Respuesta :
Answer: The empirical and molecular formula for the given organic compound is [tex]C_2H[/tex] and [tex]C_{20}H_{10}[/tex]
Explanation:
The chemical equation for the combustion of hydrocarbon having carbon and hydrogen follows:
[tex]C_xH_y+O_2\rightarrow CO_2+H_2O[/tex]
where, 'x' and 'y' are the subscripts of Carbon and hydrogen respectively.
We are given:
Mass of [tex]CO_2=11.58mg=0.01158g[/tex] (Conversion factor: 1 g = 1000 mg)
Mass of sample = 3.320 mg = 0.00332 g
For calculating the mass of carbon:
In 44 g of carbon dioxide, 12 g of carbon is contained.
So, in 0.01158 g of carbon dioxide, [tex]\frac{12}{44}\times 0.01158=0.00316g[/tex] of carbon will be contained.
Mass of hydrogen in the compound = (0.00332) - (0.00316) = 0.00016 g
To formulate the empirical formula, we need to follow some steps:
- Step 1: Converting the given masses into moles.
Moles of Carbon =[tex]\frac{\text{Given mass of Carbon}}{\text{Molar mass of Carbon}}=\frac{0.00316g}{12g/mole}=0.00026moles[/tex]
Moles of Hydrogen = [tex]\frac{\text{Given mass of Hydrogen}}{\text{Molar mass of Hydrogen}}=\frac{0.00016g}{1g/mole}=0.00016moles[/tex]
- Step 2: Calculating the mole ratio of the given elements.
For the mole ratio, we divide each value of the moles by the smallest number of moles calculated which is 0.00016 moles.
For Carbon = [tex]\frac{0.00026}{0.00016}=1.625\approx 2[/tex]
For Hydrogen = [tex]\frac{0.00016}{0.00016}=1[/tex]
- Step 3: Taking the mole ratio as their subscripts.
The ratio of C : H = 2 : 1
The empirical formula for the given compound is [tex]C_2H[/tex]
For determining the molecular formula, we need to determine the valency which is multiplied by each element to get the molecular formula.
The equation used to calculate the valency is :
[tex]n=\frac{\text{Molecular mass}}{\text{Empirical mass}}[/tex]
We are given:
Mass of molecular formula = 252.3 g/mol
Mass of empirical formula = 25 g/mol
Putting values in above equation, we get:
[tex]n=\frac{252.3g/mol}{25g/mol}=10[/tex]
Multiplying this valency by the subscript of every element of empirical formula, we get:
[tex]C_{(10\times 2)}H_{(10\times 1)}=C_{20}H_{10}[/tex]
Hence, the empirical and molecular formula for the given organic compound is [tex]C_2H[/tex] and [tex]C_{20}H_{10}[/tex]
