# Solving Mole Problems

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

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.

In this type of problem, the mass of one substance is given, usually in grams.

From this, you are to determine the amount in moles of another substance that will either react with or be produced from the given substance.

Solution: Use the molar mass of $$\ce$$ to convert the grams of $$\ce$$ to moles.

Then use the mole ratio to convert from $$\text \: \ce$$ to $$\text \: \ce$$.

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Then, the moles of the unknown are converted into mass in grams by use of the molar mass of that substance from the periodic table.

Example 12.3.2 Hydrogen sulfide gas burns in oxygen to produce sulfur dioxide and water vapor.