How many atoms of hydrogen are there in 3.0kg of ethane?

[relative atomic mass: H=1, C=12; Avogadro constant = 6.0 × 10^{23} per mol]

A. 3.6 × 10^{26}

B. 3.9 × 10^{26}

C. 6.0 × 10^{25}

D. 3.6 × 10^{23}

E. 6.0 × 10^{22}

How many atoms of hydrogen are there in 3.0kg of ethane?

[relative atomic mass: H=1, C=12; Avogadro constant = 6.0 × 10^{23} per mol]

A. 3.6 × 10^{26}

B. 3.9 × 10^{26}

C. 6.0 × 10^{25}

D. 3.6 × 10^{23}

E. 6.0 × 10^{22}

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You’ll find that question is nearly identical to the IMAT 2012 Q63. Hence, so is it’s solution.

The general formula for Alkanes is C_nH_{2n+2}, and so Ethane is C_2H_6

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

If the A_r of H=1 and that of C= 12, then (12x2)+(1x6)= 30

If one mole of Ethane would give us 30 grams of product, then how many moles would 3000 grams give us?

1 = 30

x= 3000

30x= 3000

x= 100 moles

If one mole of ethane contains 6.0 \times 10^{23} mol^{-1} molecules, then how many molecules are there in 100 moles?

1 =6.0 \times 10^{23} mol^{-1}

100 = x

x= 6\times 10^{25} total molecules of ethane

We now can tell that the number of hydrogen atoms is 6x that of ethane molecules, since there would be 6 hydrogen atoms in an ethane molecule. That would help us compute that the number of hydrogen atoms are:

6\times (6\times 10^{25})= 3.6\times 10^{26}

And our answer is A.