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Chapter 9: Problem 43

How many pennies are there in \(2.5\) moles of pennies? How many dollars does this equal? Answer both questions by using conversion factors, and show which units cancel.

Short Answer

Expert verified
There are \(1.505 \times 10^{24}\) pennies in 2.5 moles of pennies, which is equal to \(1.505 \times 10^{22}\) dollars.

Step by step solution

01

Calculate the number of pennies in 2.5 moles using the definition of moles

To find the total number of pennies in 2.5 moles, we will multiply the number of moles (2.5) by the definition of a mole (\(6.022 \times 10^{23}\) pennies/mole): \[Number\:of\:pennies = (number\:of\:moles) \times (\frac{6.022 \times 10^{23}\:pennies}{1\:mole})\]
02

Substitute the given values and solve for the number of pennies

Now, we will plug in the given number of moles (2.5) into the equation: \[Number\:of\:pennies = (2.5\:moles) \times (\frac{6.022 \times 10^{23}\:pennies}{1\:mole})\] Notice that the "moles" unit cancels out, leaving us with the number of pennies: \[Number\:of\:pennies = 2.5 \times 6.022 \times 10^{23} pennies\] \[Number\:of\:pennies = 1.505 \times 10^{24} pennies\]
03

Convert pennies into dollars using the conversion factor

Now, we will use the conversion factor of 1 dollar equals 100 pennies to convert the total number of pennies into dollars: \[Number\:of\:dollars = (Number\:of\:pennies) \times (\frac{1\:dollar}{100\:pennies})\]
04

Substitute the calculated number of pennies and solve for the number of dollars

Plug in the value of the number of pennies we calculated earlier (1.505 x 10^24 pennies) into the equation: \[Number\:of\:dollars = (1.505 \times 10^{24}\:pennies) \times (\frac{1\:dollar}{100\:pennies})\] Notice that the "pennies" unit cancels out, leaving us with the number of dollars: \[Number\:of\:dollars = 1.505 \times 10^{24} \times \frac{1}{100}\:dollars\] \[Number\:of\:dollars = 1.505 \times 10^{22}\:dollars\] Thus, there are 1.505 x 10^24 pennies in 2.5 moles of pennies. This is equal to 1.505 x 10^22 dollars.

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