# Question 2d08d

Aug 22, 2017

$\text{2.081 moles}$

#### Explanation:

The key here is the definition of the mole because if you know how many particles are needed to have exactly $1$ mole of ammonia, you can use the number of particles present in your sample to calculate how many moles it contains.

You should know that the definition of the mole is given by Avogadro's constant, which tells you the number of particles needed to have exactly $1$ mole of a given substance.

In your case, in order to have $1$ mole of ammonia, you need to have $6.022 \cdot {10}^{23}$ molecules of ammonia.

${\text{1 mole NH"_3 " " stackrel(color(white)(acolor(blue)("Avogadro's constant")aaaa))(->) " " 6.022 * 10^(23)color(white)(.)"molecules NH}}_{3}$

Now, to calculate the number of moles present in your sample, set up Avogadro's constant as a conversion factor that has the number of molecules in the denominator and $1$ mole in the numerator.

You will end up with

1.253 * 10^(24) color(red)(cancel(color(black)("molecules NH"_3))) * "1 mole NH"_3/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules NH"_3))))#

$= \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{2.081 moles NH}}_{3}}}}$

The answer is rounded to four sig figs, the number of sig figs you have for the number of molecules of ammonia present in your sample.