# Solving Mole Problems

When you are doing a large construction project, you have a good idea of how many nails you will need (lots! When you go to the hardware store, you don't want to sit there and count out several hundred nails.

When you are doing a large construction project, you have a good idea of how many nails you will need (lots! When you go to the hardware store, you don't want to sit there and count out several hundred nails.

where mass is in grams and the molar mass is in grams per mole.

Moles to Mass Calculation We can use the above equation to find the mass of a substance when we are given the number of moles of the substance.

This will be done in a single two-step calculation.

$$\text \: \ce \rightarrow \text \: \ce \rightarrow \text \: \ce$$ The mass of tin is less than one mole, but the 1:2 ratio means that more than one mole of $$\ce$$ is required for the reaction.

$\text \rightarrow \text \rightarrow \text$ The mass of the given substance is converted into moles by use of the molar mass of that substance from the periodic table.

Then, the moles of the given substance are converted into moles of the unknown by using the mole ratio from the balanced chemical equation.

So, mass of 1 mole of a pure substance = relative molecular mass in grams And, mass of 1 mole of a pure substance = molar mass of the pure substance (g mol From the table we see that 1 mole of water has a mass of 18.016 grams, which isn't very much (about the mass of water in a couple of small ice-cubes you'd make in your family freezer). If 1 mole of water has a mass of 18.016 g, then ½ mole of water must have ½ the mass: mass of ½ mole of water = ½ × mass of 1 mole of water mass of ½ mole of water = ½ × 18.016 = 9.008 g In both of the examples above, we can calculate the mass of water in grams by multiplying the moles of water by the mass of 1 mole of water in grams: mass water = moles of water × mass of 1 mole water because the mass of 1 mole of water in grams is known as its molar mass, we can write: mass water = moles of water × molar mass of water The table below compares the mass of different amounts of water in moles and the data is graphed on the right: From the data in the table we can generalise and say that for any pure substance the mass of substance in grams is equal to the moles of substance multiplied by the mass of 1 mole of the substance: mass = moles × mass of 1 mole and since mass of 1 mole of a substance (in grams) = molar mass (in grams per mole) mass (g) = moles × molar mass (g mol What if you knew the amount of a pure substance in moles and its mass? Recall that mass = moles × molar mass or m = n × M (a) We could use some algebra: divide both sides of the equation by the moles: molar mass = mass ÷ moles M = m ÷ n (b) We could use some logic: By inspection of units we see that dividing the mass in grams by the amount in moles we arrive at a quantity with the units grams per mole (g mol, is an important industrial chemical.

Chris the Chemist has an impure sample of calcium carbonate.

Let’s start really basic and ask how many moles there are in a certain number of things (atoms, ions, et al.). We know that there are 12 bagels per dozen, so we divide 36 by 12 to get 3 dozen. To find out the number of moles, divide the number of things by the number of things per mole (the Avogadro Constant) to get the number of moles.

The mole is, in essence, just a number, just how we call 12, “a dozen”. The mole is used to take gargantuan numbers and make them into a more manageable size.

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