What is the Diameter of an Oil Slick Spreading on a Lake?

[homeworkboy]

One liter ( 1000 cm^3) of oil is spilled onto a smooth lake.If the oil spreads out uniformly until

it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate

the diameter of the oil slick. Assume the oil molecules have a diameter of 2X10^-10m.

 

[LowlyPion]

One liter ( 1000 cm^3) of oil is spilled onto a smooth lake.If the oil spreads out uniformly until

it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate

the diameter of the oil slick. Assume the oil molecules have a diameter of 2X10^-10m.

Welcome to PF.

How would you approach the problem?

 

[homeworkboy]

Well i would first convert the volume of water into m3 which is 1. so...then i can't think of anythin..i need help solving this

 

[LowlyPion]

Well i would first convert the volume of water into m3 which is 1. so...then i can't think of anythin..i need help solving this

What volume of water? I will presume you mean the volume of oil. That may not be necessary.

What is the volume of an oil molecule of the given diameter? Maybe start there?

 

[homeworkboy]

sorry i meant volume of oil...well volume of oil molecule will be Pi r^2 so..22/7 * (1 * 10^-10)^2
so 3.14 X 10^-20

 

[LowlyPion]

sorry i meant volume of oil...well volume of oil molecule will be Pi r^2 so..22/7 * (1 * 10^-10)^2
so 3.14 X 10^-20

What is volume in units of again?

 

[homeworkboy]

its m3

 

[LowlyPion]

its m3

What are the units of the answer you supplied for volume?

 

[homeworkboy]

the unit is meter cube or litres

 

[LowlyPion]

the unit is meter cube or litres

No actually it's not. You supplied an answer that was in m² not m³.

The formula for volume of a sphere is not pi R².

 

[homeworkboy]

sorry volume is ( π X d³)/6

 

[LowlyPion]

sorry volume is ( π X d³)/6

OK so now what is the volume of the molecule?

Then next how many of those are there in the volume of oil?

 

[homeworkboy]

then the vol of molecule is 4.2 X 10^-30...so no. of those in 1 L are 2.4 X 10^29...what next

 

[LowlyPion]

then the vol of molecule is 4.2 X 10^-30...so no. of those in 1 L are 2.4 X 10^29...what next

You previously calculated the area that one of these would cover ... so knowing how many you have now what is the area they will spread out to according to the statement of the problem?

 

[grosenblatt]

first, convert the volume of oil from cm^3 to m^3. now we work backwards
first divide the volume of oil by the thickness of one molucule by doing this what happens is m³/(m becomes m^2 which is area, therefore you have now solved for the surface area. now since it says diameter I am assuming the lake is circular, so just plug into the equation for area of a circle and work backwards
a = ╥r²
a/╥ = r²
sqrt(a/╥) = r
now just double too find the diameter and you have your answer. its simple geometry, you probably just thought a little too hard about it.

 

[homeworkboy]

thanks a lot man..i really understood the way u explained...i have one more doubt that i posted earlier but no one replied here's the question...

For small angles theta, the numerical value of sin theta is approximately the same as the

numerical value of tan theta.Find the largest angle for which sine and tangent agree to within

two significant figures.Thank you for all the help

 

[grosenblatt]

hmm well basically its saying find the highest value of Ø such as sin(Ø) = tan(Ø) up to the second decimal place. I am guessing a lot of guessing/checking?