How do you convert between the volume of a gas at STP and the number of moles of the gas?  

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Whenever you perform a mole conversion calculation, you will need to use a mole conversion factor. The three mole conversion factors are:

1 mole = 22.4 liters (for ideal gases)

1 mole = molar mass (grams)

1 mole = `~6.02 x 10^23` particles (molecules or atoms)

Since our problem is...

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Whenever you perform a mole conversion calculation, you will need to use a mole conversion factor. The three mole conversion factors are:

1 mole = 22.4 liters (for ideal gases)

1 mole = molar mass (grams)

1 mole = `~6.02 x 10^23` particles (molecules or atoms)

Since our problem is a conversion between moles and volume, we will use the first conversion factor. The volume in this conversion factor is in liters. If the volume in your question is in mL, you will need to convert to liters before you use this conversion factor. 

To use a conversion factor in a calculation, we must write it as a ratio, i.e. 1 mole/22.4 L OR 22.4 L/1 mole. Always write the conversion factor with the given unit on the bottom.

To calculate your answer, just multiply the "given amount" times the conversion factor.

Example 1: Convert 2.00 moles of `~O_2` gas to liters.

2.00 moles is the given amount and unit.

(2.00 moles)(22.4 L/1 mole) = 44.8 L

Since the given unit was moles, we write the conversion factor with moles in the denominator so that the units cancel out.

Example 2: Convert 6.22 L of `~O_2` gas to moles.

6.22 L is the given amount and unit.

(6.22 L)(1 mole/22.4 L) = 0.278 moles

Since the given unit was liters, we write the conversion factor with liters in the denominator.

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