Problem 124 - General Chemistry

Question

Vanadium metal is added to steel to impart strength. The density of vanadium is \(5.96 \mathrm{~g} / \mathrm{cm}^{3}\). Express this in SI units \(\left(\mathrm{kg} / \mathrm{m}^{3}\right)\).

Step-by-Step Solution

Answer

The density of vanadium is 5960 kg/m^3.

Step 1: Understand the Given Information

We are given the density of vanadium in \(\text{g/cm}^3\) and need to express it in \(\text{kg/m}^3\). The given density value is 5.96 \(\text{g/cm}^3\).

Step 2: Convert Grams to Kilograms

Since 1 kilogram equals 1000 grams, we convert the mass from grams to kilograms: \(5.96 \text{ g/cm}^3 = \frac{5.96}{1000} \text{ kg/cm}^3 = 0.00596 \text{ kg/cm}^3\).

Step 3: Convert Cubic Centimeters to Cubic Meters

We need to convert the volume from cubic centimeters to cubic meters. Since \text{1 m}^3 = 10^6 \text{ cm}^3\, we multiply the density by \10^6\: \(0.00596 \frac{\text{kg}}{\text{cm}^3} \times 10^6 = 5960 \text{kg/m}^3\).

Step 4: Express the Density in SI Units

The density of vanadium in SI units \(\text{kg/m}^3\) is 5960 \(\text{kg/m}^3\).

Key Concepts

Density

Density is a fundamental concept in the physical sciences that illustrates how much mass is contained within a specific volume. To put it simply, density shows how tightly packed a substance's particles are. For instance, if you have two substances with the same volume but different masses, the one with the higher mass is denser.

• It is typically expressed in units like \( ext{g/cm}^3\) or \( ext{kg/m}^3\).
• To find density, divide an object's mass by its volume: \( ext{Density} = \frac{\text{Mass}}{\text{Volume}}\).

Understanding density helps in identifying substances and predicting their behavior under different conditions like pressure and temperature changes.

SI Units

SI units, or the International System of Units, are standardized measurement units used around the globe. This system ensures consistency in scientific communication and calculations.

• The basic SI unit for mass is the kilogram (kg).
• The SI unit for volume is the cubic meter (m\(^3\)).
• Density in SI units is thus measured in kilograms per cubic meter (kg/m\(^3\)).

Using SI units simplifies conversions and calculations as it's a unified system that avoids discrepancies in measurements.

Vanadium

Vanadium is a transition metal that is often used in metallurgy to increase the strength, hardness, and resistance to corrosion of alloys. It is particularly valued for its beneficial properties when added to steel.

• It appears silvery-grey in color.
• Vanadium's density is approximately 5.96 g/cm\(^3\), which indicates how much mass a given volume of this metal contains.
• This density is significant for determining the right amount of vanadium to add in alloy production.

Knowing the density of vanadium is crucial in industrial applications to ensure alloy mixtures contain the right proportions.

Cubic Meters

Cubic meters \(m^3\) are the SI unit for measuring volume. It is defined as the space occupied by a cube with sides of one meter in length. Cubic meters are essential for understanding larger volume measurements, especially in fields like engineering and construction.

• 1 cubic meter = 1,000,000 cubic centimeters (10\(^6\) cm\(^3\)).
• During unit conversion, knowing this equivalence is crucial, particularly when converting volumes from smaller to larger units.

Using cubic meters allows for straightforward calculations in SI units, aiding in the conversion and interpretation of measurements for practical use.

Kilograms

Kilograms (kg) are the SI unit for mass. This unit is pivotal in expressing the weight and mass of substances accurately in the scientific world and everyday life. Understanding how to convert mass into kilograms is vital for scientific calculations and everyday measurements.

• 1 kilogram is equal to 1000 grams.
• Grams to kilograms conversion is necessary when adjusting measurements to SI units.
• Using kilograms facilitates easy understanding and standardized reporting of mass across various scientific disciplines.

Utilizing kilograms in density calculations, particularly when converting units, ensures that scientific data remains precise and accurate.