Converting Mercury's Density from g/cm3 to kg/m3: A Comprehensive Guide

Understanding Density: Density is an important physical property that indicates how much mass is contained in a given volume of a substance. In the case of mercury, it has a density of 13.5 g/cm3. Unit Cancellation and Dimensional Analysis: To convert the density from grams per cubic centimeter (g/cm3) to kilograms per cubic meter (kg/m3), you can use unit cancellation techniques, a method essential in scientific calculations.

Converting Density Units Step-by-Step

To convert 13.5 g/cm3 to kg/m3, start with the original density value:

Method 1:

[13.5 , text{g/cm}^3 times frac{1 , text{kg}}{1000 , text{g}} times frac{100 , text{cm}}{1 , text{m}} 13500 , text{kg/m}^3]

Method 2:

[13.5 , text{g/cm}^3 times frac{1 , text{kg}}{1000 , text{g}} times frac{100 , text{cm}^3}{1 , text{m}^3} 1.35 times 10^4 , text{kg/m}^3]

Method 3:

[13.5 , text{g/cm}^3 times frac{1 , text{kg}}{1000 , text{g}} times frac{1 , text{cm}}{10 , text{mm}} 1.35 times 10^{-5} , text{kg/mm}^3]

Understanding the Metric System and Conversion Factors

The metric system is based on simple prefixes and the decimal system, making it easy to convert between units. Converting g/cm3 to kg/m3 involves several steps:

Step 1: Convert grams to kilograms: 1 g 0.001 kg Step 2: Convert cubic centimeters to cubic meters: 1 cm3 0.000001 m3

Example Calculation:

[13.5 , text{g/cm}^3 times frac{1 , text{kg}}{1000 , text{g}} times frac{1000 , text{cm}^3}{1 , text{m}^3} 13500 , text{kg/m}^3]

Alternatively, convert directly:

[13.5 , text{g/cm}^3 times frac{1 , text{kg}}{1000 , text{g}} times frac{1000 , text{cm}^3}{1 , text{m}^3} 13.5 times 10^3 , text{kg/m}^3]

Conclusion

Mercury has a density of 13.5 g/cm3, which can be converted to 13500 kg/m3. This conversion is crucial in various scientific and industrial applications, ensuring accuracy in calculations and measurements. Mastering unit cancellation and dimensional analysis will enhance your problem-solving skills in physics and chemistry.

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