Final answer:
To count all the atoms in a single grain of sand, we compare the number of atoms in a grain of sand to Avogadro's number (6.022 x 10^23), and then relate this to the time it would take to count to 1 trillion. Given the number of atoms likely in a single grain of sand, the number of years needed for such a count is unfathomably large, underscoring the impracticality of counting atoms directly.
Step-by-step explanation:
The question asks how many times you would have to count to 1 trillion to count all the atoms in a single grain of sand. To find the answer, we need to know the number of atoms in a single grain of sand and then see how that relates to the number 1 trillion, the figure given for a frame of reference. A mole is a unit in chemistry that represents Avogadro's number, which is approximately 6.022 × 1023 atoms. This vast number represents the number of atoms in 12 grams of carbon-12, which is a common example used to illustrate the scale of a mole.
A single grain of sand is considerably less than 12 grams, but for the sake of simplicity, let's consider that if a mole of carbon atoms can fill a cube 1.74 cm on each side, a similar amount of sand would have a comparable number of atoms. If one grain of sand has approximately 1 mg of oxygen and considering that sand is mostly made of SiO2, it contains a significant number of silicon and oxygen atoms together. If we assume we have around 6.022 × 1023 atoms in a mole, and a grain of sand is about a thousandth of this (since 1 mg is a thousandth of a gram and we're approximating to oxygen's molar mass), we would have roughly 6.022 × 1020 oxygen atoms in 1 mg of oxygen.
If it would take 31,800 years to count to 1 trillion, and there are 6.022 × 1012 trillions in 6.022 × 1020, it would take 31,800 years × 6.022 × 1012 to count all the atoms in a single grain of sand. This results in an incomprehensibly large number of years, so much so that it reinforces the concept that physically counting atoms is impossible and how astronomically large Avogadro's number is in practical terms.