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Chapter 2: Problem 63

A student weighed an empty graduated cylinder and found that it had a mass of \(25.23 \mathrm{~g}\). When filled with \(25.0 \mathrm{~mL}\) of an unknown liquid, the total mass was \(50.92 \mathrm{~g}\). What is the density of the liquid?

Short Answer

Expert verified
1.0276 g/mL

Step by step solution

01

- Find the mass of the unknown liquid

Subtract the mass of the empty graduated cylinder from the total mass when filled with the liquid. \[ 50.92 \text{ g} - 25.23 \text{ g} = 25.69 \text{ g} \]
02

- Calculate the volume of the liquid

The volume of the unknown liquid is given as \(25.0 \text{ mL}\). This information is provided in the problem.
03

- Use the density formula

Density is calculated using the formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \] Substitute the mass and volume values into the formula: \[ \text{Density} = \frac{25.69 \text{ g}}{25.0 \text{ mL}} \]
04

- Solve for density

Calculate the value: \[ \text{Density} = 1.0276 \text{ g/mL} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mass Measurement
Understanding how to measure mass accurately is essential in many scientific computations, including density calculations. Mass is typically measured using a balance or a scale. In this exercise, we used a balance to measure the mass of a graduated cylinder twice: when it was empty and when it was filled with an unknown liquid. By comparing these two measurements, we can determine the mass of just the liquid by subtracting the mass of the empty cylinder from the total mass. For example, if the total mass is 50.92 g and the mass of the empty cylinder is 25.23 g, the mass of the liquid is \(50.92 \text{ g} - 25.23 \text{ g} = 25.69 \text{ g}\).
Volume Measurement
Volume measurement is another crucial step in density calculation. In this exercise, we use a graduated cylinder, which is a tool specifically designed to measure liquid volumes accurately. The volume of the liquid should be read at eye level to avoid parallax error, which could lead to incorrect readings. The problem states that the volume of the unknown liquid is 25.0 mL, so there's no need for further measurement. However, in laboratory settings, you would fill the graduated cylinder to the desired mark and record the volume precisely.
Density Formula
The formula for density is one of the fundamental equations in science: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). This means that density is the ratio of mass to volume. In our example, we have already calculated the mass (25.69 g) and the volume (25.0 mL). Plugging these values into the density formula gives us: \( \text{Density} = \frac{25.69 \text{ g}}{25.0 \text{ mL}} \). When we solve this, we get a density of 1.03 g/mL (rounded to two decimal places). This density tells us how much mass is packed into a specific volume and can be used for identifying the liquid.
Graduated Cylinder Use
A graduated cylinder is a common laboratory instrument used to measure liquid volumes with precision. Graduated cylinders come in various sizes and have markings along the side to indicate volume in milliliters (mL). To use it accurately:
  • Place the cylinder on a flat surface.
  • Pour the liquid into the cylinder and let it settle.
  • Ensure your eyes are level with the surface of the liquid to avoid parallax error.
  • Read the volume from the bottom of the meniscus.
In this exercise, the graduated cylinder was used to measure 25.0 mL of an unknown liquid. This accurate volume measurement is critical for correctly calculating the liquid's density. Using the graduated cylinder appropriately ensures the validity and reliability of our experimental results.

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Most popular questions from this chapter

The accepted toxic dose of mercury is \(300 \mu \mathrm{g} /\) day. Dental offices sometimes contain as much as \(180 \mu \mathrm{g}\) of mercury per cubic meter of air. If a nurse working in the office ingests \(2 \times 10^{4} \mathrm{~L}\) of air per day, is he or she at risk for mercury poisoning?

Complete the following metric conversions using the correct number of significant figures: (a) \(28.0 \mathrm{~cm}\) to \(\mathrm{m}\) (b) \(1000 \mathrm{~m}\) to \(\mathrm{km}\) (c) \(9.28 \mathrm{~cm}\) to \(\mathrm{mm}\) (d) \(10.68 \mathrm{~g}\) to \(\mathrm{mg}\) (e) \(6.8 \times 10^{4} \mathrm{mg}\) to \(\mathrm{kg}\) (f) \(8.54 \mathrm{~g}\) to \(\mathrm{kg}\) (g) \(25.0 \mathrm{~mL}\) to \(\mathrm{L}\) (h) \(22.4 \mathrm{~L}\) to \(\mu \mathrm{L}\)

The first Apple computer had \(5.0\) Mbytes of storage space on its hard drive, and the cost of this computer was \(\$ 9995\). An Apple iPad Air 2 has 128 Gbytes of storage for a cost of S699. Calculate the cost per byte for each of these two Apple products. Which is a better buy?

Neutrinos are subatomic particles with a very low mass. Recent work at CERN, Europe's particle-physics lab near Geneva, Switzerland, suggests that neutrinos may have the ability to travel faster than the speed of light. If the speed of light is \(1.86 \times 10^{8} \mathrm{mi} / \mathrm{hr}\), how many nanoseconds should it take for light to travel from CERN to the Gran Sasso National Lab in Italy, a \(730.0 \mathrm{~km}\) journey? If a neutrino can travel the same distance 60 nsec faster, how many significant figures would you need to detect the difference in speed?

Write each of the following numbers in exponential notation: (a) \(0.0456\) (b) \(4082.2\) (c) \(40.30\) (d) \(12,000,000\)
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