Answer to Question #140926 in General Chemistry for Kaleigh

Question

How many years would it take you to count and Avogadro’s number of objects if you could count at the rate of five objects per second?

Answer 1

Avogadro's number is $6.022 \times 10^{23}$

So the number of objects you want to count is $6.022 \times 10^{23}$

If you count them at a rate of 5 objects per second, it'd take;

$\dfrac{6.02 \times 10^{23} \textsf{ objects}}{5 \textsf{ objects per second}}$

$=1.2046 × 10^{23}\, s$

$1 \textsf{ year} = 60 \textsf{ seconds per minute} × 60 \textsf{ minutes per hour} × 24 \textsf{ hours per day} × 365 \textsf{ days per year}\\ =31536000 \textsf{ seconds}\\ =3.1536 × 10^7 \textsf{ seconds}$

$\therefore \textsf{number of years} = \dfrac{1.2046 × 10^{23}\, s}{3.1536 × 10^7 \textsf{ seconds per year}}$

$= 3.82 × 10^{15} \textsf{ years}$

$= 382,000,000,000,000 \textsf{ years}$

$= 382,000,000,000,000 \textsf{ trillion years}$