Conversion help

[Violagirl]

Hi, I've tried doing this problem numerous times but am not seeming to find the right answer for it.

The mass of an average blueberry is 0.77 g and the mass of an automobile is 2200 kg. Find the number of automobiles whose total mass is the same as 1.0 mol blueberries. I know the key idea is to cancel units until you get to the unit you need but I'm having a difficult time trying to do it with this problem. I keep getting 1.7 as an answer but it appears to be wrong. Anyone who could show the correct way to set it up, I would greatly appreciate it!

 

[tkhunny]

It is a little odd to apply the "mol" to a blueberry. In any case...

\(\displaystyle \frac{0.77\;g\;\cdot\;6.022141\;\cdot\;10^{23}}{2200\;kg}\;=\;\frac{4.64\;g\;\cdot\;10^{23}}{2200\;kg}\;=\;\frac{4.64\;kg\;\cdot\;10^{20}}{2200\;kg}\)

Simplify. It's nowhere near 1.7.

 

[mmm4444bot]

… 1.0 mol blueberries …

… I keep getting 1.7 [automobiles] as an answer[,] but it appears to be wrong … (Highlight mine)

Hey Girl:

Yikes! Do you know how many blueberries there are in one mole?

That's 602,214,141,070,409,084,099,072 blueberries! (For all I know, that could be more blueberries that have ever lived on planet Earth.)

Obviously 1.7 cars is nowhere near the mass of that many blueberries.

It's known as Avogadro's Constant, and I'm going to use an approximate to three significant digits (since 0.77 is given to only 2).

1 mol = 6.022 × 10^23

Each of these millions of billions of blueberries has average mass 0.77 g

So, did you get (6.022 × 10^23)(0.77) grams for the aggregate mass ?

Is this what you're trying to convert to kilograms ? (And then, you divided the result by 2200?)

You didn't show any work, or explain what you're thinking, so I'm not sure why you're stuck.

Until I see that an effort has actually been made, I generally don't "do" homework. Here's an example, instead.

Convert 4.5002 × 10^16 grams of goo to kilograms.

We should know that there are 1,000 grams in one kilogram. So, we divide all those grams of goo by 1000.

(4.5002 × 10^16)/1000 = 4.5002 × 10^13

The goo weighs 4.5002 × 10^13 kg

If you prefer a "dimensional analysis" approach, then we can take the ratio of kilograms to grams as a conversion factor. Why choose the ratio 1 kg/1000 g instead of 1000 g/1 kg ? In dimensional analysis, we want units to cancel in numerators and denominators, similar to how common factors cancel in fractions.

We want grams to cancel, and be replaced with kilograms. The only way grams will cancel on top is if we put grams on bottom in our conversion factor. That's why it has to be 1 kg/1000 g.

\(\displaystyle \frac{6.022 \,\times\, 10^{23}}{1} \cdot \frac{0.77\,g}{1} \cdot \frac{1\,kg}{1000\,g}\)

See how the g units cancel? We're left with kg units.

Do the arithmetic, and you've got the mass of 1 mole of blueberries in kilograms.

Can you finish?

Next time, try to provide more information about your situation. It's hard to tutor virtual students, without input.

Cheers ~ Mark

 

[ChemHelp419]

I know its an old thread...

Okay so I have the same type of problem and I got the awnser I just dont know how to put it into "two significant numbers"