Lab Experiment 383

Density of Liquids and Solids

 

Density is a physical property of matter which is dependent on volume and mass, therefore:

 

d=m/v          or             density is equal to mass divided by volume

 

Density of a liquid or solution is typically reported in units of grams per milliliter, or g mL^-1

Density of a solid is reported in units of grams per cubic centimeter, or g cm^-3

           Because 1mL is equal to 1cm^3, these units are interchangeable.

 

To measure volume by displacement:

-pour liquid, such as water, into graduated cylinder, measure and record volume 1.

-add weighed sample of solid to the liquid in cylinder, measure and record volume 2.

-Subtract volume 1 from volume two, the difference between these volumes is the volume of the solid.

 

And that's basically all we need to work the problems in this lab: d=m/v and the procedure for determining volume by displacement. Let's work some problems!!

 

1. The density of ice at 0°C is 0.9168gmL^-1, and that of liquid water at 0°C is 0.9999gmL^-1.

What are the volumes of 1.000g of ice and 1.000g of water at 0°C?

 

So the question is asking us to find volume, not density, so we'll be doing some rearranging. Before we mess around with our equation, let's plug everything in to gain a better understanding of where everything will go:

d=m/v, starting with ice, the density is 0.9168 mL^-1 and the mass is 1.000g so our equation looks like:

0.9168mL^-1 = 1.000g/v

So we move v to the left and d to the right, so the equation is v=m/d, which looks like:

v=1.000g/0.9168mL^-1 = 1.090mL is our volume for ice at zero degrees celsius

Now let's do water:

v=1.000g/0.9999gmL^-1 = 1.000mL is our volume for water at zero degrees celsius

 

2. A sealed glass container with a capacity of exactly 100mL contains 96.0mL of liquid water at 0°C. If the water freezes will the container rupture?  

 

From the previous question, we see that water at zero degrees has a volume of 1.000mL and frozen water at the same temperature has a volume of 1.090mL. So we just need to find the percent of increase from one to the other, so we find the amount of volume gained and divide by the original volume: 1.090-1.000 = 0.090 0.090/1.000= 0.090 x 100 = 9%

So water increases in volume by 9% when it freezes, so we merely need to add 9% to 96.0mL to see how much it will expand and if that volume will be more than the 100mL the water has to expand into. 96.0x0.09 = 8.64, so 96.0mL will expand 8.64mL upon freezing, 96.0+8.64 = 104.64mL.

104.64mL>100mL so yes, the container will rupture!

 

3. The volume of the nucleus of a carbon atom is about 9.9x10^-39mL. The molar mass of carbon is 12.00g mol^-1. What is the density of the carbon nucleus?

 

So the first thing that stands out in this problem is the unit for molar mass. This won't do. Molar mass indicates how much of everything is in 12.00 grams of carbon. We need to know how much is in ONE atom of carbon. So we need incorporate Avogadro's number here to bring us down to the right scale. Avogadro's number, 6.02x10^23, is the amount of everything in one mole of a substance. Carbon having a molar mass of 12.00 indicates that there are 12 grams of Carbon in one mole. So to find the mass per atom rather than mole, divide molar mass by avogadro's number:

12.00g/mol-1/6.02x10^23 = 1.99x10^-23 is the mass of one atom of C, so we use that in our equation for mass:

d=1.99x10^-23/9.9x10^-39 = 0.2010 = 2.0 x 10^-15

So our answer is 2.0 x 10^-15 g/cm^-3 is the density of a nucleus of a carbon atom. I must dash to go wipe the sweat off my forehead.

 

 

 

 

And after that pain in the *** I am quite done, thanks.