Question

What does an average magnesium atom weigh (in amu)? What would 345 magnesium atoms weigh? How many magnesium atoms are contained in a sample of magnesium that has a mass of \(2.071 \times\) \(10^{4}\) amu?

Short answer

An average magnesium atom weighs approximately 24.3 amu. The weight of 345 magnesium atoms is 8383.5 amu. In a sample weighing \(2.071\times10^4\) amu, there are approximately 852 magnesium atoms.

Step-by-step solution

Find the atomic weight of magnesium

We can find the atomic weight of magnesium in the periodic table. Magnesium has an atomic number of 12 and an average atomic weight of approximately 24.3 amu.

Calculate the weight of 345 magnesium atoms

Multiply the atomic weight of magnesium by the number of atoms to find the total weight of 345 magnesium atoms: \[ weight = (number\:of\:atoms) \times (atomic\:weight) \] \[ weight = 345 \times 24.3 \: \text{amu} \] \[ weight = 8383.5 \: \text{amu} \] So, the weight of 345 magnesium atoms is 8383.5 amu.

Calculate the number of magnesium atoms in a sample weighing \(2.071\times10^4\) amu

Divide the mass of the sample by the atomic weight of magnesium to find the number of atoms in the sample: \[ number\:of\:atoms = \frac{mass\;of\;sample}{atomic\;weight} \] \[ number\:of\:atoms = \frac{2.071\times10^4\:amu}{24.3\;amu} \] \[ number\:of\:atoms \approx 852\] Therefore, there are approximately 852 magnesium atoms in a sample weighing \(2.071\times10^4 amu\).

Key concepts

Understanding Magnesium

Magnesium is a chemical element with the symbol Mg and atomic number 12 on the periodic table. It is classified as an alkaline earth metal and is known for its silvery-white appearance. This element plays essential roles both biologically and industrially.

Magnesium is quite abundant in the Earth's crust and is crucial for biological systems, including human health. It's a necessary ion in over 300 enzymatic reactions in the body and is vital for processes such as ATP metabolism and DNA synthesis. In the context of this exercise, we focus on its atomic properties as required for calculating its weight in atomic mass units (amu).

- Symbol: Mg - Atomic Number: 12 - Standard Atomic Weight: Approximately 24.3 amu The atomic weight reflects the average mass of magnesium atoms, considering the distribution of its natural isotopes. This average value is what we commonly use in calculations when determining the weight of multiple magnesium atoms.

What is AMU?

AMU stands for Atomic Mass Unit, which is a standard unit of mass that quantifies the weight of atoms and subatomic particles. It is approximately equal to the mass of one nucleon (either a single proton or neutron) and is defined as one-twelfth of the mass of a carbon-12 atom.

Mathematically: - 1 amu = 1.66 x 10^-24 grams Using amu allows scientists and students to talk about the mass of atoms in a more convenient way, since using standard grams would result in very small numbers that are cumbersome to work with. For example, the atomic weight of magnesium is about 24.3 amu, which means the average magnesium atom weighs 24.3 amu. To convert this to grams, you'd multiply by the amu to gram conversion factor, but generally, amu is preferred for simplicity and clarity in these calculations.

Counting Atoms in Magnesium Samples

When calculating the number of atoms in a given sample of magnesium, knowing its atomic weight in amu is crucial. This weight acts as a bridge between the microscopic atomic scale and macroscopic quantities that we can measure and work with more easily.

Here's how to count the number of magnesium atoms:

• Start by determining the total mass of the magnesium sample in amu.
• Use the formula: \[number\,of\,atoms = \frac{mass\,of\,sample}{atomic\,weight}\] This formula divides the sample's mass by the atomic weight of a single magnesium atom.
• For instance, if a sample has a mass of \(2.071 \times 10^4\) amu, dividing by the atomic weight of magnesium (24.3 amu) calculates the number of magnesium atoms, which is approximately 852 in this example.

This approach makes it practical to figure out how many individual atoms are present in large quantities that are otherwise too small to visualize directly.