What is the weight of one atom of \(\mathrm{H}\) in \(\mathrm{g}\) (at.wt. of \(\mathrm{H}=1.008\) )?

Understanding atomic mass units (amu) is fundamental to grasping basic chemistry concepts. An atomic mass unit defines the unit of mass used to express atomic and molecular weights. It is precisely set as one-twelfth the mass of an unbound neutral atom of carbon-12 at rest and in its ground state, which is equivalent to exactly 1.66 x 10^-24 grams. This incredibly small mass measurement allows chemists to compare the relative masses of different atoms on a number scale that makes practical sense. To put it into perspective, the atomic weight of Hydrogen is approximately 1.008 amu, making it the lightest element on the periodic table, since its mass is closest to 1 amu.

When we say that the atomic mass of hydrogen is 1.008 amu, it helps to visualize that we are condensing the mass of this element into a scale where carbon-12 sits neatly at the 12 amu mark. One atomic mass unit is essentially equal to the mass of a proton or a neutron, which are the heftier particles in an atom's nucleus. This standardization facilitates easier calculations and understanding of the mass particles at an atomic level.

The conversion factor in chemistry is a critical bridge between the world of atomic mass units and our everyday measurement systems. To interrelate these two, we use a specified conversion factor, which is a numerical value used to convert a quantity expressed in one unit to a quantity expressed in another unit. The conversion factor for amu to grams is 1 amu = 1.66053906660 x 10^-24 grams. Understanding this factor is crucial when dealing with quantities that are typically measured on different scales.

In practical terms, if you want to know the mass of a given number of atoms in grams, the conversion factor informs us of the equivalent mass in a unit that is more tangible in a real-world context. This is similar to knowing how to convert inches to centimeters for length measurements. When working with atomic mass, this conversion factor is key for scientists to perform experiments, communicate findings, and understand the practical implications of their work in chemical terms that can be more easily related to or visualized.

Calculating the atomic weight of an element in grams can seem daunting at first, given the tiny scale at which atomic masses are measured. However, it is a straightforward process once the conversion factor is understood. The exercise provided outlines the steps needed to calculate the weight of a single hydrogen atom in grams, starting with its atomic weight in amu. Here's how we can approach this:

First, we identify the atomic weight of the element in question, which in the exercise was hydrogen with an atomic weight of 1.008 amu. Next, using the conversion factor (1 amu = 1.66053906660 x 10^-24 grams), we multiply the atomic weight of hydrogen by this conversion factor to obtain the weight in grams. The result will give us the mass of one atom of hydrogen in grams, which is an essential figure for various scientific computations and theoretical work.

It is important to handle these numbers with precision, as calculating atomic weight in grams involves very small figures that require careful use of scientific notation and accurate arithmetic operations. For scientists and students alike, these calculations enable the analysis and understanding of chemical reactions on a molecular level, providing an intimate view of how substances interact in our universe.