Final answer:
The mass of mercury to fill a glass tube to a specified height is calculated by multiplying the volume of the cylinder by the density of mercury. The calculated mass is approximately 2100 g, but this does not match any of the answer options provided.
Step-by-step explanation:
To determine the mass of liquid mercury that would fill a cylinder (glass tube) to a certain height, we can use the volume formula of a cylinder which is V = πr²h. Given that the density (ρ) of mercury is 13.53 g/cm³, we first need to calculate the volume of the cylinder. Then we can multiply the volume by the density to find the mass.
The diameter of the glass tube is 16.0 mm, which gives us a radius (r) of 8.0 mm or 0.8 cm. The height (h) is 25.0 cm. Using these values, the volume (V) of the mercury in the cylinder would be:
V = π * (0.8 cm)² * 25.0 cm = π * 0.64 cm² * 25.0 cm = 50π cm³
To find the mass of mercury, we use:
Mass = ρ * V = 13.53 g/cm³ * 50π cm³
Mass ≈ 13.53 g/cm³ * 157.1 cm³ = 2126.813 g ≈ 2100 g
However, each of the answer options is much larger than the calculated mass, suggesting a possible error in the calculation or a typo in the answer options provided. Therefore, based on the given options, none closely match the calculated mass and this should be clarified.