A 30.0-cm-long cylindrical plastic tube, sealed at one end, is filled with acetic acid. The mass of acetic acid needed to fill the tube is found to be 89.24 g. The density of acetic acid is 1.05 g/mL. Calculate the inner diameter of the tube in centimeters.

Verified step by step guidance

1. Calculate the volume of acetic acid using its mass and density. Use the formula: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).
2. Convert the volume from milliliters to cubic centimeters, knowing that 1 mL = 1 cm³.
3. Recognize that the volume of a cylinder is given by the formula: \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height of the cylinder.
4. Rearrange the formula to solve for the radius: \( r = \sqrt{\frac{V}{\pi h}} \).
5. Double the radius to find the diameter of the tube, since \( \text{Diameter} = 2r \).

Key Concepts

Density

Density is defined as mass per unit volume and is a crucial property of substances. In this case, the density of acetic acid (1.05 g/mL) allows us to relate the mass of the acetic acid (89.24 g) to its volume. By using the formula density = mass/volume, we can rearrange it to find the volume of acetic acid in the tube, which is essential for further calculations.

Volume of a Cylinder

The volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height (or length) of the cylinder. In this problem, the height is given as 30.0 cm. Knowing the volume of acetic acid from the previous step allows us to solve for the radius, which is necessary to find the inner diameter of the tube.

Diameter Calculation

The diameter of a cylinder is twice the radius (d = 2r). Once we have calculated the radius from the volume of acetic acid, we can easily find the diameter. This step is essential for providing the final answer to the question regarding the inner diameter of the tube.