Chapter 2: Problem 48
What is the mass in grams of 13.2 amu?
Short Answer
Expert verified
The mass is approximately \(2.19391156 \times 10^{-23}\) grams.
Step by step solution
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Atomic Mass Unit (AMU)
The atomic mass unit (amu) is a standard unit of mass used to express atomic and molecular weights. It's particularly helpful when dealing with very small particles, such as atoms and molecules. One atomic mass unit is defined as one-twelfth of the mass of a carbon-12 atom. This definition allows for a uniform method of comparing mass within the atom's realm, providing clarity and precision in scientific calculations.
In practice, amu helps scientists and chemists express mass on an atomic scale, making it easier to handle them without switching to impractically small numbers. Understanding and using the amu is essential in fields that require precise measurements, such as chemistry and physics.
In practice, amu helps scientists and chemists express mass on an atomic scale, making it easier to handle them without switching to impractically small numbers. Understanding and using the amu is essential in fields that require precise measurements, such as chemistry and physics.
Conversion Factor
A conversion factor is a tool we use to convert one unit of measurement into another. In converting atomic mass units (amu) to grams, it's essential to know that 1 amu is approximately equal to a very tiny mass, specifically, \(1.66053906660 \times 10^{-24}\) grams.
This factor is derived from the relationship established between the atomic scale and more conventional units like grams. By using this factor, you can easily translate measurements in amu to grams, allowing for a more comprehensive understanding and applicability of data beyond purely atomic contexts.
When converting units, ensure your conversion factors are accurate and consistent. This helps maintain accuracy in scientific work.
This factor is derived from the relationship established between the atomic scale and more conventional units like grams. By using this factor, you can easily translate measurements in amu to grams, allowing for a more comprehensive understanding and applicability of data beyond purely atomic contexts.
When converting units, ensure your conversion factors are accurate and consistent. This helps maintain accuracy in scientific work.
Mass Calculation
Mass calculation refers to the process of determining the mass of an object or substance. In our exercise, we're interested in calculating the mass in grams from a given mass in amu. The equation to use this involves multiplying the known mass in amu by the conversion factor from amu to grams:
\[ \text{mass in grams} = \text{mass in amu} \times 1.66053906660 \times 10^{-24} \]
By substituting the values into this equation — for example, 13.2 amu as in our exercise — you can compute the mass in grams by performing the multiplication. Mass calculations like these help in translating atomic-level data into practical, tangible figures for broader scientific uses.
\[ \text{mass in grams} = \text{mass in amu} \times 1.66053906660 \times 10^{-24} \]
By substituting the values into this equation — for example, 13.2 amu as in our exercise — you can compute the mass in grams by performing the multiplication. Mass calculations like these help in translating atomic-level data into practical, tangible figures for broader scientific uses.
Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a concise form, commonly used in science and engineering. It simplifies numbers by representing them as a product of a number between 1 and 10 and a power of ten.
For example, the conversion factor from amu to grams is expressed in scientific notation as \(1.66053906660 \times 10^{-24}\). This format makes it easier to read, write, and perform calculations involving very small quantities.
In our mass calculation, the result was also expressed in scientific notation: \(2.19391156 \times 10^{-23}\) grams. Employing scientific notation is critical not only for simplicity but also for precision in scientific calculations involving extremely large or small numbers.
For example, the conversion factor from amu to grams is expressed in scientific notation as \(1.66053906660 \times 10^{-24}\). This format makes it easier to read, write, and perform calculations involving very small quantities.
In our mass calculation, the result was also expressed in scientific notation: \(2.19391156 \times 10^{-23}\) grams. Employing scientific notation is critical not only for simplicity but also for precision in scientific calculations involving extremely large or small numbers.
