/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 74 A ln an experiment, you need 0.1... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 74

A ln an experiment, you need 0.125 mol of sodium metal. Sodium can be cut easily with a knife (Figure 2.12 ), so if you cut out a block of sodium, what should the volume of the block be in cubic centimeters? If you cut a perfect cube, what is the length of the edge of the cube? (The density of sodium is \(0.97 \mathrm{g} / \mathrm{cm}^{3} .\) )

Short Answer

Expert verified
Volume is approximately 2.963 cm鲁; edge length is about 1.43 cm.

Step by step solution

01

Determine Mass from Moles

To find the mass of sodium needed, we use the formula:\[ \text{mass} = \text{moles} \times \text{molar mass} \]Given that the molar mass of sodium (Na) is approximately 22.99 g/mol, we calculate the mass required for 0.125 mol:\[ \text{mass} = 0.125 \times 22.99 = 2.87375 \text{ g} \]
02

Calculate the Volume

Using the density formula \( \text{density} = \frac{\text{mass}}{\text{volume}} \), we rearrange to find the volume:\[ \text{volume} = \frac{\text{mass}}{\text{density}} \]Substitute the known values (2.87375 g for mass and 0.97 g/cm鲁 for density):\[ \text{volume} = \frac{2.87375}{0.97} \approx 2.963 \text{ cm}^3 \]
03

Determine Edge Length of the Cube

To find the edge length of a cube with a given volume, use the formula for the volume of a cube \( V = s^3 \) where \(s\) is the edge length. Solve for \(s\):\[ s = \sqrt[3]{V} = \sqrt[3]{2.963} \approx 1.43 \text{ cm} \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Molar Mass
Molar mass plays a crucial role in chemical calculations, helping you convert between grams and moles. It is the mass of one mole of a substance and is usually expressed in grams per mole (g/mol).
  • To find the molar mass, you often refer to the periodic table. Each element's atomic mass is approximately equal to its molar mass.
  • For sodium (\[ ext{Na}\]), this value is about 22.99 g/mol. This means that one mole of sodium atoms weighs 22.99 grams.
By knowing the molar mass, you can easily calculate the mass required for a specific mole quantity, as shown in the exercise. When you need 0.125 mol of sodium, you multiply the molar mass by the number of moles:\[ ext{mass} = 0.125 imes 22.99 = 2.87375 ext{ g}\] This result tells you that 0.125 moles of sodium weighs approximately 2.874 grams, which is essential for experiments requiring precise amounts.
Volume Calculation
Volume calculation is essential when dealing with solid materials, especially when converting from mass using density. Density is defined as mass per unit volume and can be rearranged to find the volume.
  • To calculate volume, use the formula: \[ \text{volume} = \frac{\text{mass}}{\text{density}} \]
  • This formula allows you to determine how much space an object will occupy based on its mass and density.
In the context of the exercise, once you calculate the mass of sodium as 2.874 grams, you can use the given density of sodium (\[0.97\text{ g/cm}^3\]) to find the volume: \[ \text{volume} = \frac{2.87375}{0.97} \approx 2.963 \text{ cm}^3 \] This calculation tells you that this mass of sodium occupies around 2.963 cubic centimeters.
Edge Length of a Cube
When you want to cut a material into a perfect cube, knowing the cube's volume allows you to determine the length of each edge.
  • The formula for the volume of a cube is \[ V = s^3 \], where \(s\) is the edge length.
  • To find the edge length (\(s\)), simply take the cube root of the volume.
Using the calculated volume from the previous section, we find the edge length this way:\[ s = \sqrt[3]{2.963} \approx 1.43 \text{ cm} \] This calculation reveals that to achieve the volume of a perfect cube, each side of the sodium block must be about 1.43 cm long. Knowing this helps in evenly cutting the sodium for an accurate experimental setup.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A Although carbon-12 is now used as the standard for atomic masses, this has not always been the case. Farly attempts at classification used hydrogen as the standard, with the mass of hydrogen being set equal to 1.0000 u. Later attempts defined atomic masses using oxygen (with a mass of \(16.0000 \mathrm{u}\) ). In each instance, the atomic masses of the other elements were defined relative to these masses. (To answer this question, you need more precise data on current atomic masses: \(\mathrm{H}, 1.00794 \mathrm{u} ; \mathrm{O}\) \(15.9994 \mathrm{u} .)\) (a) If \(\mathrm{H}=1.0000 \mathrm{u}\) was used as a standard for atomic masses, what would the atomic mass of oxygen be? What would be the value of Avogadro's number under these circumstances? (b) Assuming the standard is \(\mathrm{O}=16.0000 \mathrm{u}\), determine the value for the atomic mass of hydrogen and the value of Avogadro's number.

Give the symbol for a metalloid in the third period and then identify a property of this element.

Fill in the blanks in the table (one column per element). Symbol \(\quad$$58 \mathrm{Ni}$$\quad$$^{86} \mathrm{Kr}$$\quad\)____\(\quad\)____ Number of protons _____ \(\quad\)_____\(\quad\) 78 \(\quad\)____ Number of neutrons _____ \(\quad\)_____\(\quad\) 117\(\quad\)46 Number of electrons in the neutral atom _____ \(\quad\)_____\(\quad\)_____\(\quad\)35 Name of element_____ \(\quad\)_____\(\quad\)_____\(\quad\)____

Reviewing the periodic table: (a) Name an element in Group 2 B. (b) Name an element in the fifth period. (c) Which element is in the sixth period in Group \(4 \mathrm{A} ?\) (d) Which element is in the third period in Group \(6 \mathrm{A} ?\) (e) Which alkali metal is in the third period? (f) Which noble gas element is in the fifth period? (g) Name the element in Group \(6 A\) and the fourth period. Is it a metal, nonmetal, or metalloid? (h) Name a metalloid in Group \(5 \mathrm{A}\).

Which of the following are isotopes of element X, the atomic number for which is \(9:^{19} \mathrm{X},^{20} \mathrm{X}, 18 \mathrm{X},\) and \(^{21} \mathrm{X} ?\)
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Reactions

Read Explanation

Inorganic Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Organic Chemistry

Read Explanation

Kinetics

Read Explanation

Chemical Analysis

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.