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Density

A cylindrical bar of gold that is 1.5 in. high and 0.25 in. in diameter has a mass of 23.1987g, as determined on an analytical balance. An empty graduated cylinder is weighed on a triple beam balance and has a mass of 73.7g. After pouring a small amount of liquid into the graduated cylinder, the mass is 79.16g. When the gold cylinder is placed in the graduated cylinder (the liquid covers the top of the gold cylinder), the volume indicated on the graduated cylinder is 8.5 mL. Assume that the temperature of the gold bar and the liquid are 86 degrees Fahrenheit .If the density of the liquid decreases by 1.0 % for each 10 degrees Celsius rise in temperature (over a range of 0 to 50 degrees Celsius), determine

a) The density of the gold at 86 degrees Fahrenheit
b) The density of the liquid at 40 degrees Fahrenheit.

Solution Preview

(a) Mass of gold bar = 23.1987g
<br>Volume of gold bar = pi*d^2*l/4 = 3.1416*0.25^2*1.5/4 = 0.073631in^3
<br>Therefore density of gold at 86F = mass/volume = 23.1987/0.073631
<br>= 315.067 g/in^3
<br>But 1 inch = 2.54 cm
<br>Therefore density of gold = 315.067 g/(2.54cm)^3 = 19.23 g/cc
<br>
<br>(b) Mass of ...

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