QuestionFind the number of atoms in: A) 32 grams of $S_{8}$ B) $3 \times 10^{23}$ molecules of $\mathrm{CaO}$ .

Studdy Solution

STEP 1

Assumptions1. The molecular weight of $_{8}$ is256 g/mol (since the atomic weight ofulfur () is32 g/mol and there are8 atoms in $_{8}$ ). . Avogadro's number is $6.022 \times10^{23}$ , which is the number of atoms in one mole.
3. The molecular weight of $\mathrm{Ca}$ is56 g/mol (since the atomic weight of Calcium (Ca) is40 g/mol and Oxygen () is16 g/mol).

STEP 2

First, we will solve part A of the problem. We need to find the number of moles in32 grams of $_{8}$ . We can do this by dividing the given mass by the molecular weight.
$\text{Number of moles} = \frac{\text{Given mass}}{\text{Molecular weight}}$

STEP 3

Now, plug in the given values for the given mass and molecular weight to calculate the number of moles.
$\text{Number of moles} = \frac{32 \text{ g}}{256 \text{ g/mol}}$

STEP 4

Calculate the number of moles.
$\text{Number of moles} = \frac{32 \text{ g}}{256 \text{ g/mol}} =0.125 \text{ mol}$

STEP 5

Now that we have the number of moles, we can find the number of atoms by multiplying the number of moles by Avogadro's number.
$\text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number}$

STEP 6

Plug in the values for the number of moles and Avogadro's number to calculate the number of atoms.
$\text{Number of atoms} =0.125 \text{ mol} \times6.022 \times10^{23}$

STEP 7

Calculate the number of atoms in32 grams of $_{}$ .
$\text{Number of atoms} =0.125 \text{ mol} \times6.022 \times10^{23} =7.5275 \times10^{22}$

STEP 8

Next, we will solve part B of the problem. We need to find the number of atoms in $3 \times10^{23}$ molecules of $\mathrm{Ca}$ . Since each molecule of $\mathrm{Ca}$ contains2 atoms (1 Calcium and1 Oxygen), we can find the total number of atoms by multiplying the number of molecules by2.
$\text{Number of atoms} = \text{Number of molecules} \times2$

STEP 9

Plug in the given number of molecules to calculate the number of atoms.
$\text{Number of atoms} =3 \times^{23} \times2$

STEP 10

Calculate the number of atoms in $3 \times10^{23}$ molecules of $\mathrm{Ca}$ .
$\text{Number of atoms} =3 \times10^{23} \times2 =6 \times10^{23}$ So, the number of atoms in32 grams of $_{8}$ is $7.5275 \times10^{22}$ and the number of atoms in $3 \times10^{23}$ molecules of $\mathrm{Ca}$ is $6 \times10^{23}$ .

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