A pycnometer is a precisely weighted vessel that is used for highly accurate density determinations. Suppose that a pycnometer has a mass of 27.60 g when it is empty and has a mass of 45.65 g when it is completely filled with water at 20 °C. A 9.5 g metal ingot is placed in the pycnometer. When it is then filled with water at 20 °C, the total mass is 56.83 g. If the density of water at 20 °C is 998.2 kg/m3, what is the density of the metal ingot in grams per cubic centimeter.

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Question:

A pycnometer is a precisely weighted vessel that is used for highly accurate density determinations. Suppose that a pycnometer has a mass of 27.60 g when it is empty and has a mass of 45.65 g when it is completely filled with water at 20 °C. A 9.5 g metal ingot is placed in the pycnometer. When it is then filled with water at 20 °C, the total mass is 56.83 g. If the density of water at 20 °C is 998.2 kg/m3, what is the density of the metal ingot in grams per cubic centimeter.

Answer:5.758 is the density of the metal ingot in grams per cubic centimeter.Explanation:1) Mass of pycnometer = M = 27.60 gMass of pycnometer with water ,m= 45.65 gDensity of water at 20 °C = d =[tex]998.2 kg/m^3[/tex]1 kg = 1000 g[tex]1 m^3=10^6 cm^3[/tex][tex]998.2 kg/m^3=\frac{998.2 \times 1000 g}{10^6 cm^3}=0.9982 g/cm^3[/tex]Mass of water ,m'= m - M = 45.65 g - 27.60 g =18.05 gVolume of pycnometer = Volume of water present in it = V[tex]Density=\frac{Mass}{Volume}[/tex][tex]V=\frac{m'}{d}=\frac{18.05 g}{0.9982 g/cm^3}=18.08 cm^3[/tex]2) Mass of metal , water and pycnometer = 56.83 gMass of metal,M' = 9.5 gMass of water when metal and water are together ,m''= 56.83 g - M'- M56.83 g - 9.5 g - 27.60 g = 19.7 gVolume of water when metal and water are together = v[tex]v=\frac{m''}{d}=\frac{19.7 g}{0.9982 g/cm^3}=19.73 cm^3[/tex]Density of metal = d'Volume of metal = v' =[tex]\frac{M'}{d'}[/tex]Difference in volume will give volume of metal ingot. v' = v - V[tex]v'=19.73 cm^3-18.08 cm^3=[/tex][tex]v'=1.65 cm^3[/tex]Since volume cannot be in negative .Density of the metal =d'=[tex]d'=\frac{M'}{v'}=\frac{9.5 g}{1.65 cm^3}=5.758 g/cm^3[/tex]

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