# 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?

##### 2 Answers

#### Explanation:

For starters, you should know that in order to have **mole** of dime coins, you need to have **dime coins**.

#color(blue)(ul(color(black)("1 mole of dime coins" = 6.022 * 10^(23)color(white)(.)"dime coins"))) -># 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 **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 **equal** to the mass of **mole** of dime coins will be

#1.373 * 10^(19) color(red)(cancel(color(black)("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**.

#### Explanation: