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

Calculate the volume of acetic acid using its mass and density. Use the formula: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).

Convert the volume from milliliters to cubic centimeters, knowing that 1 mL = 1 cm³.

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.

Rearrange the formula to solve for the radius: \( r = \sqrt{\frac{V}{\pi h}} \).

Double the radius to find the diameter of the tube, since \( \text{Diameter} = 2r \).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

Recommended video:

Guided course

02:28

Stoichiometric Rate Calculations

Related Practice

Textbook Question

A 32.65-g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.00 mL. The solid and toluene together weigh 58.58 g. The density of toluene at the temperature of the experiment is 0.864 g/mL. What is the density of the solid?

views

Textbook Question

Automobile batteries contain sulfuric acid, which is commonly referred to as “battery acid.” Calculate the number of grams of sulfuric acid in 1.00 gal of battery acid if the solution has a density of 1.28 g/mL and is 38.1% sulfuric acid by mass.

Textbook Question

Gold is alloyed (mixed) with other metals to increase its hardness in making jewelry. (a) Consider a piece of gold jewelry that weighs 9.85 g and has a volume of 0.675 cm3. The jewelry contains only gold and silver, which have densities of 19.3 and 10.5 g/cm³, respectively. If the total volume of the jewelry is the sum of the volumes of the gold and silver that it contains, calculate the percentage of gold (by mass) in the jewelry. (b) The relative amount of gold in an alloy is commonly expressed in units of carats. Pure gold is 24 carat, and the percentage of gold in an alloy is given as a percentage of this value. For example, an alloy that is 50% gold is 12 carat. State the purity of the gold jewelry in carats.

Textbook Question

Judge the following statements as true or false. If you believe a statement to be false, provide a corrected version. (a) Air and water are both elements.

views

Textbook Question

Judge the following statements as true or false. If you believe a statement to be false, provide a corrected version. (b) All mixtures contain at least one element and one compound.

views