Length and moles

[jimmyp]

Here's a problem I'm trying to solve:

A piece of silver wire has a diameter of 0.510 mm. If silver has a density of 10.5 g/cc, how long (in meters) should you cut a piece of wire to obtain 0.0178 moles of silver?


Not sure how to approach it. I know D = M / V, but I don't really know what to do with this info. The "moles" part is throwing me off... Any help and info would be appreciated.

Thanks. :)

[Sonic]

Here's a problem I'm trying to solve:

A piece of silver wire has a diameter of 0.510 mm. If silver has a density of 10.5 g/cc, how long (in meters) should you cut a piece of wire to obtain 0.0178 moles of silver?


Not sure how to approach it. I know D = M / V, but I don't really know what to do with this info. The "moles" part is throwing me off... Any help and info would be appreciated.

Thanks. :)

Start with converting your moles to grams.

m = n*Ar where m is mass, n is number of moles and Ar is relative atomic mass which is 107.868 g/mol but you should use whatever your periodic table tells you

m = 0.510*107.868 = 55.01268g

We can also assume the wire is cylindrical and has a cross sectional area of pi/4*d^2 and a volume of a prism (a cylinder is a prism) is

V = cross sectional area * length

As you know density and mass you can find volume and therefore length.

----------------------------------

You can also use substitution to solve using one equation which reduces rounding errors but is harder to follow

D = [n*(Ar)]/(A*l) = [4n*(Ar)]/(pi*d^2*l)

l = [4n*(Ar)]/(pi*d^2*D)

Where:


l = length (m)
n = number of moles (mol)
Ar = Relative Atomic Mass (g/mol) [to change g into kg divide by 1000]
d = Diameter (m)
D = density (kg m^-3)

[jimmyp]

Start with converting your moles to grams.

m = n*Ar where m is mass, n is number of moles and Ar is relative atomic mass which is 107.868 g/mol but you should use whatever your periodic table tells you

m = 0.510*107.868 = 55.01268g

We can also assume the wire is cylindrical and has a cross sectional area of pi/4*d^2 and a volume of a prism (a cylinder is a prism) is

V = cross sectional area * length

As you know density and mass you can find volume and therefore length.


Alright so:

V = pi / 4 * 10.5 ^ 2 * Length?

For V = pi / 4 * 10.5 I got the final answer equal to 86.59.


Sorry but I'm still a bit confused with the equation. Can you give me some further guidance? Thanks for the second eq. by the way, although its a bit confusing now, its useful. :)



EDIT: I reread what you said a few times and I'm getting this now...

V = m / d
= 55.0g / 10.5 g/cc
= 5.24 cc

V = pi / 4*d^2*length

THUS:

L = 5.24 * pi / 4 * (0.510mm)^2

= 1.07 m ...


Is this correct? Did I do any mm to m conversions wrong? Sorry I'm just pretty confused. :P

[Sonic]

Alright so:

V = pi / 4 * 10.5 ^ 2 * Length?

For V = pi / 4 * 10.5 I got the final answer equal to 86.59.


Sorry but I'm still a bit confused with the equation. Can you give me some further guidance? Thanks for the second eq. by the way, although its a bit confusing now, its useful. :)



EDIT: I reread what you said a few times and I'm getting this now...

V = m / d
= 55.0g / 10.5 g/cc
= 5.24 cc

V = pi / 4*d^2*length

THUS:

L = 5.24 * pi / 4 * (0.510mm)^2

= 1.07 m ...


Is this correct? Did I do any mm to m conversions wrong? Sorry I'm just pretty confused. :P

You worked out V fine.

V = pi*d^2/4 * l therefore l = 4V/(pi*d^2)

(the 4 goes to the top because of the way fractions act when divided)

As you've found V in cc then I suggest converting d to cm and then the final answer to m

l = (4*5.24)/(pi*[10.5*10^-1]^2) = 6.05cm = 0.0605m

(because there are 10^-1 cm in 1mm). To avoid nasty powers of ten in the calculations it's best not to mix units

[jimmyp]

Okay great, I see everything you've done now. For the record though, that pi formula you gave me is the same as pi * r ^2 * h, correct?


Thanks for everything sonic. :)

[Sonic]

Okay great, I see everything you've done now. For the record though, that pi formula you gave me is the same as pi * r ^2 * h, correct?


Thanks for everything sonic. :)

Yes it is, I got used to being always given diameter so I just used pi*d^2/4.

As d = 2r -----> r = d/2

V = pi*r^2*h = pi*(d/2)^2*h = pi*d^2*h*1/4 :]