Question

Iron has a density of \(7.87 \mathrm{~g} / \mathrm{cm}^{3}\). If \(52.4 \mathrm{~g}\) of iron is added to \(75.0 \mathrm{~mL}\) of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise?

Short answer

The final volume reading in the graduated cylinder after adding 52.4 g of iron to 75.0 mL of water will be 81.656 mL.

Step-by-step solution

Determine the volume of Iron

We are given the mass and density of Iron. To calculate the volume, we can rearrange the density formula: Volume = mass / density Now, plug in the values given in the exercise: Volume = \( \frac{52.4 \mathrm{~g}}{7.87 \mathrm{~g} / \mathrm{cm}^{3}} \)

Calculate the volume of Iron

Perform the division to find the volume of Iron: Volume = \( \frac{52.4}{7.87} \) = 6.656 \(\mathrm{cm}^{3}\) The volume of Iron is 6.656 \(\mathrm{cm}^{3}\).

Find the final volume of the graduated cylinder

Now, we simply add the initial volume of water in the cylinder (75.0 mL) to the volume of Iron (6.656 \(\mathrm{cm}^{3}\)) to find the final volume reading: Final volume = 75.0 \(\mathrm{mL}\) + 6.656 \(\mathrm{cm}^{3}\) = 81.656 \(\mathrm{mL}\) Therefore, after adding 52.4 g of iron to 75.0 mL of water in the graduated cylinder, the water level will rise to a volume reading of 81.656 mL.

Key concepts

Volume Measurement

Volume measurement is the process of quantifying the amount of three-dimensional space that a substance or shape occupies. It is an essential concept in various scientific fields, including chemistry and physics. Volume can be measured using different methods and units, depending on the type and state of the substance being measured.

In this exercise, we deal with calculating the volume of a solid substance, specifically iron. By using the formula for density, which is \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]we can rearrange it to find the volume, given the mass and density:\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]This approach is used when the object is irregularly shaped or cannot be directly measured using tools like rulers. Like with iron, once we know the volume, it represents exactly how much space this substance would occupy in a container.

• It helps in understanding how different substances interact when placed together.
• It provides accuracy when estimating capacities and creating material mixtures.

Iron Density

Understanding the concept of density is crucial in material science and engineering. Density is the measure of how much mass is contained in a given volume. For iron, with a known density of 7.87 g/cm³, this implies that each cubic centimeter of iron weighs 7.87 grams.

This consistency allows us to make precise calculations about the volume of iron when its mass is known, as illustrated in the calculation:\[ \text{Volume} = \frac{52.4 \, \text{g}}{7.87 \, \text{g/cm}^3} = 6.656 \, \text{cm}^3 \]By knowing the density, we can also predict how iron will behave in relation to other materials. For example, iron's density is much greater than that of water (approximately 1 g/cm³), leading iron to sink when dropped into water. Such insights are important in designing and constructing structures or equipment that make use of iron and other metals.

Graduated Cylinder

A graduated cylinder is a common piece of laboratory equipment used to measure the volume of a liquid. It is marked with a series of graduations that allow for precise measurement of liquid volumes. Graduated cylinders represent a fundamental tool in experiments related to volume measurement.

When using a graduated cylinder, one must ensure to view the liquid level at eye level. This helps in avoiding a parallax error, which occurs if the cylinder is viewed from an angle. To measure the volume correctly, the measurement should be taken at the bottom of the meniscus, which is the curved surface of the liquid.

In this specific exercise, the graduated cylinder is initially filled with 75.0 mL of water. After adding 52.4 g of iron, the final volume reading is measured again, considering the physical displacement of the water due to the solid iron. By adding the initial liquid volume to the iron's volume, we use the principle of displacement:\[ \text{Final Volume} = \text{Initial Water Volume} + \text{Volume of Iron} \]Using a graduated cylinder makes it easy to visualize how much the water level rises, providing an intuitive understanding of volume displacement and density.