Question

5.85×10^{23} atoms → grams

Explanation:

1. First, we need to know Avogadro's number ($N_A = 6.022\times10^{23}\text{ atoms/mol}$) and the molar - mass concept. But since the element is not specified, let's assume we are dealing with a general monatomic element for the sake of showing the process.

• Calculate the number of moles ($n$):
• The formula to calculate the number of moles from the number of atoms ($N$) is $n=\frac{N}{N_A}$.
• Given $N = 5.85\times10^{23}$ atoms and $N_A=6.022\times10^{23}\text{ atoms/mol}$, then $n=\frac{5.85\times10^{23}\text{ atoms}}{6.022\times10^{23}\text{ atoms/mol}}\approx0.971\text{ mol}$.
• Now, if we assume the element is, for example, carbon (with molar - mass $M = 12.01\text{ g/mol}$), we can calculate the mass ($m$) using the formula $m = n\times M$.
• Substituting $n = 0.971\text{ mol}$ and $M = 12.01\text{ g/mol}$, we get $m=0.971\text{ mol}\times12.01\text{ g/mol}\approx11.66\text{ g}$.
• In general, if the molar - mass of the element is $M$ (in g/mol), the mass $m$ in grams is $m=\frac{5.85\times10^{23}}{6.022\times10^{23}}\times M=\frac{5.85}{6.022}M$.

Step1: Calculate number of moles

$n=\frac{5.85\times10^{23}}{6.022\times10^{23}}\text{ mol}$

Step2: Calculate mass (assuming molar - mass }M\text{)

$m = n\times M=\frac{5.85\times10^{23}}{6.022\times10^{23}}\times M\text{ g}$

Answer:

If the molar - mass of the element is $M\text{ g/mol}$, the mass is $\frac{5.85}{6.022}M\text{ g}\approx0.971M\text{ g}$