Math

QuestionWhat is the empirical formula for styrene (C8H8)\left(\mathrm{C}_{8} \mathrm{H}_{8}\right)? A) CH4\mathrm{CH}_{4} B) CH3\mathrm{CH}_{3} C) CH\mathrm{CH} D) C6H6\mathrm{C}_{6} \mathrm{H}_{6} E) CH2\mathrm{CH}_{2}

Studdy Solution

STEP 1

Assumptions1. Styrene is made up of C8H8\mathrm{C}_{8} \mathrm{H}_{8} monomer units. . The empirical formula is the simplest, most reduced ratio of elements in a compound.

STEP 2

First, we need to find the simplest ratio of carbon to hydrogen in the styrene molecule. We can do this by dividing the number of each atom by the greatest common divisor.
C8H8=C8gcd(8,8)H8gcd(8,8)\mathrm{C}_{8} \mathrm{H}_{8} = \mathrm{C}_{\frac{8}{gcd(8,8)}} \mathrm{H}_{\frac{8}{gcd(8,8)}}

STEP 3

Now, plug in the given values for the number of carbon and hydrogen atoms to calculate the empirical formula.
C8gcd(8,8)H8gcd(8,8)=C88H88\mathrm{C}_{\frac{8}{gcd(8,8)}} \mathrm{H}_{\frac{8}{gcd(8,8)}} = \mathrm{C}_{\frac{8}{8}} \mathrm{H}_{\frac{8}{8}}

STEP 4

Calculate the empirical formula.
C88H88=C1H1\mathrm{C}_{\frac{8}{8}} \mathrm{H}_{\frac{8}{8}} = \mathrm{C}_{1} \mathrm{H}_{1}The empirical formula for styrene is CH\mathrm{CH}, which corresponds to option C.

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