While prospecting, Bob finds a gold nugget which has a mass density of 19.2g/cm^3. When Bob dropped it into water in a graduated cylinder the water level increased by 15.0mL. How many grams of gold did Bob have?
Can someone tell me the answer to this as well as HOW to SOLVE it.
A key concept to this question is that 1 mL = 1 cm^3. From here you do two things.
1. Solve the equation for density (D=m/V) for m (mass)
D=m/V –> Multiply by V
DV=m
2. Convert the volume into a unit used in the density
15.0mL * 1cm^3 = 15.0 cm^3
———– ———–
…………….1mL
(Note that mL is on the top and bottom of the fraction bar thus it cancels. )
Now insert the Volume and Density values into the equation
Keep in mind that 19.2 g/cm^3 is the same as 19.2 g / 1 cm^3
m=DV
m = 19.2 g * 15.0cm^3 = 288 g
…….———
…….1 cm^3
(Note that cm^3 is on the top and bottom of the fraction bar thus it cancels. )
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15.0mL x 19.2gAu/1mL = 288g Au
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Density = Mass/ Volume
or
Mass = Density X Volume
= 19.2 g/cm^3 X 15.0 ml
= 288 g (Answer)
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