### Mole Conversions

Calculating the Mass of One Molecule

When calculating the mass of one molecule, do the following:

- Calculate the molar mass of the substance
- Divide it by Avogadro's Number

Make sure you have a periodic table and a calculator handy.

By the way, the tecnique to calculate the mass of one atom of an element is exactly the same as for calculating the mass of one molecule of a compound.

**Problem #1:** What is the mass of one molecule of H_{2}O?

Step #1 - the molar mass of water is 18.015 g/mol. This was calculated by multiplying the atomic weight of hydrogen (1.008) by two and adding the result to the weight for one oxygen (15.999).

Please remember that you need the molar mass first when trying to find the mass of one molecule.

Step #2 - divide the substance's molar mass by Avogadro's Number.

18.015 grams/mol ÷ 6.022 x 10^{23} mol¯^{1} = 2.992 x 10¯^{23} grams

Note that the final answer has been rounded to four significant figures (from 2.9915 - note use of rounding with five rule) and that the unit of mole cancels.

**Problem #2:** calculate the mass (in grams) of one molecule of CH_{3}COOH

The molar mass of CH_{3}COOH is 60.06 g/mol. The solution is:

60.06 g/mol ÷ 6.022 x 10^{23} mol¯^{1} = 9.973 x 10¯^{23} g

**Problem #3:** Determine the mass in grams of one atom of gold.

The molar mass (an older name for this is the gram-atomic weight) for gold is 196.666 g/mol. The solution is:

196.666 g/mol ÷ 6.022 x 10^{23} mol¯^{1} = 3.266 x 10¯^{22} g

**Problem #4:** Determine the mass (in grams) of an atom of gold-198.

Note that this question asks about one specific isotope. For that, we must find the gram-atomic weight for that one isotope (often called the isotopic mass), not the molar mass (also called the average atomic weight) for gold (the value we used in example #3). Wikipedia has a table listing the masses for all the isotopes of gold.

The value for gold-198 is 197.968 g/mol. So, the solution is:

197.968 g/mol ÷ 6.022 x 10^{23} mol¯^{1} = 3.287 x 10¯^{22} g

### Practice Problems

Calculate the mass (in grams) for one molecule of:

1) H_{2}

2) PCl_{5}

3) UF_{6}

4) F_{2}

5) CH_{4}

Answers

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