In order to determine how many atoms are in this sample, we need to convert this sample into moles. Calcium has a molar mass of $\displaystyle \small 40.08$ grams per mole.

$\displaystyle 50g\ Ca*\frac{1mol\ Ca}{40.08g\ Ca}=1.25mol\ Ca$

Avogadro's number tells us that there $\displaystyle 6.022*10^{23}$ atoms in one mole of any element. We can use this conversion to find the total number of atoms in the sample.

$\displaystyle 1.25 moles* \frac{6.022*10^{23}atoms}{1mol} = 7.5*10^{23} atoms$

To do this problem we have to first convert grams to moles, then moles to atoms using Avogadro's number:

$\displaystyle 47.5g*\frac{1mol\ B}{10.8g\ B}*\frac{6.022*10^{23}\ \text{atoms}}{1mol}=2.65*10^{24}\text{atoms}$

To solve, we need to convert atoms to moles using Avogadro's number:

$\displaystyle 25.125*10^{27}\text{atoms}*\frac{1mol}{6.022*10^{23}\text{atoms}}=4.17*10^4mol$

To answer this question, we have to find the number of moles of sodium in this compound. Note that there are two sodium atoms per molecule. Then, multiply the total moles of sodium by Avogadro's number.

$\displaystyle 3 mol\ Na_{2}S*\frac{2mol\ Na}{1 mol\ Na_{2}S}*\frac{6.022*10^{23}\text{atoms\ Na}}{1 mole\ Na}=3.61*10^{24}\text{atoms Na}$

The elemental charge is the magnitude of charge, in Coulombs, that each electron or proton has. Because electrons have a negative charge, don't forget to add a negative sign into the equation.

$\displaystyle q=-(\#\ of\ electrons)(e)$

$\displaystyle q= -(21000)(1.6\cdot 10^{-19})$

$\displaystyle q= -3.36\cdot 10^{-15}$

When you convert the answer to microcoulombs, the answer is $\displaystyle -3.36\cdot 10^{-9}\mu C$:

$\displaystyle -3.36\cdot 10^{-15} C\cdot\frac{1.0\cdot10^6 \mu C}{1 C}= -3.36\cdot 10^{-9}\mu C$

$\displaystyle 5.34\times10^{15}\hspace{1 mm}particles\hspace{1 mm}C_2H_6\times \frac{1\hspace{1 mm}mole\hspace{1 mm}C_2H_6}{6.022\times 10^{23}\hspace{1 mm}particles\hspace{1 mm} C_2H_6}\times \frac{30.0\hspace{1 mm}g\hspace{1 mm}C_2H_60=}{1\hspace{1 mm}mole\hspace{1 mm}C_2H_6}=2.66\times 10^{-7}g\hspace{1 mm}C_2H_6$

This question requires an understanding of what avogadro's number actually represents.  Avogadro's number, 6.022 * 10²³ is the number of things in one mole.  The question indicates that there is 1 mole of H₂.  Thus there are 6.022 * 10²³ molecules of H₂.  However the question is asking for the amount of atoms in 1 mole of H₂.  Thus we must consider the makeup of an H₂ molecule, where we see that it is a diatomic molecule.  Thus we must multiply 6.022 * 10²³ by 2 to calculate the number of individual atoms present in 1 mole of H₂.  We find our answer to be 1.2044 * 10²⁴.

$\displaystyle 4.37\times 10^{-3}g\hspace{1 mm}CH_3CH_2OH\times \frac{1\hspace{1 mm}mole\hspace{1 mm}CH_3CH_2OH}{46\hspace{1 mm}g\hspace{1 mm}CH_3CH_2OH}\times\frac{6.022\times 10^{23}\hspace{1 mm}molecules\hspace{1 mm} CH_3CH_2OH}{1\hspace{1 mm}mole\hspace{1 mm}CH_3CH_2OH}=5.72\times10^{19}\hspace{1 mm}molecules\hspace{1 mm}CH_3CH_2OH$

To determine the number of hydrogen atoms, divide the mass of ethanol by its molar mass to get moles of ethanol.

$\displaystyle MM=(12)+6(1)+(16)=34\frac{g}{mol}$

$\displaystyle 46.3g*\frac{1mol}{34g}=1.36mol\ CH_6O$

Multiply this by six atoms of hydrogen per molecule of ethanol and by Avogadro's number to get the number of hydrogen atoms.

$\displaystyle 1.36mol\ CH_6O*\frac{6mol\ H}{1mol\ CH_6O}=8.17mol\ H$

$\displaystyle 8.17mol\ H*\frac{6.022*10^{23}\text{atoms}}{1mol}=4.9*10^{24}\text{atoms}$

Use the density of water, the molar mass of water, and Avogadro's number to calculate the number of molecules of water.

We have 500mL of water. Use the density to convert this to grams; then use the molar mass of water to convert this to moles.

$\displaystyle 500mL*\frac{1g}{1mL}*\frac{1mol}{18g}=27.78mol\ H_2O$

There are two moles of hydrogen atoms per one mole of water.

$\displaystyle 27.78mol\ H_2O*\frac{2mol\ H}{1mol\ H_2O}=55.56mol\ H$

Finally, multiply by Avogadro's number.

$\displaystyle 55.56mol\ H*\frac{6.022*10^{23}\text{atoms}}{1mol}=3.35*10^{25}\text{atoms}$