QuestionHow many atoms are in a $6.21 \mu \mathrm{mol}$ helium sample? Answer with correct sig figs using ${ }^{*} 10^{\wedge}$ .

Studdy Solution

STEP 1

Assumptions1. The given amount of helium is $6.21 \mu \mathrm{mol}$ . The Avogadro's number is $6.02214076 \times10^{23}$ atoms/mol3. The number of atoms in a sample can be calculated by multiplying the amount in moles by Avogadro's number

STEP 2

First, we need to convert the amount of helium from $\mu \mathrm{mol}$ to $\mathrm{mol}$ . We know that $1 \mathrm{mol} =10^6 \mu \mathrm{mol}$ .
$Amount\, in\, moles = Amount\, in\, \mu \mathrm{mol} /10^6$

STEP 3

Now, plug in the given value for the amount in $\mu \mathrm{mol}$ to calculate the amount in $\mathrm{mol}$ .
$Amount\, in\, moles =6.21 \mu \mathrm{mol} /10^6$

STEP 4

Calculate the amount in moles.
$Amount\, in\, moles =6.21 /10^6 =6.21 \times10^{-6} \mathrm{mol}$

STEP 5

Now that we have the amount in moles, we can find the number of atoms in the sample. This can be done by multiplying the amount in moles by Avogadro's number.
$Number\, of\, atoms = Amount\, in\, moles \times Avogadro's\, number$

STEP 6

Plug in the values for the amount in moles and Avogadro's number to calculate the number of atoms.
$Number\, of\, atoms =6.21 \times10^{-6} \mathrm{mol} \times6.02214076 \times10^{23} \mathrm{atoms/mol}$

STEP 7

Calculate the number of atoms.
$Number\, of\, atoms =6.21 \times10^{-6} \times6.02214076 \times10^{23} =3.74 \times10^{18} \mathrm{atoms}$ The number of atoms in a $6.21 \mu \mathrm{mol}$ sample of pure helium is $3.74 \times10^{18}$ atoms.

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