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Chapter 1: Problem 103

Express in base SI unitsmmol \(\mathrm{dm}^{-3}\)

Short Answer

Expert verified
In base SI units, mmol \( \mathrm{dm}^{-3} \) is expressed as mol \( \mathrm{m}^{-3} \).

Step by step solution

01

Understand the Units

The unit mmol \( \mathrm{dm}^{-3} \) consists of millimoles per cubic decimeter. We need to convert millimoles to moles and cubic decimeters to cubic meters for base SI units.
02

Convert Millimoles to Moles

1 millimole (mmol) is equal to \( 10^{-3} \) moles. Therefore, expressing mmol in SI units would be multiplying by \( 10^{-3} \).
03

Convert Cubic Decimeters to Cubic Meters

1 cubic decimeter (\( \mathrm{dm}^{3} \)) is equal to \( 10^{-3} \) cubic meters (\( \mathrm{m}^{3} \)). Therefore, \( \mathrm{dm}^{-3} \) becomes \( \mathrm{m}^{-3} \) in base SI units.
04

Combine the Conversions

Combine the conversions from Steps 2 and 3. So, mmol \( \mathrm{dm}^{-3}\) converts to \( 10^{-3} \) moles per \( 10^{-3} \) cubic meters. The result in base SI units is mol \( \mathrm{m}^{-3} \).

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Key Concepts

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

Understanding Millimoles
Millimoles are a subunit of moles, a fundamental concept in chemistry used to express the quantity of a chemical substance. A millimole is one-thousandth of a mole. Generally, chemical reactions and solutions often deal with small quantities, making millimoles a convenient unit.

Here's how millimoles relate to moles:
  • 1 mole = 1000 millimoles (mmol)
  • 1 millimole = 0.001 moles or \(10^{-3}\) moles
By converting millimoles into moles, you align your calculations with the base SI unit for the amount of substance, ensuring clarity and consistency in scientific communication.
Exploring Cubic Decimeters
Cubic decimeters are a measure of volume and are directly related to liters, a common unit of volume in everyday contexts. One cubic decimeter (\(\mathrm{dm}^3\)) is equivalent to one liter. In scientific terms, we often need to switch to cubic meters to adhere to the SI unit system, which provides a standardized way to measure larger volumes.

Important conversions include:
  • 1 cubic decimeter = 0.001 cubic meters or \(10^{-3}\) cubic meters
  • Because of this equivalence, \(\mathrm{dm}^{-3}\) converts to \(\mathrm{m}^{-3}\), representing the concentration of substances within a cubic meter in SI units.
Understanding this conversion is essential when expressing concentrations such as molarity in terms of SI units.
Conversion in Chemistry
Conversion is an everyday task in chemistry, enabling scientists to work with standard units for accurate results. Converting quantities into SI units is crucial because it standardizes measurements and facilitates communication and documentation of scientific data internationally.

The concept involves the following:
  • Aligning units such as time, length, mass, and volume to the International System of Units (SI).
  • Converting concentrations, like mmol/\(\mathrm{dm}^3\), into mol/\(\mathrm{m}^3\) for consistency.
  • For instance, converting millimoles per cubic decimeter to moles per cubic meter involves adjusting both numerator and denominator by \(10^{-3}\), leading to \(1\) mol/\(\mathrm{m}^{3}\).
This streamlined conversion ensures that results are widely understood and correctly interpreted worldwide, vital for collaborative and reproducible scientific work.

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