Detour: converting grams into moles
Now that we know the molecular weight of sugar (180 g), how can we use that to convert grams of sugar into moles of sugar? Stop me if you've heard this one before...
Step 1: Make a conversion fraction. Here's an example: 1 mol/ 180 g. What's a conversion fraction? It's a fraction where the numerator + denominator are equal, and therefore the value of the fraction is 1. However, the numerator and denominator are expressed in different units, so the fraction can be used to convert a measurement. How do you do that? Go to Step 2.
Step 2: Do a test to see if you can multiply your original measurement by the conversion fracton, like this:
100 g sugar * 1 mol sugar / 100 g sugar
Notice how you can cancel the "grams" units to get 100/180 mols sugar, or 0.56 moles. Cool! You're done.
Step 3: If step 2 didn't work, you would need to "flip" your conversion fraction, which is OK since the top and bottom are equal:
100 g sugar * 180 g sugar / 1 mol sugar
So if you make the convertion fraction wrong, you can fix it here.
Finally, we can find the concentration of our sugar goo by dividing the moles of glucose by the volume of water in liters (900g of water has a volume of 0.9 L):
Concentration = 0.56 moles / 0.9 L = 0.62 moles/L
Voila, if you put 100g of glucose into 900mL of water, you have a solution that is 0.62 moles/L, often abbreviated 0.62M.
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