Calculating the mass and number of atoms of a structural I beam.

[hsbc2003]

Homework Statement

A structural I beam is made of iron> A view of its cross-section and its dimensions is shown in the figure, where d = 2 cm, w= 31 cm, h= 28 cm and the length (not shown) of the beam is L= 1.53 m.

The density of iron is 7560 kg/m^3. The atomic weight of iron is 55.85 g/mol and Avagadro number is Na= 6.02214e23/mol.

What is the mass of a section 1.53 m long? (in kg)
How many atoms are there in this section? (in units of atoms)

The Attempt at a Solution

I calculated the volume of the I beam ( (h*w*l)-(the volume of the empty space))
and then I multiply it by the density of iron to get the mass.

but the answer was wrong, thus i I tried to calculate the number of atoms using Avagadro's number the answer will be wrong as well...

I hope you help me calculating the mass...

Thank you

 

[PhanthomJay]

Your method is fine, you probably made a math error in calculating the dimensions of the empty space, or perhaps you forgot to convert centimeters to meters. You should show your work so that we can point out the errors. You might want to calculate the volume in another way, by looking at the volume of the three separate parts of the beam (top, bot, and middle pieces) and add them up, as a check on your work.

 

[hsbc2003]

Thanks for your reply PhanthomJay

I used the method that you suggested for calculating the volume

((0.31)*(0.02)*(1.53))*2 + (0.24)*(0.02)*(1.53) = 0.026316 m^2

thus, mass= 0.026316 m^2 * density of iron= 198.949 Kg
I rounded it to 1 significant figures and I got 2.0e2 kg

Good news ... answer is correct

thanks a lot for the help