Question

a balloon contains 5.42x10^23 atoms of argon gas. calculate the mass in grams of ar.
a. 0.900 grams ar
b. 36.0 grams ar
c. 8.15x10^45 grams ar
d. 3.26x10^47 grams ar

Explanation:

Step1: Use Avogadro's number

Avogadro's number ($N_A = 6.022\times10^{23}\text{ atoms/mol}$) is used to convert atoms to moles. The number of moles ($n$) of argon is given by $n=\frac{N}{N_A}$, where $N = 5.42\times 10^{23}$ atoms. So, $n=\frac{5.42\times 10^{23}\text{ atoms}}{6.022\times10^{23}\text{ atoms/mol}}$.

Step2: Calculate the number of moles

$n=\frac{5.42\times 10^{23}}{6.022\times10^{23}}\text{ mol}\approx0.900\text{ mol}$.

Step3: Use molar - mass to find mass

The molar mass of argon ($M$) is $M = 39.95\text{ g/mol}$. The mass ($m$) of argon is given by the formula $m=n\times M$. Substituting $n = 0.900\text{ mol}$ and $M=39.95\text{ g/mol}$, we get $m = 0.900\text{ mol}\times39.95\text{ g/mol}\approx36.0\text{ g}$.

Answer:

B. 36.0 grams Ar