Respuesta :
Answer: The molecular formula for the given organic compound is [tex]C_4H_8O_2[/tex]
Explanation:
We are given:
Percentage of C = 54.5 %
Percentage of H = 9.1 %
Percentage of O = 36.4 %
Let the mass of compound be 100 g. So, percentages given are taken as mass.
Mass of C = 54.5 g
Mass of H = 9.1 g
Mass of O = 36.4 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{54.5g}{12g/mole}=4.54moles[/tex]
Moles of Hydrogen = [tex]\frac{\text{Given mass of Hydrogen}}{\text{Molar mass of Hydrogen}}=\frac{9.1g}{1g/mole}=9.1moles[/tex]
Moles of Oxygen = [tex]\frac{\text{Given mass of oxygen}}{\text{Molar mass of oxygen}}=\frac{36.4g}{16g/mole}=2.28moles[/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 2.28 moles.
For Carbon = [tex]\frac{4.54}{2.28}=1.99\approx 2[/tex]
For Hydrogen  = [tex]\frac{9.1}{2.28}=3.99\approx 4[/tex]
For Oxygen  = [tex]\frac{2.28}{2.28}=1[/tex]
Step 3: Taking the mole ratio as their subscripts.
The ratio of C : H : O = 2 : 4 : 1
Hence, the empirical formula for the given compound is [tex]C_2H_{4}O_1=C_2H_4O[/tex]
Mass of empirical formula = [tex]C_2H_4O[/tex] Â = 2(12) + 4(1) + 16 = 44 g/eq.
Now we have to determine the molar mass of compound by using ideal gas equation.
[tex]PV=nRT\\\\PV=\frac{w}{M}RT[/tex]
where,
P = pressure of gas = 1.00 atm
V = volume of gas = 120 mL = 0.120 L
T = temperature of gas = [tex]100^oC=273+100=373K[/tex]
w = mass of gas = 0.345 g
M = molar mass of gas = ?
R = gas constant = 0.0821 L.atm/mol.K
Now put all the given values in the above formula, we get:
[tex]PV=\frac{w}{M}RT[/tex]
[tex](1.00atm)\times (0.120L)=\frac{0.345g}{M}\times (0.0821L.atm/mol.K)\times (373K)[/tex]
[tex]M=88.04g/mol[/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 = 88.04 g/mol
Mass of empirical formula = 44 g/mol
Putting values in above equation, we get:
[tex]n=\frac{88.04g/mol}{44g/mol}=2[/tex]
Multiplying this valency by the subscript of every element of empirical formula, we get:
[tex]C_2H_4O=(C_2H_4O)_n=(C_2H_4O)_2=C_4H_8O_2[/tex]
Thus, the molecular formula for the given compound is [tex]C_4H_8O_2[/tex]
The empirical formula of the given compound is [tex]\bold {C_2H_4O}[/tex]. The empirical formula is the smallest whole-number ratio of the compound.
Assume the mass of the compound is 100 g. So, the percentages given are taken as mass.
Mass of C = 54.5 g  = 4.54 moles
Mass of H = 9.1 g  = 9.1 moles
Mass of O = 36.4 g = 2.28 moles
To formulate the empirical formula, Calculate the molar ratio by dividing moles by the smallest number,
For the mole ratio, we divide each value of the moles by the smallest number of moles, we get.
For Carbon = 2
For Hydrogen  =4
For Oxygen  = 1
Therefore, the empirical formula of the given compound is [tex]\bold {C_2H_4O}[/tex].
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