# What mass of aluminum contains twice as many atoms as 35.00 grams of copper?

Aug 19, 2017

$29.72 g A l$

#### Explanation:

$\frac{35 g C u}{63.546 \frac{g}{m o l} C u} = 0.55078 m o l C u$

$0.55078 m o l \cdot 2 = 1.1015 m o l A l$

$1.1015 m o l A l \cdot 26.982 \frac{g}{m o l} A l = 29.72 g A l$

Aug 19, 2017

$\text{29.72 g Al}$ contains twice the number of atoms of $\text{35.00 g Cu}$.

#### Explanation:

In order to determine the mass of Al that contains twice as many atoms of Cu in 35.00 g, first determine the number of Cu atoms found in 35.00 g. Then multiply by 2 to get the number of atoms of Al, then determine the mass of Al.

To determine the number of atoms of copper in $\text{35.00 g}$, calculate the moles $\text{Cu}$ and multiply by $6.022 \times {10}^{23}$ atoms/mol.

Atoms of Cu

The molar mass of $\text{Cu}$ is $\text{63.546 g/mol}$. To get moles, divide the given mass by the molar mass. Since g/mol is a fraction, $\text{g"/"mol}$, multiply the given mass by the inverse of the molar mass. Then multiply by $6.022 \times {10}^{23}$ atoms/mol.

35.00color(red)cancel(color(black)("g Cu"))xx(1color(red)cancel(color(black)("mol Cu")))/(63.546color(red)cancel(color(black)("g Cu")))xx(6.022xx10^23"atoms Cu")/(1color(red)cancel(color(black)("mol Cu")))=3.317xx10^23"atoms Cu"

Mass of Al (molar mass = 26.982 g/mol)

Do the reverse of finding the atoms of $\text{Cu}$.

Atoms of Al:

$2 \times \left(3.317 \times {10}^{23}\right) = 6.634 \times {10}^{23} \text{atoms Al}$

Mass of Al:

6.634xx10^23color(red)cancel(color(black)("atoms Al"))xx(1color(red)cancel(color(black)("mol Al")))/(6.022xx10^23color(red)cancel(color(black)("atoms Al")))xx(26.982"g Al")/(1color(red)cancel(color(black)("mol Al")))="29.72 g Al"