IMAT 2012 Q63 [Hydrogen Atoms]

The Avogadro constant is {6.0\times 10^{23} mol^{-­1}}.
How many hydrogen atoms are there in 0.420 g of cyclohexane?
[Ar: H = 1; C = 12]

A. 1.8\times 10^{23}
B. 1.8\times 10^{22}
C. 3.0\times 10^{21}
D. 3.0\times 10^{22}
E. 3.6\times 10^{22}

The general formula for cyclic Alkanes is C_nH_{2n}

Meaning the formula for cyclohexane is C_6H_{12}

The first step we can take is finding the M_r of cyclohexane.

If the A_r of H=1 and that of C= 12, then (12x6)+(1x12)= 84

If one mole of cyclohexane would give us 84 grams of product, then how many moles would 0.420 grams give us?

1 = 84
x= 0.420
84x= 0.420
x= 0.005 moles

If one mole of cyclohexane contains 6.0 \times 10^{23} mol^{-1} molecules, then how many molecules are there in 0.005 moles?

1 =6.0 \times 10^{23} mol^{-1}
0.005 = x
x= 3\times 10^{21} total molecules of cyclohxane

We now can tell that the number of hydrogen atoms is 12x that of cyclohexane molecules, since there would be 12 hydrogen atoms in a cyclohexane molecule. That would help us compute that the number of hydrogen atoms are:

12\times (3\times 10^{21})= 3.6\times 10^{22}

Our answer is E.