**How much gas is there?**

Avogadro was interested in studying gases. He theorized that equal volumes of gases under the same conditions contained the same number of particles. Other researchers studied how many gas particles were in a specific volume of gas. Eventually, scientists were able to develop the relationship between number of particles and mass using the idea of moles.

### Conversions Between Mass and Number of Particles

In "Conversions between Moles and Mass," you learned how to convert back and forth between moles and the number of representative particles. Now you have seen how to convert back and forth between moles and mass of a substance in grams. We can combine the two types of problems into one. Mass and number of particles are both related to grams. In order to convert from mass to number of particles or vice-versa, it will first require a conversion to moles.

#### Sample Problem: Converting Mass to Particles

How many molecules is 20.0 g of chlorine gas, Cl_{2}?

*Step 1: List the known quantities and plan the problem.*

Known

- molar mass Cl
_{2}= 70.90 g/mol - 20.0 g Cl
_{2}

Unknown

- number of molecules of Cl
_{2}

Use two conversion factors. The first converts grams of Cl_{2} to moles. The second converts moles of Cl_{2} to the number of molecules.

*Step 2: Calculate.*

\begin{align*}20.0 \ \text{g} \ \text{Cl}_2 \times \frac{1 \ \text{mol} \ \text{Cl}_2}{70.90 \ \text{g} \ \text{Cl}_2} \times \frac{6.02 \times 10^{23} \ \text{molecules Cl}_2}{1 \ \text{mol} \ \text{Cl}_2}=1.70 \times 10^{23} \ \text{molecules Cl}_2\end{align*}

The problem is done using two consecutive conversion factors. There is no need to explicitly calculate the moles of Cl_{2}.

*Step 3: Think about your result.*

Since the given mass is less than half of the molar mass of chlorine, the resulting number of molecules is less than half of Avogadro’s number.

### Summary

- Calculations are illustrated for conversions between mass and number of particles.

### Review

- Why can’t we convert directly from number of particles to grams?
- How many atoms of chlorine are present in the problem above?
- The periodic table says the atomic weight of chlorine is 35.5. Why can’t I use that value in my calculations?