (84.16 g/mol). This suggests an error in the calculations or the given information.
Considering the molecular formula, if we assume the empirical formula (CH2) and calculate the molar mass as 12 + 2 = 14 g/mol, it does not match the expected molar mass of cyclohexane and leads to an incorrect molecular formula.
In conclusion, based on the given information and calculations, there seems to be an error as the calculated molar mass and molecular formula do not match the expected values for cyclohexane. It is recommended to verify the given conditions and data to work on the problem accurately.