A compound contains only nitrogen and hydrogen and is 87.4% nitrogen by mass. A gaseous sample of the compound has a density of 0.977 g/L at 680. torr and 84.1°C. What is the molecular formula of the compound?
Take a 100 g sample. That will give you
87.4 g nitrogen
100-87.4 g hydrogen.
Convert grams to moles. moles = g/atomic mass.
87.4/14 = ??
12.6/1 = ??
Find the ratio of the two atoms with the smallest number being 1. The easy way to do that is to divide the smaller number by itself; therefore,that number will be 1.000. Divide the other number by the same small number. That gives you the formula of
NxHy. The empirical mass can be calculated from that.
The second part of the problem is to determine the molar mass of the gas. That can be done by using a modified gas law of P*molar mass = density*R*T
Solve for molar mass.
Divide molar mass/empirical mass, round to a whole number and that will be z in the following.
(NxHy)z
Empirical NH2
Chemical N2H4
Well understood.
Why did the nitrogen and hydrogen go see a movie together? Because they heard it was N2Hilarious!
To find the molecular formula of the compound, we need to consider the ideal gas law. 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 in Kelvin.
First, let's convert the given temperature of 84.1°C to Kelvin. Adding 273.15 to 84.1°C, we get 357.25K.
Next, let's convert the density of the compound to molar mass. The molar mass of a compound is the mass of one mole of that compound. From the given density and the ideal gas law, we can determine the molar mass.
Density = mass/volume. Rearranging the equation, mass = density * volume.
Mass = 0.977 g/L * 1 L = 0.977 g.
Next, since we know the compound is 87.4% nitrogen by mass, we can calculate the mass of nitrogen in the compound.
Nitrogen mass = 0.874 * 0.977 g = 0.852698 g.
Now, we can calculate the number of moles of nitrogen in the compound. We divide the mass of nitrogen by the molar mass of nitrogen, which is 14.01 g/mol.
Moles of nitrogen = 0.852698 g / 14.01 g/mol ≈ 0.0609004 mol.
Since the ratio of nitrogen to hydrogen in the compound can be expressed as a whole number, we need to find the simplest ratio between nitrogen and hydrogen.
Dividing the moles of nitrogen by the smallest number of moles (0.0609004) gives us approximately 1 mole of nitrogen.
Now, we can use the ideal gas law to calculate the molar mass of the compound.
PV = nRT
n = PV/RT,
where P = 680. torr = 0.895 atm, V = 1 L, R = 0.0821 L·atm/(mol·K), and T = 357.25 K.
n = (0.895 atm * 1 L) / (0.0821 L·atm/(mol·K) * 357.25 K) ≈ 0.0289 mol.
Since we have approximately 0.0289 moles of the compound, and we previously found that we have approximately 1 mole of nitrogen, the simplest ratio between nitrogen and the compound is 1:0.0289.
To get whole numbers, we can multiply by 35.322, which rounds to 35.
Therefore, the molecular formula of the compound is N35H.
To determine the molecular formula of the compound, we need to analyze the given information and use the concept of molar mass, molar volume, and the ideal gas law. Here's how we can approach the problem step by step:
Step 1: Calculate the mass percentage of hydrogen.
Since the compound is 87.4% nitrogen by mass, the remaining percentage would be assigned to hydrogen.
Mass percentage of hydrogen = 100% - 87.4% = 12.6%
Step 2: Assume a sample size for calculation purposes.
Let's assume we have a 100g sample of the compound. This means that:
Mass of nitrogen = 87.4g (87.4% of 100g)
Mass of hydrogen = 12.6g (12.6% of 100g)
Step 3: Convert the masses of nitrogen and hydrogen to moles.
To determine the number of moles, we divide the mass of each element by their respective molar masses.
Molar mass of nitrogen (N₂) = 14.01 g/mol
Molar mass of hydrogen (H₂) = 2.02 g/mol
Number of moles of nitrogen = Mass of nitrogen / Molar mass of nitrogen
Number of moles of nitrogen = 87.4g / 14.01 g/mol ≈ 6.24 mol
Number of moles of hydrogen = Mass of hydrogen / Molar mass of hydrogen
Number of moles of hydrogen = 12.6g / 2.02 g/mol ≈ 6.24 mol
Step 4: Determine the empirical formula.
The empirical formula represents the simplest whole number ratio between the atoms present in the compound.
In this case, we can see that both nitrogen and hydrogen have the same number of moles, 6.24 mol. Therefore, the empirical formula would be NH.
Step 5: Determine the molar volume of the compound.
The molar volume of a gas is the volume occupied by one mole of the gas at a specific temperature and pressure.
Given:
Density of the compound = 0.977 g/L
Temperature (T) = 84.1°C = (84.1 + 273.15) K = 357.25 K
Pressure (P) = 680. torr = 680. / 760. = 0.895 atm
Using the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature, we can rearrange the equation to solve for molar volume (V):
V = (nRT) / P
Molar volume = (6.24 mol * 0.0821 L·atm/mol·K * 357.25 K) / 0.895 atm
Molar volume ≈ 197.58 L/mol
Step 6: Calculate the molecular formula.
To calculate the molecular formula of the compound, we need to determine the ratio between the empirical formula and the molecular formula using the molar mass.
Molar mass of the empirical formula (NH) = 14.01 g/mol + 1.01 g/mol = 15.02 g/mol
The molar mass of the compound can be calculated by dividing the mass of the 100g sample by the molar volume:
Molar mass of the compound = 100g / 197.58 L/mol ≈ 0.506 g/L/mol
Now, we need to determine the number of empirical formula units (EFU) in one molecular formula unit (MFU).
EFU/MFU = (Molar mass of the compound) / (Molar mass of the empirical formula)
EFU/MFU ≈ 0.506 g/L/mol / 15.02 g/mol ≈ 0.034
Since the ratio is approximately 0.034, we can round it to the nearest whole number to determine the molecular formula:
EFU/MFU ≈ 0.034 ≈ 0
Therefore, the molecular formula of the compound is NH.
So, the molecular formula of the compound is NH (Ammonia).