One more density problem- Please help me out?

Question

A pycnometer is a device used to measure density. It weighs 20.455 g empty and 31.486g when filled with water (density of water is 1.00 g/cm3). Pieces of an alloy are put into the empty, dry pycnometer. The mass of the alloy and the meter together is 28.689 g. Water is added to the alloy to exactly fill the meter. The mass of the meter, water, and alloy together is 38.689g. What is the density of the alloy?

Can someone please explain this to me, step by step? I'm really confused- I've been trying to do this for an hour now! Thanks so much for your help.

Answer 1

OK, Good Problem

Density of the alloy = mass of the alloy / volume of the alloy ....(i)

Now, mass of alloy can be found out using (Mass of the alloy + meter) - (Mass of the meter)  = 28.689 - 20.455 = 8.234 g   ... ... (ii)

Now volume of alloy = Volume of the water originally - Volume of water after putting the alloy. (by archimedes principle)  .....(iii)

Volume of water originally = (31.486 - 20.455) / (1g/cm3) = 11.031 cm3    

Now we don't know the volume of the water after putting the alloy directly, we can find this like this

[(Mass of the water + meter + alloy) - (Mass of meter + alloy)] / (1gm/cm3)

= (38.689 - 28.689) / 1 = 10 ml

Now using (iii)

volume of alloy used = 11.031 - 10 = 1.031 ml  . ......(iv)

Now simply use (ii) and (iv) to get the density of the alloy

= 8.234 / 1.031

= 7.9864209 gm/ml

(Probably a Bronze-Sn alloy)