An unknown compound analyzes to be 42.85% C, 7.20% H, and 49.95% N. A 0.915 g sample of the gas occupies 250. mL at 760. mm Hg and 100.°C. Type your answers using the format CH4 for CH4. Enter the elements in the order given.

I have calculated the emperical formula to be CH2N, but I'm not sure how to calculate the molecular formula.

I didn't check the empirical formula. We will assume that is correct. The empirical formula weight is 12+2+14 = 28.

Use PV = nRT to calculate n = number of moles. Remember P is in atm and T in Kelvin. Then since moles = grams/molar mass, you have moles and grams, calculate molar mass.
Then molar mass/empirical mass = some number. Round to whole number, which I will call x. The molecular formula, then, is (CH2N)x

To calculate the molecular formula, you will need the molar mass of the empirical formula.

First, let's find the molar mass of the empirical formula CH2N:

The molar mass of carbon (C) is approximately 12.01 g/mol.
The molar mass of hydrogen (H) is approximately 1.008 g/mol.
The molar mass of nitrogen (N) is approximately 14.01 g/mol.

Molar mass of CH2N = (12.01 g/mol) + (1.008 g/mol) × 2 + (14.01 g/mol) = 28.04 g/mol

Next, let's find the molar mass of the unknown compound. We have the following information:

Mass of the gas sample = 0.915 g
Volume of the gas sample = 250. mL
Pressure = 760. mm Hg
Temperature = 100.°C

First, let's convert the volume of the gas sample to liters:

Volume of the gas sample = 250. mL ÷ 1000 = 0.250 L

Next, let's convert the pressure from mm Hg to atm:

Pressure = 760. mm Hg ÷ 760 = 1 atm

Now, we can use the ideal gas law equation to calculate the number of moles of the gas:

PV = nRT

P = Pressure in atm = 1 atm
V = Volume in L = 0.250 L
n = number of moles
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature in Kelvin (K)

To convert the temperature from Celsius to Kelvin, add 273.15:

Temperature = 100.°C + 273.15 = 373.15 K

Plugging in the values into the ideal gas law equation:

(1 atm) × (0.250 L) = n × (0.0821 L·atm/(mol·K)) × (373.15 K)

n = (1 atm × 0.250 L) ÷ (0.0821 L·atm/(mol·K) × 373.15 K) = 0.011 mol

Now, we can calculate the molar mass of the unknown compound:

Molar mass = Mass of the gas sample / Number of moles
Molar mass = 0.915 g / 0.011 mol = 83.18 g/mol

Finally, we can calculate the molecular formula:

Molar mass of the molecular formula / Molar mass of the empirical formula = integer ratio

Molar mass of the molecular formula = 83.18 g/mol
Molar mass of the empirical formula = 28.04 g/mol

Integer ratio = (83.18 g/mol) ÷ (28.04 g/mol) ≈ 2.97

Since the ratio is close to 3, we multiply the empirical formula by 3:

(CH2N)3 = C3H6N3

Therefore, the molecular formula of the unknown compound is C3H6N3.

To calculate the molecular formula from the empirical formula, you need to know the empirical formula's molar mass and the compound's actual molar mass.

Since you have determined the empirical formula to be CH2N, we can calculate its empirical molar mass using the atomic weights of carbon (C), hydrogen (H), and nitrogen (N) from the periodic table.

The atomic weight of carbon (C) is approximately 12.01 g/mol, the atomic weight of hydrogen (H) is approximately 1.01 g/mol, and the atomic weight of nitrogen (N) is approximately 14.01 g/mol.

Using these values, we can calculate the empirical molar mass as follows:

Empirical molar mass = (mass of carbon x atomic weight of carbon) + (mass of hydrogen x atomic weight of hydrogen) + (mass of nitrogen x atomic weight of nitrogen)

Now we substitute the given percentages to find the mass of each element in a 100 g sample:

Mass of C = 42.85 g/100 g x 100 g = 42.85 g
Mass of H = 7.20 g/100 g x 100 g = 7.20 g
Mass of N = 49.95 g/100 g x 100 g = 49.95 g

Next, we calculate the number of moles of each element:

Moles of C = Mass of C / Atomic weight of C
Moles of H = Mass of H / Atomic weight of H
Moles of N = Mass of N / Atomic weight of N

Now divide each number of moles by the smallest number of moles calculated. In this case, the smallest number of moles is the number of moles of carbon (C). By dividing all the moles by the smallest number, you obtain the empirical formula's subscripts.

So, the empirical formula is CH2N, as you have calculated.

To determine the molecular formula, you need to know the compound's actual molar mass. In this case, you have the mass of a 0.915 g sample.

First, we calculate the number of moles of the empirical formula:

Moles of CH2N = (Mass of sample / Empirical molar mass)

Next, we calculate the empirical formula's molar mass:

Empirical molar mass of CH2N = (Atomic weight of carbon x number of atoms of carbon) + (Atomic weight of hydrogen x number of atoms of hydrogen) + (Atomic weight of nitrogen x number of atoms of nitrogen)

Then, divide the actual molar mass by the empirical formula's molar mass to find the molecular formula's subscript multiplier:

Subscript multiplier = (Actual molar mass / Empirical molar mass)

Finally, multiply the empirical formula's subscripts by the subscript multiplier to obtain the molecular formula:

Molecular formula = (Empirical formula) x (Subscript multiplier)

Using this approach, you will be able to calculate the molecular formula from the empirical formula.