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

##### 2 Answers

See the explanation.

#### Explanation:

One mole of anything, including atoms, is

The following example will show you how to do that.

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**Example:**

How many atoms of gold are in

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

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**First Step: Mass #rarr#Moles**

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

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 #rarr#Atoms**

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

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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

Once you have moles, multiply by Avogadro's number to calculate the number of atoms. This is

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**Try this one:**

How many atoms of zinc, Zn, are in

**Answer:**

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:

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

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!