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Chapter 2: Problem 150

A sample of a liquid solvent has a density of \(0.915 \mathrm{~g} / \mathrm{mL}\). What is the mass of \(85.5 \mathrm{~mL}\) of the liquid?

Short Answer

Expert verified
The mass of the liquid sample is approximately 78.21 grams.

Step by step solution

01

Write down the density formula

The equation we need to use is: \(Density = \frac{Mass}{Volume}\)
02

Rearrange the formula for mass

To find the mass, we need to rearrange the formula. Multiply both sides by the volume to isolate the mass on one side of the equation: \(Mass = Density \times Volume\)
03

Insert given values into the formula

Now that we have the formula for mass, we can insert the values from the exercise into the formula: \(Mass = 0.915 \frac{g}{mL} \times 85.5mL\)
04

Calculate the mass

Multiply the density by the volume to obtain the mass of the liquid sample: \(Mass = 0.915 \times 85.5\) \(Mass = 78.2075g\) So, the mass of the liquid sample is approximately 78.21 grams.

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Key Concepts

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

Mass Calculation
The concept of mass calculation is essential when working with density and volume. To calculate mass from density and volume, you rearrange the density formula. This involves multiplying the density by the volume to find the mass of an object or substance. In mathematical terms, the formula becomes:\[ Mass = Density \times Volume \]
  • Density indicates how much mass is contained in a unit volume of a substance.
  • Volume refers to the space the substance occupies.
  • By multiplying these two values, we find the total mass.
Understanding this relationship helps you calculate the mass when you know the density and volume, just like in our exercise. Here, a liquid solvent's density and volume are used to find its mass, providing a real-world application of these principles.
Density Formula
The density formula is the foundation for understanding mass and volume. Density is a measure of how much mass is contained in a given amount of volume. It is calculated using the formula:\[ Density = \frac{Mass}{Volume} \]
  • Mass is the amount of matter in the object or substance.
  • Volume is the amount of space that the object or substance occupies.
  • The density formula can be rearranged to solve for either mass or volume when given the other two variables.
For instance, if you know the density and the volume of a liquid, you can easily determine its mass. This principle is particularly useful in scenarios where measuring mass directly is difficult but volume is measurable. By manipulating the formula, you gain flexibility in solving problems related to density.
Volume
Volume is an important concept when dealing with density and mass. It refers to the three-dimensional space occupied by a substance and is usually measured in liters ( L) or milliliters ( mL) for liquids. The relationship between volume and the other two variables (density and mass) is crucial.
  • Volume is necessary for calculating mass if density is known.
  • It plays a key role in determining how densely packed a substance is within a given space.
  • In practical applications, accurately measuring volume allows you to use the density formula effectively.
In the given problem, the volume of the liquid solvent needed to be multiplied by its density to find the mass. This illustrates how volume functions as a vital part of many scientific calculations involving density.

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Most popular questions from this chapter

The following water measurements are made: \(18 \mathrm{~mL}\) of water measured with a beaker, \(128.7 \mathrm{~mL}\) of water measured with a graduated cylinder, and \(23.45 \mathrm{~mL}\) of water measured with a buret. If all of these water samples are then poured together into one container, what total volume of water should be reported? Support your answer.

Write each of the following numbers in standard scientific notation. See the Appendix if you need help multiplying or dividing numbers with exponents. a. \(1 / 10^{2}\) b. \(1 / 10^{-2}\) c. \(55 / 10^{3}\) d. \(\left(3.1 \times 10^{6}\right) / 10^{-3}\) e. \(\left(10^{6}\right)^{1 / 2}\) f. \(\left(10^{6}\right)\left(10^{4}\right) /\left(10^{2}\right)\) g. \(1 / 0.0034\) h. \(3.453 / 10^{-4}\)

Evaluate each of the following and write the answer to the appropriate number of significant figures. a. \((2.0944+0.0003233+12.22) /(7.001)\) b. \(\left(1.42 \times 10^{2}+1.021 \times 10^{3}\right) /\left(3.1 \times 10^{-1}\right)\) c. \(\left(9.762 \times 10^{-3}\right) /\left(1.43 \times 10^{2}+4.51 \times 10^{1}\right)\) d. \(\left(6.1982 \times 10^{-4}\right)^{2}\)

Would an automobile moving at a constant speed of \(100 \mathrm{~km} / \mathrm{h}\) violate a 65 -mph speed limit?

Indicate the number of significant digits in the answer when each of the following expressions is evaluated (you do not have to evaluate the expression). a. \((6.25) /(74.1143)\) b. (1.45)(0.08431)\(\left(6.022 \times 10^{23}\right)\) c. \((4.75512)(9.74441) /(3.14)\)
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