# The average mass of a dime coin is "2.28 g" and the mass of an automobile is 2.0 * 10^3 "kg". What is the number of automobiles whose total mass is the same as 1.0 mole of dimes?

Aug 20, 2017

$6.9 \cdot {10}^{17}$

#### Explanation:

For starters, you should know that in order to have $1$ mole of dime coins, you need to have $6.022 \cdot {10}^{23}$ dime coins.

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{1 mole of dime coins" = 6.022 * 10^(23)color(white)(.)"dime coins}}}} \to$ Avogadro's constant

Now, you know that the mass of single dime coin is equal to

2.28 color(red)(cancel(color(black)("g"))) * "1 kg"/(10^3color(red)(cancel(color(black)("g")))) = 2.28 * 10^(-3)color(white)(.)"kg"

Use the mass of a single dime coin to calculate the mass of $1.0$ mole of dime coins

6.022 * 10^(23)color(red)(cancel(color(black)("dime coins"))) * (2.28 * 10^(-3)color(white)(.)"kg")/(1color(red)(cancel(color(black)("dime coin")))) = 1.373 * 10^(19)color(white)(.)"kg"

The mass of an automobile is equal to $2.0 \cdot {10}^{3}$ $\text{kg}$, so you can say that the number of automobiles that will be equal to the mass of $1.0$ mole of dime coins will be

$1.373 \cdot {10}^{19} \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{kg"))) * "1 automobile"/(2.0 * 10^3 color(red)(cancel(color(black)("kg")))) = color(darkgreen)(ul(color(black)(6.9 * 10^(17)color(white)(.)"automobiles}}}}$

The answer is rounded to two sig figs.

Aug 20, 2017

$6.86 \times {10}^{17}$ cars

#### Explanation:

$2.28 \frac{g r a m s}{u n i t} \cdot 6.022 x {10}^{23}$ units/mole$= 13.7 \times {10}^{23}$ grams/mole
$2.0 \times {10}^{3} k g \cdot 1000 \frac{g}{\text{kg}} = 2.0 \times {10}^{6} \frac{g}{c a r}$
$\frac{13.7 \times {10}^{23}}{2.0 \times {10}^{6}} = 6.86 \times {10}^{17}$ cars