How many miles deep would one mole of M&M's cover the State of Washington?

Question

this is for my chemistry class. if u didnt get the question its, if you covered washington state in one mole of M&M's how many miles deep would it cover? i figured out that there is 22 M&M's per 25 mL or 22 M&M's per 25 cm^3. I dont know where to go from there and i need to show all my math steps. some helpful conversions he gave me were 1 mole = 6.022 x 10^23. 1 mL = 1 cm^3. and 1 mile = 1.6093 km. and washington state area = 68,182 miles^2 HELP!

Answer 1

Start with:
1 mole = 6.022 x 10^23 M&Ms.

22 M&Ms = 25 cm^3

So divide the number of M&Ms by 22 and multiply by 25.

6.022 x 10^23 x 25 / 22

= 6.8432 x 10^23 cm^3

This is the volume in cubic cm.

Next we know that there are 100cm in a meter and 1000m in a kilometer. That's 100,000 (10^5) cm in a kilometer.

If you cube that, you get 100,000 x 100,000 x 100,000 = 10^15 cm^3 in a km^3.

So take your volume in cm^3 and divide by 10^15 to get the volume in km^3.

6.8432 x 10^23
------------------------
10^15

When dividing 10^23 by 10^15, you simply subtract the exponents.

The volume of the M&Ms would be:

= 6.8432 x 10^8 km^3

Now let's figure the area of Washington. We are told it is 68,182 miles²

But we want it in km².

Again, 1 mile = 1.6093 km.
1 sq. mile = (1.6093 km)²
= 2.58984649 km²

So multiply 68,182 by this result to get the area in km².
68,182 x 2.58984649 = 176,581 km²

The last step is to divide the volume in km^3, by the area of Washington State in km² and that will give you the depth of the M&Ms in kilometers.

6.8432 x 10^8 km^3
------------------------------
176,581 km²

We can also write the denominator in scientific notation to make it easier:

6.8432 x 10^8 km^3
------------------------------
1.76581 x 10^5 km²

6.8432 / 1.76581 = 3.875
10^8 / 10^5 = 10^3

So the answer is 3.875 x 10^3

In standard notation, this is 3,875 km deep (or approximately 2,408 miles deep). That's a *lot* of M&Ms!

P.S. The answerer below made an error when converting km^3 to mi^3. Rather than dividing by 1.6093^3 , they should have multiplied. When you invert, this puts them off by a factor of 17.37... divide and you'll see you get 2,408 miles (or 3,875 km) same as my answer.

Answer 2

Mile And Mole

Answer 3

you know 22m&m/25cm^3 so you multiply this by 40000 to get 880000m&m/m^3 then multiply this by 1000^3 to get 8.8*(10^14)m&m/km^3 then multiply by 1.6093^3 to get 3.6676991615942*(10^14)m&m/mile^3 then multiply by 68182 to get 2.50071064235*(10^19)m&m/miles on washington. Then divide by 6.022*(10^23) to get 4.1526247797378*(10^-5)mols of m&m/mile over washington then I woud divide 1 by 4.1526247797378*(10^-5) to get 24081.154764557miles over washington/mol

Answer 4

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