Question

1. a balloon contains 4.50×10²¹ atoms of helium (he) gas. calculate the mass of helium in grams.

0.185 g
0.0185 g
0.0747 g
0.299 g
clear all

Explanation:

Step1: Recall Avogadro's number

Avogadro's number ($N_A$) is $6.022\times 10^{23}$ atoms/mol. First, find the number of moles ($n$) of helium. The formula for the number of moles is $n=\frac{N}{N_A}$, where $N$ is the number of atoms. Given $N = 4.50\times 10^{21}$ atoms.
$n=\frac{4.50\times 10^{21}}{6.022\times 10^{23}}$ mol

Step2: Calculate the number of moles

$n=\frac{4.50\times 10^{21}}{6.022\times 10^{23}}=\frac{4.50}{6.022}\times10^{21 - 23}\approx0.747\times 10^{- 2}$ mol $ = 7.47\times 10^{-3}$ mol

Step3: Use molar - mass of helium

The molar mass of helium ($M$) is approximately $4.00$ g/mol. The mass ($m$) of a substance is given by the formula $m = n\times M$.
$m=(7.47\times 10^{-3}\text{ mol})\times4.00\text{ g/mol}$

Step4: Calculate the mass

$m = 0.0299$ g

Answer:

$0.0299$ g