Question

Naphthalene contains 93.7% carbon and 6.29% hydrogen, if its molecular mass is 128 g/mol. Calculate its molecular formula.

Answer 1

Answer:

C

10

H

8

Explanation:

Assuming that is a mass amount, divide each proportion by the atomic weight of the component. Normalize to obtain the empirical formula and then use the molecular mass to determine the actual molecular formula.

93.91

12

=

7.83

relative moles of carbon

6.29

1

=

6.29

relative moles of hydrogen

Ratio of C:H is 7.83:6.29 or 1.2. Nearest whole multiple is 5, resulting in ratio of 6:5. 6-C and 5-H would have a molecular weight of

(

6

×

12

)

+

(

5

×

1

)

=

77

The actual molecular weight is 128, so the formula must be

128

77

=

1.67

×

C

6

H

5

.

C

10

H

8

Subsequent note on Whole Multiple:

A chemical compound MUST have whole numbers of atoms - we can't have a compound with a "partial" atom! The observed/calculated math just gives us ratios of the mass. We need to insure that our final mass contains WHOLE atoms. Thus, when we find our molar ratio of C:H is 7.83:6.29 or 1.2:1 we need to convert that to one with whole numbers in the numerator as well as the denominator.

In this case, with the denominator already "normalized" at 1, we only need to find a factor to make the 1.2 a whole number. The key that 0.2 part - we need to make it

1.0

.

0.2

×

?

=

1.0

?

=

1.0

0.2

=

5

Applying this to our original

1.2

1

ratio we obtain:

5

×

1.2

1

=

6

5

So, our atomic molar ratio is 6-C and 5-H, as used in the rest of the original answer derivation.

Answer 2

Using the percentage composition of the elements present in the compound we can compute the empirical formula as follows:

1. Element: Carbon

Percentage mass: 93.7

Atomic mass: 12

Number of atoms: $\frac { 93.7 }{ 12 } \quad =\quad 7.81$

Simplest ratio i.e., divide by least factor: $\frac { 7.81 }{ 6.24 } \quad =\quad 1.25$

2. Element: Hydrogen

Percentage mass: 6.29

Atomic mass: 1.008

Number of atoms: $\frac { 6.29 }{ 1.008 } \quad =\quad 6.24$

Simplest ratio i.e., divide by least factor: $\frac { 6.24 }{ 6.24 } \quad =\quad 1$

In order to change, the decimal into whole number multiply both the numbers in the simplest ratio by a convenient number. Here $1.25 \times 4$ = 5 and $1 \times 4$ = 4

Now the empirical formula of naphthalene is ${ C }_{ 5 }{ H }_{ 4 }$ and hence the empirical mass is $\left[ \left( 5\quad \times \quad 12 \right) \quad +\quad \left( 4\quad \times \quad 1 \right)  \right] \quad =\quad 64\quad g/mol.$

Dividing the given molecular mass by empirical mass will give us n- the number with which we have to multiply the empirical formula to get the molecular formula

Here it is 2. Thus, molecular formula of naphthalene is $\left( { C }_{ 5 }{ H }_{ 4 } \right) \quad \times \quad 2\quad =\quad { C }_{ 10 }{ H }_{ 8 }$.