Question

make the following conversions. show your work

1. convert 1.51 x 10²⁵ atoms si to moles

1. convert 4.25 x 10² moles of no₂ to molecules

1. convert 8.95 x 10²⁶ molecules of ccl₄ to moles

1. convert 5.90 moles of ca to atoms

Explanation:

Step1: Recall Avogadro's number

Avogadro's number \(N_A = 6.022\times 10^{23}\text{ atoms/mole}\) or \(6.022\times 10^{23}\text{ molecules/mole}\). The formula for converting number of atoms/molecules (\(N\)) to moles (\(n\)) is \(n=\frac{N}{N_A}\), and for converting moles to atoms/molecules is \(N = n\times N_A\).

Step2: Solve problem 7

Given \(N = 1.51\times 10^{25}\text{ atoms Si}\). Using \(n=\frac{N}{N_A}\), we substitute \(N = 1.51\times 10^{25}\) and \(N_A=6.022\times 10^{23}\).

$$n=\frac{1.51\times 10^{25}}{6.022\times 10^{23}}=\frac{1.51}{6.022}\times10^{25 - 23}\approx0.251\times 10^{2}=25.1\text{ moles}$$

Step3: Solve problem 8

Given \(n = 4.25\times 10^{2}\text{ moles NO}_2\). Using \(N=n\times N_A\), substitute \(n = 4.25\times 10^{2}\) and \(N_A = 6.022\times 10^{23}\).

$$N=(4.25\times 10^{2})\times(6.022\times 10^{23})=(4.25\times6.022)\times10^{2 + 23}\approx25.6\times 10^{25}=2.56\times 10^{26}\text{ molecules}$$

Step4: Solve problem 9

Given \(N = 8.95\times 10^{26}\text{ molecules CCl}_4\). Using \(n=\frac{N}{N_A}\), substitute \(N = 8.95\times 10^{26}\) and \(N_A=6.022\times 10^{23}\).

$$n=\frac{8.95\times 10^{26}}{6.022\times 10^{23}}=\frac{8.95}{6.022}\times10^{26-23}\approx1.49\times 10^{3}\text{ moles}$$

Step5: Solve problem 10

Given \(n = 5.90\text{ moles Ca}\). Using \(N=n\times N_A\), substitute \(n = 5.90\) and \(N_A = 6.022\times 10^{23}\).

$$N=(5.90)\times(6.022\times 10^{23})=(5.90\times6.022)\times10^{23}\approx35.5\times 10^{23}=3.55\times 10^{24}\text{ atoms}$$

Answer:

1. \(25.1\text{ moles}\)
2. \(2.56\times 10^{26}\text{ molecules}\)
3. \(1.49\times 10^{3}\text{ moles}\)
4. \(3.55\times 10^{24}\text{ atoms}\)