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Concept explainers
Interpretation:
Molecular formula of compound used to make PVC and take 7.73 min to effuse has to be determined.
Concept Introduction:
Subscript of empirical formula is multiplied by value of n to give molecular formula. The value of n can be calculated through division of molecular mass by empirical formula mass as follows:
n=molecular massempirical formula mass
Effusion is explained as movement of the gas molecule through small hole.
Diffusion can be explained as when one gas molecule mix with another gas molecule by random motion.
Graham’s law of effusion gives relation of rate of effusion with molar mass. Rate of effusion and square root of molar mass are inversely related. The mathematical expression is as follows:
Effusion rate of AEffusion rate of B=√MBMA
Here,
MB is molar mass of gas B.
MA is molar mass of gas A.
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Answer to Problem 3D.8E
The molecular formula for compound used to make PVC and take 7.73 min to effuse is C2H3Cl.
Explanation of Solution
Compound PVC has 38.4 % C, 4.82 % H, and 56.8 % Cl. Consider mass of compound be 100 g. Thus 100 g of PVC compound would contain 38.4 g C, 4.82 g H, and 56.8 g Cl.
The expression to determine moles is as follows:
Moles(mol)=Given mass(g)Molar mass(g/mol) (1)
Substitute 38.4 g for given mass and 12.011 g/mol for molar mass in equation (1) to calculated moles of C.
Moles(mol)=38.4 g12.011 g/mol=3.20 mol
Substitute 4.82 g for given mass and 1.00794 g/mol for molar mass in equation (1) to calculated moles of H.
Moles(mol)=4.82 g1.00794 g/mol=4.78 mol
Substitute 56.8 g for given mass and 35.45 g/mol for molar mass in equation (1) to calculated moles of Cl.
Moles(mol)=56.8 g35.45 g/mol=1.60 mol
Since each mole value should be divided by smallest value thus divide all mole values by 1.60 to determined subscripts of respective elements.
The subscripts for C can be calculated as follows:
Subscript for C=3.20 mol C1.60=2 mol C
The subscripts for H can be calculated as follows:
Subscript for H=4.78 mol H1.60≃3 mol H
The integer or mixed fraction for Cl can be calculated as follows:
Subscript for Cl=1.60 mol Cl1.60=1 mol Cl
The final empirical formula for PVC is C2H3Cl.
Let molecular formula of compound is C2nH3nCln.
The expression for molar masses of C2nH3nCln and Ar gases and their time for effusion is as follows:
Time for C2nH3nCln to effuseTime for Ar to effuse=√MC2nH3nClnMAr (2)
Rearrange equation (2) to calculate value of MC2nH3nCln.
MC2nH3nCln=(MAr)(Time for C2nH3nCln to effuseTime for Ar to effuse)2 (3)
Substitute 39.95 g/mol for MAr, 7.73 min for time for C2nH3nCln to effuse, and 6.18 min for time for Ar to effuse in equation (2).
MC2nH3nCln=(39.95 g/mol)(7.73 min6.18 min)2=62.50 g/mol
Thus molar mass of C2nH3nCln is 62.50 g/mol.
The empirical formula mass can be calculated as follows:
Mass(C2H3Cl)=[2(atomic mass of C)+3(atomic mass of H)+1(atomic mass of Cl)] (3)
Substitute 12.011 g for atomic mass of C, 1.00794 g for atomic mass of H, and 35.45 g for atomic mass of H in equation (3).
Mass(C2H3)=[2(12.011 g)+3(1.00794 g)+1(35.45 g)]=62.50 g
The value of n can be calculated through division of molecular mass by empirical formula mass as follows:
n=molecular massempirical formula mass (4)
Substitute 62.50 g for molecule mass and 62.50 g for empirical formula mass in equation (4).
n=62.50 g62.50 g≈1
Hence, molecular formula for compound is C2H3Cl.
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