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 $m_{moon}=7.35\times 10^{22}\ kg\times1000\ g/kg = 7.35\times 10^{25}\ g$.

Step2: Calculate number of pennies

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

Step3: Calculate number of moles of pennies

One - mole of any substance contains $N_A = 6.022\times 10^{23}$ entities. The number of moles of pennies $N$ is $N=\frac{n}{N_A}=\frac{2.94\times 10^{25}}{6.022\times 10^{23}}$.
$N=\frac{2.94}{6.022}\times10^{25 - 23}\approx0.488\times 10^{2}=48.8\approx49$ (rounded to 2 significant digits as 2.50 has 3 significant digits and 7.35 has 3 significant digits).

Answer:

$49$