Gold Density Question. IMPORTANT! NEED BY TOMORROW

Question

A "pure gold" bracelet has a mass of 105.36 grams. When placed in a graduated cylinder which you read to contain 25.5 mL of water, the water level rises to read 32.0 mL. Find the density of pure gold from a reference source and from the data determine if your bracelet really is pure gold. What is the percent error from the true value? 

 

(Please let me know if more information is needed to answer this. I plan to purchase the services of whoever can answer this for me :) 

Answer 1

The increase in the container water volume when the pure gold" bracelet is place =  The pure gold" bracelet volume

 The pure gold" bracelet volume =  32.0 mL - 25.5mL  = 6.5 mL

The pure gold" bracelet = 105.36 grams / 6.5 mL = 16.2092 grams / mL

From the internet, I've found the density of pure gold as 19.282 grams per mL .

% error  =  [absolute value of ( density of bracelet - density of real gold ) / density of real gold ]  * 100%

              = [absolute value of (16.2092 - 19.282) / 19.282] *100% = 15.94 %

Answer 2

The volume in the beaker is equal to:

 

Volume of water + volume of bracelet.

 

From the problem, we have

volume of water = 25.5 mL

volume of water + volume of bracelet = 32 mL (this is the reading from the graduated cylinder after the bracelet is completely submerged).

 

Therefore,

 

volume of bracelet = 32 - 25.5 = 6.5 mL.

 

Density is defined as mass/volume.  We have just solved for volume (6.5 mL), and were already given the mass (105.36 g) as part of the problem.

 

So, density = 105.36/6.5 [g/mL]

= 16.2092 g/mL, rounded to 4 decimal places.

 

From the internet, I've found the density of pure gold as 19.282 grams per mL.

 

It seems the "pure gold" bracelet has been cut with a lighter substance! It is definitely too light to be pure gold.

 

I'm using vertical lines to show absolute values in the calculation below.  And, to maximize readability of the formula I'm using, we'll use the following symbols:  

 

D_B = density of bracelet

D_G = density of real gold

 

% error = |D_B - D_G| / D_G * 100

= |16.2092 - 19.282| / 19.282 * 100

= 15.94 %