# Question 32d5f

May 14, 2015

The relationship between moles and grams involves the concept of molar mass, which represents the exact mass in grams of 1 mole of a substance.

Remember that 1 mole of a substance is defined as exactly $6.022 \cdot {10}^{23}$ atoms or molecules of that substance - this is known as Avogadro's number.

Depending on what substance you're dealing with, the mass of $6.022 \cdot {10}^{23}$ atoms or molecules of that substance will vary. For example, one mole of hydrogen atoms will weigh less than 1 mole of lead atoms because each individual atom of hydrogen is lighter than each individual lead atom.

This is where molar mass comes into play. If you know the mass of 1 mole of a substance, you can use the following relationship

Simply put, you can go from moles to grams and vice versa by using the mass of 1 mole of that substance, i.e its molar mass.

For example, the molar mass of carbon is 12.011 g/mol. This means that 1 mole of carbon, or $6.022 \cdot {10}^{23}$ atoms of carbon, weigh 12.011 g.

So, if you have 2 moles of carbon, you'll have

2cancel("moles C") * "12.011 g"/(1cancel("mole C")) = "24.022 g"

Likewise, if you have 54 g of carbon, you'll have

54cancel("g") * "1 mole C"/(12.011cancel("g")) = "4.5 moles C"#