A nitrogen and oxygen composition of 4,6g contains 3,2g of oxygen
a)if it is known that 46g of the gas at STD occupies 11,2dm cube , calculate the molecular formula of the compound
To find the molecular formula of the compound, we need to find the molar masses of nitrogen and oxygen and determine the ratio of nitrogen to oxygen in the compound.
Molar mass of nitrogen (N) = 14.01 g/mol
Molar mass of oxygen (O) = 16.00 g/mol
First, let's find the number of moles of oxygen in the composition:
Number of moles of oxygen = mass of oxygen / molar mass of oxygen
Number of moles of oxygen = 3.2 g / 16.00 g/mol = 0.20 mol
Next, let's find the number of moles of nitrogen in the composition:
Number of moles of nitrogen = total number of moles - number of moles of oxygen
Number of moles of nitrogen = (4.6 g / molar mass of nitrogen) - 0.20 mol
To find the molar mass of the compound, we can use the given information that 46 g of the gas occupy 11.2 dm³ at standard temperature and pressure (STP). We can use the ideal gas law equation PV = nRT, where P = pressure, V = volume, n = number of moles, R = ideal gas constant, and T = temperature in Kelvins.
At STP, the pressure (P) is 1 atm and the temperature (T) is 273.15 K. Rearranging the equation to solve for the volume (V), we get:
V = nRT / P
V = (total number of moles of gas)(R)(T) / P
11.2 dm³ = (total number of moles)(0.0821 L*atm/mol*K)(273.15 K) / 1 atm
Since we have already found the number of moles of oxygen, we can substitute the number of moles of nitrogen into the equation:
11.2 dm³ = [(total number of moles - 0.20 mol)(0.0821 L*atm/mol*K)(273.15 K)] / 1 atm
Solving this equation for the total number of moles, we find:
(total number of moles - 0.20 mol) = (11.2 dm³)(1 atm) / [(0.0821 L*atm/mol*K)(273.15 K)]
(total number of moles - 0.20 mol) = 11.2 dm³ / 24.4654 L/mol
Now, we can substitute the calculated values back into the equation for the number of moles of nitrogen:
Number of moles of nitrogen = (4.6 g / molar mass of nitrogen) - 0.20 mol
Number of moles of nitrogen = (4.6 g / 14.01 g/mol) - 0.20 mol
Finally, we can determine the ratio of nitrogen to oxygen in terms of moles:
Ratio (in moles) = moles of nitrogen / moles of oxygen
And the molecular formula of the compound would be the simplest whole number ratio that represents this ratio.
To find the molecular formula of the compound, we need to determine the number of moles of nitrogen and oxygen in the given composition.
1. Calculate the number of moles of oxygen:
Mass of oxygen = 3.2 g
Molar mass of oxygen (O) = 16 g/mol
Number of moles = Mass / Molar mass = 3.2 g / 16 g/mol = 0.2 mol
2. Calculate the number of moles of nitrogen:
Mass of nitrogen = Mass of composition - Mass of oxygen = 4.6 g - 3.2 g = 1.4 g
Molar mass of nitrogen (N) = 14 g/mol
Number of moles = Mass / Molar mass = 1.4 g / 14 g/mol = 0.1 mol
3. Calculate the ratio of nitrogen to oxygen in moles:
Nitrogen:Oxygen = 0.1 mol : 0.2 mol
Simplifying the ratio by dividing by 0.1, we get:
Nitrogen:Oxygen = 1:2
The simplified ratio tells us that the molecular formula of the compound is N1O2.