Chapter 1: Problem 84
Lithium is the least dense metal known (density = \(\left.0.53 \mathrm{~g} / \mathrm{cm}^{3}\right)\). What is the volume occupied by \(3.15 \times 10^{3} \mathrm{~g}\) of lithium?
Short Answer
Expert verified
The volume is approximately 5943.40 cm³.
Step by step solution
01
Recall the formula for volume
The volume of an object can be found using the formula: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \). We will use this formula to calculate the volume occupied by lithium.
02
Identify the given values
From the problem, we have the mass of lithium as \( 3.15 \times 10^{3} \; \text{g} \) and the density of lithium as \( 0.53 \; \text{g/cm}^3 \).
03
Apply the values to the formula
Substitute the given mass and density into the volume formula: \[ \text{Volume} = \frac{3.15 \times 10^{3} \; \text{g}}{0.53 \; \text{g/cm}^3} \]
04
Perform the calculation
Calculate the volume by doing the division:\[ \text{Volume} = \frac{3.15 \times 10^{3}}{0.53} \approx 5943.40 \; \text{cm}^3 \]
05
State the final answer
The volume occupied by \( 3.15 \times 10^{3} \) grams of lithium is approximately \( 5943.40 \; \text{cm}^3 \).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Lithium Properties
Lithium is a fascinating metal, mainly because it is the least dense metal known. Its density is about \( 0.53 \, \text{g/cm}^3 \), making it much lighter than other metals like iron or copper. This low density gives lithium several unique properties. For instance, it floats on water, unlike most metals that sink.
As an alkali metal, lithium is very reactive, especially with water, but its low density makes it ideal for lightweight applications. You often find lithium in batteries, especially where weight is a concern, like in smartphones and electric cars. Additionally, lithium is soft and has a silvery-white appearance.
As an alkali metal, lithium is very reactive, especially with water, but its low density makes it ideal for lightweight applications. You often find lithium in batteries, especially where weight is a concern, like in smartphones and electric cars. Additionally, lithium is soft and has a silvery-white appearance.
Volume Formula
The concept of volume is key when dealing with the physical properties of objects and materials. To calculate the volume of a material, we use its mass and density. The volume formula is expressed as:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
This formula tells us how much space a quantity of material, like lithium in this case, occupies. In it, volume is usually measured in cubic centimeters (\(\text{cm}^3\)) or other similar units.
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
This formula tells us how much space a quantity of material, like lithium in this case, occupies. In it, volume is usually measured in cubic centimeters (\(\text{cm}^3\)) or other similar units.
Density Formula
Density helps us understand how much matter is packed into a certain volume of a substance. The formula for density is straightforward. It is defined by:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
In this equation, density is typically measured in grams per cubic centimeter (\(\text{g/cm}^3\)). It plays a key role in distinguishing different materials. A substance with a lower density like lithium means it has a large amount of space between its particles, unlike high-density materials such as lead or mercury.
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
In this equation, density is typically measured in grams per cubic centimeter (\(\text{g/cm}^3\)). It plays a key role in distinguishing different materials. A substance with a lower density like lithium means it has a large amount of space between its particles, unlike high-density materials such as lead or mercury.
Mass and Volume Relationship
The relationship between mass and volume is essential for understanding physical characteristics of matter. By manipulating the formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \), we can find that:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
This lets us calculate the volume if we know an object's mass and density. The inverse applies too—with known volume and density, one can find mass. This relationship is vital for applications across science and engineering, helping predict how substances will behave in different environments. It also shows how the same amount of material can occupy different spaces if densities change.
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
This lets us calculate the volume if we know an object's mass and density. The inverse applies too—with known volume and density, one can find mass. This relationship is vital for applications across science and engineering, helping predict how substances will behave in different environments. It also shows how the same amount of material can occupy different spaces if densities change.
