Question

styrofoam is made by blowing a gas into a polymer called polystyrene, which in turn is made from styrene. Styrene is 92.26% carbon and the rest is hydrogen 7.02 * 10^18 molecules of styrene weigh 1.22 mg. what is the molecular formula for it

Answer 1

Answer : The molecular of the compound is, $C_8H_8$

Solution :

If percentage are given then we are taking total mass is 100 grams.

So, the mass of each element is equal to the percentage given.

Mass of C = 92.26 g

Mass of H = 100 - 92.26 = 7.74 g

Molar mass of C = 12 g/mole

Molar mass of H = 1 g/mole

Step 1 : convert given masses into moles.

Moles of C = $\frac{\text{ given mass of C}}{\text{ molar mass of C}}= \frac{92.26g}{12g/mole}=7.688moles$

Moles of H = $\frac{\text{ given mass of H}}{\text{ molar mass of H}}= \frac{7.74g}{1g/mole}=7.74moles$

Step 2 : For the mole ratio, divide each value of moles by the smallest number of moles calculated.

For C = $\frac{7.688}{7.74}=0.99\approx 1$

For H = $\frac{7.74}{7.74}=1$

The ratio of C : H = 1 : 1

The mole ratio of the element is represented by subscripts in empirical formula.

The Empirical formula = $C_1H_1$

The empirical formula weight = 1(12) + 1(1) = 13 gram/eq

Now we have to calculate the molecular mass of polymer.

As, the mass of polymer of $7.02\times 10^{18}$ molecules = 1.22 mg = 0.00122 g

So, the mass of polymer of $6.022\times 10^{23}$ molecules = $\frac{6.022\times 10^{23}}{7.02\times 10^{18}}\times 0.00122g=104.6g/mol$

Now we have to calculate the molecular formula of the compound.

Formula used :

$n=\frac{\text{Molecular formula}}{\text{Empirical formula weight}}$

$n=\frac{104.6}{13}=8$

Molecular formula = $(C_1H_1)_n=(C_1H_1)_8=C_8H_8$

Therefore, the molecular of the compound is, $C_8H_8$