91Ó°ÊÓ

Number of atoms in one mole are$6.02×{10}^{23}$

Mass of H atom is $1.0\mathrm{u}$

Mass of O atom is$16\mathrm{u}$

Mass of C atom is$12\mathrm{u}$

This is an estimation problem. So, you need to assume the mass and the composition of the cat and find out the total number of atoms in the cat. From that, you can find the number of moles in the cat. Let’s assume the mass of the cat is 10 kg.

Assume the mass of cat is 10 kg.

Assuming that $60\%$of the cat is water and remaining $40\%$is carbon, you can find the number of atoms of the cat.

40% of C would give you 4000 g of C.

$\frac{4000}{12}×6.02×{10}^{23}=2×{10}^{26}\mathrm{atoms}\mathrm{of}\mathrm{carbon}$

Thus, there are localid="1654587806688" $2×{10}^{26}\mathrm{atoms}\mathrm{of}\mathrm{carbon}$

In ${\mathrm{H}}_2\mathrm{O}$there are two hydrogens and one oxygen, therefore,

$\left(1\mathrm{u}×2\right)+16\mathrm{u}=18\mathrm{u}$.

You have $16\mathrm{u}$of oxygen in $18\mathrm{u}{\mathrm{H}}_2\mathrm{O}$, therefore, $6000\mathrm{g}$of${\mathrm{H}}_2\mathrm{O}$will be,

$6000\mathrm{g}×\frac{16\mathrm{u}}{18\mathrm{u}}=5333.33\mathrm{g}$of oxygen.

So, the number of oxygen atoms would be,

$\frac{5333.33}{16}×6.02×{10}^{23}=2×{10}^{26}$

Thus, there are$2×{10}^{26}$$\mathrm{atoms}\mathrm{of}\mathrm{oxygen}$.

You have $2\mathrm{u}$of oxygen in $18\mathrm{u}{\mathrm{H}}_2\mathrm{O}$, therefore, $6000\mathrm{g}$of${\mathrm{H}}_2\mathrm{O}$will have,

$6000\mathrm{g}×\frac{2\mathrm{u}}{18\mathrm{u}}=666.667\mathrm{g}$of hydrogen.

So, number of hydrogen atoms would be,

$\frac{666.667}{1}×6.02×{10}^{23}=4×{10}^{26}$

Thus, there are$4×{10}^{26}$.

The total number of atoms in the cat would be,

$\left(2×{10}^{26}\right)+\left(2×{10}^{26}\right)+\left(4×{10}^{26}\right)=8×{10}^{26}$

To find the number of moles $\left(n\right)$, you have to divide the number of atoms by Avogadro’s number.

$$\begin{gathered} \mathrm{n}=\frac{\mathrm{Number}\mathrm{of}\mathrm{atoms}}{\mathrm{Avogadro}\text{'}\mathrm{s}\mathrm{number}} \\ =\frac{8×{10}^{26}}{6.02×{10}^{23}} \\ =1328.90\mathrm{mol}\mathrm{of}\mathrm{atoms} \end{gathered}$$

To the nearest order of magnitude, it would be 1000 moles.

Thus, the number of moles in a large domestic cat is 1000.