Question

A hydrocarbon contains 10.5 gr of carbon per gr of H. One liter vapors of hydrocarbon at 127°C and 1 atm pressure weighs 2.8 gr. The molecular formula of hydrocarbon is
(A) C6H8
(B) C7H8
(C) C5H12
(D) C8H4​

Answer 1

Given :-

Volume, V = 1L

Temperature, T = 127°C = 400K

Pressure, P = 1 atm

Weight, W = 2.8g

To Find :-

Molecular formula of hydrocarbon.

Solution :-

We know :-

$\bf PV=nRT$

Here ,

$\sf n= \dfrac{W}{M}$

$\implies\bf PV= \dfrac{W}{M}RT$

Substitute the values :-

$:\implies \sf 1 \times 1 = \dfrac{2.8}{M} \times 0.0821 \times 400$

$: \implies \sf M = 2.8 \times 0.0821 \times 400$

$: \implies \sf M = 91.95 \approx 92$

Molecular mass of hydrocarbon :- 92g

Let the molecular formula of hydrocarbon be $\sf C_xH_y$.

So,

$\sf 12x+y= 92$

Given that, hydrocarbon contains 10.5 gram of carbon per gram of hydrogen.

So,

$\sf \dfrac{12x}{y} = 10.5$

$\sf 12x= 10.5y$

Substitute the values :-

$: \implies \sf 10.5y+y = 92$

$: \implies \sf 11.5y = 92$

$: \implies \bf y = 8$

$: \implies\sf 12x = 10.5\times 8$

$: \implies \sf x = \dfrac{10.5\times 8 }{12}$

$: \implies \bf x= 7$

Molecular formula of hydrocarbon :- $\bf C_7H_8$

Correct option :- B

Answer 2

Given :-

A hydrocarbon contains 10.5 gr of carbon per gr of H. One liter vapors of hydrocarbon at 127°C and 1 atm pressure weighs 2.8 gr.

To Find :-

Molecular formula of hydrocarbon is

Solution :-

PV = nRT

P = Pressure

V = Volume

n = No. of moles

R = Universal gas constant

T = Temperature

No. of moles = Given Mass/Molar Mass

So,

PV = G/M × RT

1 × 1 = 2.8/M × 0.0821 × 400

1 = 2.8/M × 32.84

M = 2.8 × 32.84

M = 91.952 = 92 g

Now

Let us assume the formula is $C_{p}H_{q}$

Now

12p + q = 92 (1)

12p/q = 10.5 (according to the statement)

12p = q × 10.5

12p = 10.5q

10.5q + q = 92

11.5q = 92

q = 92/11.5

q = 8

Using 1

12p + 8 = 92

12p = 92 - 8

12p = 84

p = 84/12

p = 7

Hence

Molecular formula = C₇H₈

If we said to find molar mass

Molar mass = C × 7 + H × 8

Molar mass = 12 × 7 + 1 × 8

Molar mass = 84 + 8

Molar mass = 92 g/mol

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