indicate which of the following metals you think the object is and why.

Question

Perform the following calculation. A metal object is placed in 24.5 mL of water. The cylinder weighs 18.222 g. After the cylinder is placed in the water, the water rises to the 27.2 mL mark. Show all steps in your work and calculate the density of the cylinder. Be sure to use symbols and numbers and units in each step. Include units in each step as well. Then indicate which of the following metals you think the object is and why.

Answer 1

ρ_m = M_m/V_WD m means metal and the WD is the water displaced by the volume of the metal.

In this case, V_WD = V_WAfter - V_WBefore BTW, ρ is the usual symbol for density.

Do calculation with the units given. Remember that the units combine when divided and multiplied. Also, that ml are the same as cm³ which are more appropriate for a solid.

Answer 2

Hi Vilona!

So to find the known metal of the object, you need to find the density of the metal cylinder first!

Remember, Density = Mass(g)/Volume(mL)

You are given your mass which m = 18.222 g.

To find the volume of the cylinder, you need to see how much water is displaced when dropping the cylinder in the water.

An example of such would be throwing a rock in a cup of water. The water placed before dropping the rock has a volume of 100 mL. But when you drop the rock in the water, the volume of the water in the cup rises to 120 mL. Finding the difference between the V(f) - final volume - and V(i) - initial volume - will get you the volume of the rock.

120mL - 100 mL = 20 mL <-- the volume of the rock*

*In terms of a solid, 1 mL = 1 cm^3, so the volume of the rock is 20 cm^3. In this case, we will keep the units consistent and for volume, we will use mL.

So to find the volume of the cylinder, you can see that the water started off at 24.5 mL and rose to 27.2 mL. So the total displaced volume: 27.2 mL - 24.5 mL = 2.7 mL <-- the volume of the metal cylinder.

Now to find the density, we use the formula I introduced at the beginning.

Density = Mass(g)/Volume(mL)

Density = 18.222g/2.7mL = 6.748888... g/mL ~ 6.74 g/mL

Now to find what metal comes close to the density of this unknown metallic cylinder, you are to be given a list of possible know metals and their corresponding densities.

https://sites.google.com/site/chempendix/densities-of-pure-metals

This link provided gives the density of all the known pure metals of the Periodic Table. Use this to find and match which metal comes close to the density you calculated.

As I can see, some metals that can be of the metal cylinder are the following:

Cerium

Praseodymium

These 2 metals have a density of 6.77 g/mL which is really close to 6.74 g/mL which we calculated.