A 1.325 g sample of an unknown vapor occupies 386 mL at 114 celsius and 946 mmHg. The simplest formula of the compound is NO2. What is the molecular formula of the compound?
(I have N2O4, is this correct and if not, why not? We never went over this type of question in class!
Dr. Bob222, in answer to your question, I'm not sure if I know how to work this. I tried to. Could you walk me through it?!!
To determine the molecular formula of a compound, we need to use data from the experiment and apply the principles of stoichiometry. We'll follow these steps:
Step 1: Convert the given mass of the sample to moles.
To convert grams to moles, we use the molar mass of the compound. In this case, the molar mass of NO2 is:
N = 14.01 g/mol (molar mass of nitrogen)
O = 16.00 g/mol (molar mass of oxygen)
Total molar mass of NO2 = 14.01 g/mol + (2 * 16.00 g/mol) = 46.01 g/mol
Given mass of sample = 1.325 g
Moles = given mass / molar mass
Moles of sample = 1.325 g / 46.01 g/mol ≈ 0.0288 mol
Step 2: Convert the given volume of the gas to moles at STP.
STP stands for standard temperature and pressure, which is 0 degrees Celsius (273 K) and 1 atm or 760 mmHg.
To convert the given volume of the gas to moles at STP, we need to use the ideal gas law:
PV = nRT
Where:
P = pressure (946 mmHg)
V = volume (386 mL)
n = moles of the gas (unknown)
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, convert the given temperature to Kelvin:
114 degrees Celsius + 273 = 387 K
Now, rearrange the ideal gas law equation to solve for n:
n = (PV) / (RT)
n = (946 mmHg * (386 mL / 1000)) / (0.0821 L·atm/mol·K * 387 K)
n = (946 * 386 * 1) / (0.0821 * 387)
n ≈ 49.71 moles
Step 3: Determine the empirical formula.
The empirical formula shows the simplest whole-number ratio of atoms in a compound. To find the empirical formula, divide the moles of each element by the smallest value obtained.
In the given molecular formula, NO2, we have:
N : O = 1 : 2
Therefore, the empirical formula is NO2.
Step 4: Determine the molecular formula.
The molecular formula represents the actual number of atoms of each element in a compound. To find the molecular formula, we need to know the molar mass of the compound.
To calculate the molar mass of the compound, we need the actual mass of the sample:
Actual mass of sample = empirical formula mass × empirical formula multiplier
Given mass of sample = 1.325 g (from the question)
Empirical formula mass = (molar mass of N + 2 * molar mass of O)
Empirical formula mass = (14.01 g/mol + 2 * 16.00 g/mol) = 46.01 g/mol
Empirical formula multiplier = actual mass of sample / empirical formula mass
Empirical formula multiplier = 1.325 g / 46.01 g/mol ≈ 0.0288
Therefore, the empirical formula is NO2, and the molecular formula is the same as the empirical formula in this case, which is NO2.
Since the given answer is N2O4, it is incorrect. This is because the mole ratios of the empirical formula NO2 are already the simplest whole-number ratio, and there is no need to multiply it by an integer to obtain a different molecular formula.