(a) After the label fell off a bottle containing a clear liquid believed to be benzene, a chemist measured the density of the liquid to verify its identity. A 25.0-mL portion of the liquid had a mass of 21.95 g. A chemistry handbook lists the density of benzene at 15 °C as 0.8787 g/mL. Is the calculated density in agreement with the tabulated value? (b) An experiment requires 15.0 g of cyclohexane, whose density at 25 °C is 0.7781 g/mL. What volume of cyclohexane should be used? (c) A spherical ball of lead has a diameter of 5.0 cm. What is the mass of the sphere if lead has a density of 11.34 g/cm3? (The volume of a sphere is (4/3) πr3, where r is the radius.)
![](data:image/png;base64,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)
Calculated density corresponds to the benzene, so an unknown liquid is benzene.
b) Volume necessary for the experiment can be calculated as:
![](data:image/png;base64,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)
c) First we should calculate the volume of a sphere, knowing that radius equals half of the diameter:
![](data:image/png;base64,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)
Then we calculate the mass as:
![](data:image/png;base64,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)
(a) After the label fell off a bottle containing a clear liquid believed to be benzene, a chemist measured the density of the liquid to verify its identity. A 25.0-mL portion of the liquid had a mass of 21.95 g. A chemistry handbook lists the density of benzene at 15 °C as 0.8787 g/mL. Is the calculated density in agreement with the tabulated value? (b) An experiment requires 15.0 g of cyclohexane, whose density at 25 °C is 0.7781 g/mL. What volume of cyclohexane should be used? (c) A spherical ball of lead has a diameter of 5.0 cm. What is the mass of the sphere if lead has a density of 11.34 g/cm3? (The volume of a sphere is (4/3) πr3, where r is the radius.)
Calculated density corresponds to the benzene, so an unknown liquid is benzene.
b) Volume necessary for the experiment can be calculated as:
c) First we should calculate the volume of a sphere, knowing that radius equals half of the diameter:
Then we calculate the mass as: