Question

on find the number moles of

1. 3.011 x $10^{23}$ molecules of $CaCO_3$
2. 1.5055 x $10^{22}$ molecules of $H_2SO_4$

Answer 1

1. 0.5 moles of $CaCO_3$
2. 0.025 moles of $H_2SO_4$

Answer 2

To find the number of moles from a given number of molecules, we use Avogadro's number ($N_A$), which states that one mole of any substance contains $6.022 \times 10^{23}$ particles (molecules, atoms, ions, etc.).

The formula to calculate the number of moles is: $\text{Number of moles} = \frac{\text{Given number of molecules}}{\text{Avogadro's number} (N_A)}$ Where $N_A = 6.022 \times 10^{23} \text{ molecules/mol}$.

1) For 3.011 x $10^{23}$ molecules of $CaCO_3$:

$\text{Number of moles} = \frac{3.011 \times 10^{23} \text{ molecules}}{6.022 \times 10^{23} \text{ molecules/mol}}$ $\text{Number of moles} = \frac{3.011}{6.022} \text{ mol}$ $\text{Number of moles} = 0.5 \text{ mol}$

2) For 1.5055 x $10^{22}$ molecules of $H_2SO_4$:

$\text{Number of moles} = \frac{1.5055 \times 10^{22} \text{ molecules}}{6.022 \times 10^{23} \text{ molecules/mol}}$ $\text{Number of moles} = \frac{1.5055}{6.022} \times \frac{10^{22}}{10^{23}} \text{ mol}$ $\text{Number of moles} = 0.25 \times 10^{-1} \text{ mol}$ $\text{Number of moles} = 0.025 \text{ mol}$

Explanation of the solution:

The number of moles is calculated by dividing the given number of molecules by Avogadro's number ($6.022 \times 10^{23}$ molecules/mol).

1. For $3.011 \times 10^{23}$ molecules of $CaCO_3$: $(3.011 \times 10^{23}) / (6.022 \times 10^{23}) = 0.5$ moles.
2. For $1.5055 \times 10^{22}$ molecules of $H_2SO_4$: $(1.5055 \times 10^{22}) / (6.022 \times 10^{23}) = 0.025$ moles.