Question

a penny has a mass of 2.50 g and the moon has a mass of 7.35×10²² kg. use this information to answer the question below. be sure your answers have the correct number of significant digits. how many moles of pennies have a mass equal to the mass of the moon?

Explanation:

Step1: Convert Moon's mass to grams

Since 1 kg = 1000 g, the mass of the Moon in grams is $m_{moon}=7.35\times 10^{22}\text{ kg}\times1000\text{ g/kg}=7.35\times 10^{25}\text{ g}$.

Step2: Find number of pennies

The number of pennies $n$ with mass equal to the Moon's mass is $n=\frac{m_{moon}}{m_{penny}}$, where $m_{penny} = 2.50\text{ g}$. So $n=\frac{7.35\times 10^{25}\text{ g}}{2.50\text{ g}}=2.94\times 10^{25}$ pennies.

Step3: Convert number of pennies to moles

1 mole = $6.022\times 10^{23}$ entities. Let the number of moles of pennies be $N$. Then $N=\frac{n}{6.022\times 10^{23}}=\frac{2.94\times 10^{25}}{6.022\times 10^{23}}$.
Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, we have $N=\frac{2.94}{6.022}\times10^{25 - 23}\approx0.488\times 10^{2}=4.88\times 10^{1}$.

Answer:

$4.88\times 10^{1}$