# How do you calculate the number of atoms of an element if you know the mass of the sample?

Apr 29, 2017

See the explanation.

#### Explanation:

One mole of anything, including atoms, is $6.022 \times {10}^{23}$ (Avogadro's number) of them. Usually you will have a given mass of an element. There are two basic steps to get from the given mass to the number of atoms. They are:

$\text{Mass}$$\rightarrow$$\text{Moles}$ and $\text{Moles}$$\rightarrow$$\text{Atoms}$

The following example will show you how to do that.

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Example:

How many atoms of gold are in $\text{58.27 g}$ of gold?

The periodic table shows us that gold, Au, has the atomic weight

$\text{196.967 u}$. This means that its molar mass is $\text{196.967 g/mol}$.

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First Step: Mass$\rightarrow$Moles

To calculate moles of Au, multiply the given mass by the reciprocal of the molar mass.

58.27color(red)cancel(color(black)("g Au"))xx(1"mol Au")/(196.967color(red)cancel(color(black)("g Au")))="0.295836 mol Au"

I'm keeping a couple of guard digits to reduce rounding errors. The final answer will be rounded to four significant figures.

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Second Step: Moles$\rightarrow$Atoms

To calculate atoms of Au, multiply moles Au by Avogadro's number.

0.295836color(red)cancel(color(black)("mol Au"))xx(6.022xx10^23"atoms Au")/(1color(red)cancel(color(black)("mol Au")))="1.782"xx"10"^23 "atoms Au" rounded to four significant figures due to $\text{58.72 g}$

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So, if you are given the mass of an element, you use the periodic table to find its molar mass, and multiply the given mass by the reciprocal of the molar mass. This is $\text{Mass}$$\rightarrow$$\text{Moles}$.

Once you have moles, multiply by Avogadro's number to calculate the number of atoms. This is $\text{Moles}$$\rightarrow$$\text{Atoms}$.

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Try this one:

How many atoms of zinc, Zn, are in "120.71 g Zn"?
Answer: $\text{1.112"xx"10"^24 "atoms Zn}$

Apr 29, 2017

See below.

#### Explanation:

Number of atoms are calculated using a number known as "Avogadro's number."

Okay, lets see a breakdown of this. Let's say that you are given an amount of grams of a substance. For this case, lets say that that substance is Carbon (C). And, lets assume that you are given 4.01 g of Carbon, and you are tasked to find the number of atoms in that mass of Carbon. The breakdown would be as follows, with dimensional anaysis:

$4.01 \text{ g Carbon" ((1 " mol Carbon")/(12.01 " g Carbon")) ((6.022 * 10^23 atms Carbon)/(1 " mol Carbon")) = 2.01 * 10^23 " atms Carbon}$

Basically, I first wrote down the amount in grams, and I used the molar mass of Carbon (which can be found on the periodic table under Carbon) 12.01 g/mol to convert 4.01 g of Carbon to moles of Carbon. Then, I used "Avogadro's Number", or $6.022 \cdot {10}^{23} \text{ atoms per mole}$ to convert the mole amount to atoms of Carbon.

The process should be very similar with other such atoms, just make sure to keep your periodic table and calculator handy.

I hope that helps!