Question

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?

Answer 1

`6.9 * 10^(17)`

Explanation:

For starters, you should know that in order to have `1` mole of dime coins, you need to have `6.022 * 10^(23)` 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 `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 * 10^3` `"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 * 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.

Answer 2

`6.86 xx 10^17` cars

Explanation:

`2.28 (grams)/(unit) * 6.022 x 10^23` units/mole`= 13.7 xx 10^23` grams/mole
`2.0 xx 10^3 kg * 1000g/"kg" = 2.0 xx 10^6 g/(car)`
`(13.7 xx 10^23)/(2.0 xx 10^6) = 6.86 xx 10^17` cars