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
Aug 20, 2017

Answer:

#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.

Aug 20, 2017

Answer:

# 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