__Using the grid & bridge concepts__ **(Std
3 in
Ch 8)**

** **

** bridge 1 bridge 2 bridge 3**

milligrams <---> grams <---> moles <---> atoms or molecules

bridge
to work, the top and bottom of the fraction must equal each other . That is why the value of all bridges = 1. |

The following equivalent equations will be made into bridges (fractions that = 1) to do go back and forth from one unit of measure to another:

** **

__bridge____ type 1 (3 kinds)__

1000 milligrams = 1 gram

1000 grams = 1 kg

1.0 x 10^{6} mg (microgram) = 1 gram

** **

__bridge____ type 2__

1 molar mass in grams (or gram molecular wt if we are using elements) = 1 mole

** **

__bridge____ type 3__

6.022 x 10^{23} atoms (or molecules) = 1
mole (remember Avogadro !!! )

Your job is to create fractions that will take you the way you need to go. The example will use both the bridge concept and conversion grids. Here’s the example:

You are given 850 mg of Ca and asked to find out how many atoms that represents. Each bridge is made as follows:

**bridge**** 1**
1000 mg = 1 g

** bridge 2 **40.1 g Ca = 1
mole Ca

** bridge 3 **1 mole = 6.02
x 10^{23} atoms

** **

We make each
fraction from the bridge that takes us from one unit of measure to
another. The side of the fraction that
goes on top, is the one with unit of measure we ** are
changing to**. Here is how it
works:

starting
fraction: __850 mg/1 (the number one)__ ending fraction: __atoms/1__

** bridge 1
bridge 2
bridge 3
**

850 mg Ca |
1 g |
1 mol Ca |
6.02 x 10 |

1 |
1000 mg |
40.1 g Ca |
1 mol Ca |

Now let’s see what the grid looks like when we cancel units:

850 |
1 |
1 mol |
6.02 x 10 |

1 |
1000 |
40.1 |
1 mol |

The final fraction looks like this:

5,117 x 10 |

40,100 |

Now all we have to do is divide the two numbers at the end:

0.128 x 10^{23} Ca atoms

For correct scientific notation we must move the
decimal one place to the right. When we
do that we must adjust the exponent of 10 to be one number less, or we change
the value of the number.

**FINAL
ANSWER = ** __1.28 x 10 ^{22} Ca atoms__

You are given 4.35 x 10^{19} atoms of
Mg. You are supposed to find how many
grams that represents.

First let’s see what the grid looks like:

** bridge
1
bridge 2 bridge 3**

4.35 x 10 |
1 mole |
24.3 g Mg |

1 |
6.20 x 10 |
1 mole Mg |

Now let’s cancel units and see what is left:

4.35 x 10 |
1 |
24.3 g Mg |

1 |
6.02 x 10 |
1 |

This is equal to:

105.7 x 10 |

6.02 x 10 |

As in Example 1, we now divide the numbers. This time though we do the “normal” numbers separately from the 10’s with the exponents:

105.7 / 6.02 =
17.6 10^{19} / 10^{23} = 10^{-4}

Now we “reassemble” the numbers to read

17.6 x 10^{-4}

This time to change to scientific notation we must move the decimal to the left one place. In order to keep the same number we must adjust the exponent of 10 to be 3.

** FINAL
ANSWER = 1.76 x 10**

**If this didn’t make sense to you, go back over
it slowly a few times and let it “sink in”.
**