styrene

[BodybldgDoc]

what mass of styrene(molarmass=104.1) will contain 4.5*10^20 molecules of styrene?
A. 0.00778g
B. 7.78*10^-4 g
C. 7.78*10^3 g
D. 7.78*10^-2 g
E. 7.78* 10^4 g

I know how to solve this problem. I was just wondering how would someone solve the math on this problem without a calculator on the test.
4.5*10^20 molecules * 1 mol/6.022*10^23 molecules*104.1g/1 mol of styrene=7.78*10^-2 g <-- I used a calculator to find the answer.

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[CyborgNinjaX]

what mass of styrene(molarmass=104.1) will contain 4.5*10^20 molecules of styrene?
A. 0.00778g
B. 7.78*10^-4 g
C. 7.78*10^3 g
D. 7.78*10^-2 g
E. 7.78* 10^4 g

I know how to solve this problem. I was just wondering how would someone solve the math on this problem without a calculator on the test.
4.5*10^20 molecules * 1 mol/6.022*10^23 molecules*104.1g/1 mol of styrene=7.78*10^-2 g <-- I used a calculator to find the answer.

This is how I would do it:

4.5x10^20 / 6.022x10^23 = approx. 7.5x10^-4 mol. (I calculated the exponential part with a calc. - I was getting 10^-3 with mental math)

104.1g --->1.04x10^2

Separate the exponents and the base: 10^-4 +10^2 = 10^-2

7.5x1.04=7.8 ----------> combine with the exponent, 7.8x10^-2

 

[BodybldgDoc]

I was able to get the 7.5*10^-4 with mental math but didnt think of doing this --> 104.1g --->1.04x10^2.
Thanks bro, that just made it a whole lot simpler.

 

[CyborgNinjaX]

I was able to get the 7.5*10^-4 with mental math but didnt think of doing this --> 104.1g --->1.04x10^2.
Thanks bro, that just made it a whole lot simpler.

No problem... just explain to me why its 10^-4 and not 10^-3.... 20-23 is -3....

 

[BodybldgDoc]

No problem... just explain to me why its 10^-4 and not 10^-3.... 20-23 is -3....

If you divide 4.5*10^20/6.0*10^23, you can take 4.5/6.0 or 45/60=3/4 which gives you 0.75*10^-3, so when you move the decimal one over to the right you get 7.5*10^-4 instead of 10^-3.