Question

Calculate the number of carbon atoms in 25.0 grams of isopropyl alcohol (c3h8o)

Answer 1

Answer : The number of carbon atoms present in isopropyl alcohol is, $7.51\times 10^{23}$

Solution : Given,

Mass of isopropyl alcohol = 25 g

Molar mass of isopropyl alcohol = 60 g/mole

In isopropyl alcohol molecule, there are 3 carbon atoms and 8 hydrogen atoms and 1 oxygen atom present.

First we have to calculate the moles of isopropyl alcohol.

$\text{Moles of }C_3H_8O=\frac{\text{Mass of }C_3H_8O}{\text{Molar mass of }C_3H_8O}=\frac{25g}{60g/mole}=0.416moles$

As we know that 1 mole of gas contains $6.022\times 10^{23}$ number of atoms

As, 1 mole of gas contains $3\times 6.022\times 10^{23}$ number of carbon atoms

So, 0.416 mole of gas contains $0.146\times 3\times 6.022\times 10^{23}=7.51\times 10^{23}$ number of carbon atoms

Therefore, the number of carbon atoms present in isopropyl alcohol is, $7.51\times 10^{23}$

Answer 2

First, let's determine the number of moles of carbon atoms by using molar mass. Then, using Avogadro's number, we can find the number of C atoms:
*1 mole of C3H8O= (12.0x3)+(1.0x8)+(16.0x1) = 60.0g/mol

25.0 grams C3H8O x (1 mole C3H8O/60.0 grams) = 0.417 mol

0.417mol C3H8O has (3 x 0.417 moles) C atoms = 1.251 moles C atoms

1.251 moles C atoms x(6.022x10^23 atoms/mol) = 9.42x10^23 C atoms.

The answer is in 3 significant figures, as that's what we have in the given, and we matched it with our rounding of the atomic masses from the periodic table.
You can do this all in one equation written left to right, just exclude the intermediate answers. Just easier to show it this way on the computer screen.