A compound contains only hydrogen and nitrogen and is 12.6% hydrogen by mass. A gaseous sample of the compound has density of 0.925g/L at 690 torr and 110 degree Celsius. What is the molecular formula of the compound?
To determine the molecular formula of the compound, we need to follow a series of steps:
Step 1: Calculate the molar mass of the compound.
First, we need to calculate the molar mass of the compound before we can determine its molecular formula. To do this, we need to consider the percent composition of hydrogen and nitrogen.
Assume we have a 100g sample of the compound. Since the compound is 12.6% hydrogen by mass, we have 12.6g of hydrogen. Similarly, the amount of nitrogen can be calculated using the remaining mass of the compound (100g - 12.6g = 87.4g).
Next, we need to convert the masses of hydrogen and nitrogen into moles. The molar mass of hydrogen (H) is approximately 1 g/mol, and the molar mass of nitrogen (N) is approximately 14 g/mol.
Moles of hydrogen: 12.6g / 1 g/mol = 12.6 mol
Moles of nitrogen: 87.4g / 14 g/mol ≈ 6.24 mol
Step 2: Determine the empirical formula.
The empirical formula represents the simplest ratio of atoms in a compound. To determine the empirical formula, we need to find the ratio of the number of moles of each element.
Divide each number of moles by the smallest number of moles to obtain the simplest ratio:
Moles of hydrogen: 12.6 mol / 6.24 mol ≈ 2.02 ≈ 2
Moles of nitrogen: 6.24 mol / 6.24 mol = 1
The empirical formula is therefore H2N.
Step 3: Calculate the molar mass of the empirical formula.
The molar mass of the empirical formula, H2N, can be calculated by summing the atomic masses of its constituent elements:
(2 * molar mass of H) + (1 * molar mass of N)
(2 * 1 g/mol) + (1 * 14 g/mol) = 16 g/mol
Step 4: Calculate the molar mass of the molecular formula.
The empirical formula is multiplied by a whole number, n, to obtain the molecular formula. To find this value of n, we divide the molar mass of the compound by the molar mass of the empirical formula.
Given the molar mass of the compound, we can calculate it using the ideal gas law at the given temperature and pressure.
First, we need to convert the density of the gas from g/L to g/mL (since 1 L is equal to 1000 mL):
Density of the gas = 0.925 g/L = 0.925 g/mL
We can also convert the given temperature from degrees Celsius to Kelvin by adding 273.15:
Temperature = 110°C + 273.15 = 383.15 K
Now, we can solve the ideal gas law for the molar mass (M):
PV = nRT → M = (mRT) / (PV)
Where:
m = mass (density * volume)
R = ideal gas constant (0.08206 L·atm/mol·K)
T = temperature (in Kelvin)
P = pressure (in atm)
V = volume (in L)
First, we need to calculate the mass (m):
mass = density * volume = 0.925 g/mL * 1 L = 0.925 g
Now we can calculate the molar mass (M):
M = (0.925 g * 0.08206 L·atm/mol·K * 383.15 K) / (690 torr/760 torr/atm * 1 L)
M ≈ 31.93 g/mol
To calculate the value of n in the molecular formula, divide the molar mass of the compound by the molar mass of the empirical formula:
n = molar mass of the compound / molar mass of the empirical formula
n ≈ 31.93 g/mol / 16 g/mol
n ≈ 1.996 ≈ 2
Step 5: Write the molecular formula.
Multiply the empirical formula (H2N) by the value of n:
H2N * 2 = H4N2
Therefore, the molecular formula of the compound is H4N2.