Question

1. how much would a sample of 28.3 x 10^{24} atoms of carbon weigh in grams?

Explanation:

Step1: Calculate the number of moles

Use Avogadro's number \(N_A = 6.022\times10^{23}\text{ atoms/mol}\). The number of moles \(n\) of carbon is given by the formula \(n=\frac{N}{N_A}\), where \(N = 28.3\times 10^{24}\text{ atoms}\).

$$n=\frac{28.3\times 10^{24}}{6.022\times10^{23}}$$

$$n=\frac{28.3}{6.022}\times10$$

$$n\approx47.0\text{ mol}$$

Step2: Calculate the mass

The molar mass of carbon \(M = 12.01\text{ g/mol}\). Use the formula \(m=n\times M\).

$$m = 47.0\times12.01$$

$$m=564.47\text{ g}$$

Answer:

\(564.47\text{ g}\)