Diacetyl, a substance contributing to the characteristic flavor and aroma of butter, consists of 55.8% C, 7.03% H, and 37.17% O. In the gaseous state at 100 degrees celsius and 747 torr, a 0.30 gram sample occupies a volume of 111 ml. What is the molecular formula of diacetyl?
Take 100 grams sample.
That gives you
55.8 g C
7.03 g H
37.17 g O
Convert to moles
55.8/12 = 4.65 moles C
7.03/
37.17/
Now find the ratio of these numbers to each other using small whole numbers. The easy way to do that is to divide the smallest number by itself, then divide all of the other numbers by the same small number. This gives you the empirical formula.
Now use PV = nRT to determine n.
Then n = grams/molar mass
Calculate molar mass and from there the molecular formula.
Post your work if you get stuck.
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To determine the molecular formula of diacetyl, we need to follow the steps outlined below:
Step 1: Calculate the number of moles of diacetyl
To calculate the number of moles, we will use the ideal gas law formula: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.
First, let's convert the temperature to Kelvin:
T(K) = t(C) + 273.15
T(K) = 100°C + 273.15 = 373.15K
Next, let's convert the pressure from torr to atm:
P(atm) = P(torr) / 760
P(atm) = 747 torr / 760 = 0.9829 atm
Now we can rearrange the ideal gas law formula to solve for n:
n = PV / RT
n = (0.9829 atm)(0.111 L) / (0.0821 L·atm/mol·K)(373.15K) = 0.00374 mol
Step 2: Determine the empirical formula
The empirical formula gives the simplest whole number ratio of the elements in a compound. We need to convert the percentages of each element into moles.
The given percentages of C, H, and O are:
C: 55.8%
H: 7.03%
O: 37.17%
Let's assume we have 100 grams of diacetyl, so we can directly convert the percentages into grams:
C: 55.8 g
H: 7.03 g
O: 37.17 g
Next, we need to convert the grams of each element into moles using their molar masses:
Molar mass of C: 12.01 g/mol
Molar mass of H: 1.01 g/mol
Molar mass of O: 16.00 g/mol
Moles of C = 55.8 g / 12.01 g/mol = 4.65 mol
Moles of H = 7.03 g / 1.01 g/mol = 6.96 mol
Moles of O = 37.17 g / 16.00 g/mol = 2.32 mol
Dividing each mole value by the smallest value (2.32 mol) gives us the mole ratio:
C: 4.65 mol / 2.32 mol = 2
H: 6.96 mol / 2.32 mol = 3
O: 2.32 mol / 2.32 mol = 1
Therefore, the empirical formula of diacetyl is C2H3O.
Step 3: Determine the molecular formula
To determine the molecular formula, we need to know the molar mass of diacetyl, which can be calculated by adding up the molar masses of the empirical formula.
Molar mass of C2H3O = (2 * 12.01 g/mol) + (3 * 1.01 g/mol) + (1 * 16.00 g/mol) = 58.06 g/mol
Now we can calculate the ratio of the molar mass of the empirical formula to the molar mass of diacetyl:
Molar mass of diacetyl / Molar mass of empirical formula = 58.06 g/mol / 58.06 g/mol = 1
Since the ratio is 1, the empirical formula is also the molecular formula.
Therefore, the molecular formula of diacetyl is C2H3O.
To determine the molecular formula of diacetyl, we need to find the empirical formula first and then use the molar mass to deduce the molecular formula.
Step 1: Finding the empirical formula:
To find the empirical formula, we need to calculate the moles of each element in diacetyl.
Given:
Mass of C = 55.8% = 0.558 g
Mass of H = 7.03% = 0.0703 g
Mass of O = 37.17% = 0.3717 g
For each element, we divide the given mass by the atomic mass:
Moles of C = 0.558 g / 12.01 g/mol = 0.0465 mol
Moles of H = 0.0703 g / 1.008 g/mol = 0.0698 mol
Moles of O = 0.3717 g / 16.00 g/mol = 0.0232 mol
Next, we divide the number of moles of each element by the smallest number of moles to get the simplest integer ratio:
Dividing by 0.0232 (smallest value):
Moles of C = 0.0465 mol / 0.0232 mol = 2
Moles of H = 0.0698 mol / 0.0232 mol = 3
Moles of O = 0.0232 mol / 0.0232 mol = 1
The empirical formula of diacetyl is C2H3O.
Step 2: Finding the molecular formula:
To find the molecular formula, we need to know the molar mass of diacetyl.
Given:
Mass of sample = 0.30 g
Volume of sample = 111 ml
Temperature = 100 degrees Celsius
Pressure = 747 torr
We need to convert the volume to liters and the temperature to Kelvin:
Volume = 111 ml = 0.111 L
Temperature = 100 degrees Celsius + 273.15 = 373.15 K
Using the Ideal Gas Law equation: PV = nRT, we can calculate the number of moles (n):
n = PV / RT
= (747 torr * 0.111 L) / (0.0821 L·atm/mol·K * 373.15 K)
≈ 0.0417 mol
Now we can calculate the molar mass (M) of diacetyl:
M = mass / moles
= 0.30 g / 0.0417 mol
≈ 7.2 g/mol
The molar mass of diacetyl is approximately 7.2 g/mol.
To find the molecular formula, we compare the molar mass of the empirical formula (C2H3O) with the calculated molar mass (7.2 g/mol).
Empirical formula molar mass = 12.01 g/mol (C) + 1.008 g/mol (H) + 16.00 g/mol (O)
= 28.03 g/mol
Since the molecular mass (7.2 g/mol) is greater than the empirical formula mass (28.03 g/mol), it means that the empirical formula should be multiplied by a whole number to obtain the molecular formula.
Dividing the molecular mass (7.2 g/mol) by the empirical formula mass (28.03 g/mol) gives us the whole number multiplier:
Multiplier = molecular mass / empirical formula mass
= 7.2 g/mol / 28.03 g/mol
≈ 0.256
The multiplier approximation 0.256 rounds up to 1, which means the molecular formula is the same as the empirical formula.
Therefore, the molecular formula of diacetyl is C2H3O.