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Moles to Mass
How heavy is 1.5 mol of lead? How many moles in 22.34g of water? Calculating the mass of a sample from the number of moles it contains is quite simple. We use the molar mass (mass of one mole) of the substance to convert between mass and moles. When writing calculations, we denote the molar mass of a substance by an upper case “M” (e.g. M(Ne) means “the molar mass of neon”). As always, “n” stands for the number of moles and “m” indicates the mass of a substance. To find the solutions to the two questions we just asked, let’s apply some dimensional analysis:
Can you see how the units cancel to give you the answer you want?
Deriving Grams from Moles for an Element
A liter of air contains 9.2 × 10−4 mol argon. What is the mass of Ar in a liter of air?
Solution
The molar amount of Ar is provided and must be used to derive the corresponding mass in grams. Since the amount of Ar is less than 1 mole, the mass will be less than the mass of 1 mole of Ar, approximately 40 g. The molar amount in question is approximately one-one thousandth (~10−3) of a mole, and so the corresponding mass should be roughly one-one thousandth of the molar mass (~0.04 g):
In this case, logic dictates (and the factor-label method supports) multiplying the provided amount (mol) by the molar mass (g/mol):
9.2×10−4 mol Ar (39.95 g/ mol Ar) = 0.037g Ar
The result is in agreement with our expectations, around 0.04 g Ar.
Check Your Learning
What is the mass of 2.561 mol of gold?
ANSWER:
504.4 g
Deriving Grams from Moles for a Compound
Vitamin C is a covalent compound with the molecular formula C6H8O6. The recommended daily dietary allowance of vitamin C for children aged 4–8 years is 1.42 × 10−4 mol. What is the mass of this allowance in grams?
Solution
As for elements, the mass of a compound can be derived from its molar amount as shown:
The molar mass for this compound is computed to be 176.124 g/mol. The given number of moles is a very small fraction of a mole (~10−4 or one-ten thousandth); therefore, we would expect the corresponding mass to be about one-ten thousandth of the molar mass (~0.02 g). Performing the calculation, we get:
1.42×10−4 mol vitamin C (176.124 g/mol vitamin C) = 0.0250g vitamin C
This is consistent with the anticipated result.
Check Your Learning
What is the mass of 0.443 mol of hydrazine, N2H4?
ANSWER: 14.2 g
Mass to Moles
But we had one more question: “How many moles in 22.34 g of water?” This is just as easy:
Where did the 18 g H2O come from? We looked at the periodic table and simply added up the atomic masses of two hydrogens and an oxygen to get the molecular weight of water. This turned out to be 18, and since all the masses on the periodic table are given with respect to 1 mole, we knew that 1 mol of water weighed 18 grams. This gave us the relationship above, which is really just (again) watching units cancel out!
Deriving Moles from Grams for an Element
According to nutritional guidelines from the US Department of Agriculture, th