Question

If we assume that there are \(7.0\) billion people on the Earth, how many moles of people is this?

Short answer

1.16 \times 10^{-14} moles

Step-by-step solution

- Understand the Problem

We need to convert the population of the Earth from people to moles. This involves using Avogadro's number, which is the number of entities (atoms, molecules, etc.) in one mole.

- Convert People to Moles Using Avogadro's Number

Avogadro's number is approximately \(\text{6.022} \times \text{10}^{23}\) entities per mole. Since we have \(7.0 \text{ billion} = \text{7.0} \times \text{10}^{9}\) people, we can use the conversion: \[ \text{Number of moles} = \frac{\text{Number of People}}{\text{Avogadro's Number}} \] Here, the calculation is: \[ \text{Number of moles} = \frac{7.0 \times 10^{9}}{6.022 \times 10^{23}} \]

- Perform the Calculation

Perform the division to find the number of moles: \[ \text{Number of moles} = \frac{7.0 \times 10^{9}}{6.022 \times 10^{23}} \]

- Simplify the Result

Simplify the result obtained from the division to get the final answer: \[ \text{Number of moles} \approx 1.16 \times 10^{-14} \]

Key concepts

Avogadro's Number

Avogadro's number is a fundamental constant used in chemistry to quantify the number of entities in a mole. Named after the scientist Amedeo Avogadro, this number is approximately \(6.022 \times 10^{23}\). It's used to express quantities of atoms, molecules, ions, or even people when comparing at the molecular level.
For instance, one mole of any substance contains exactly \(6.022 \times 10^{23}\) of its elementary entities, whether particles, atoms, or molecules. This large number helps bridge the gap between the microscopic world of atoms and molecules and the macroscopic quantities we can observe and measure.
Understanding Avogadro's number allows us to calculate and relate quantities in chemistry and physics more effectively. In the given exercise, converting billions of people into moles offers a practical example of applying Avogadro's number in real life!

Mole Concept

The mole is a central concept in chemistry that measures the amount of substance. One mole is defined as the number of atoms in 12 grams of pure carbon-12, which equates to \(6.022 \times 10^{23}\) atoms. This provides a bridge between the atomic and macroscopic worlds.
In simpler terms, a mole allows scientists to count particles by weighing them. This is essential because counting individual atoms or molecules directly is practically impossible due to their incredibly small size.
By using moles, conversions between mass, volume, and the number of particles become straightforward. For example, in the exercise above, converting the Earth's population into moles facilitates understanding the scale of the number of people relative to atomic quantities. The mole concept isn't limited to chemistry; it is applicable in various fields where large quantities of small entities are involved.

Scientific Notation

Scientific notation is a way of expressing very large or very small numbers more compactly. When dealing with numbers like Avogadro's number, which has 24 digits, scientific notation helps make the calculations manageable and less error-prone.
Any number in scientific notation is written as the product of a coefficient (between 1 and 10) and a power of 10. For example, \7.0 \times 10^{9}\ represents 7 billion, and \6.022 \times 10^{23}\ represents Avogadro's number.
In the exercise, we use scientific notation to convert 7 billion people into moles. First, we convert 7 billion to \(7.0 \times 10^{9}\). Then, we divide this number by Avogadro's number, \(6.022 \times 10^{23}\). The resulting fraction is simplified to \( \approx 1.16 \times 10^{-14}\) moles. Using scientific notation simplifies these operations, making them easier to perform and understand.