AP Chemistry - Using Avogadro's Number

How many moles of carbon are in a sample of $25.125*10^{27}$ atoms?

$4.17*10^{4} mol$

$4.17*10^{3} mol$

$1.51*10^{4} mol$

$1.51*10^{6} mol$

Explanation

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

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

What is the mass of $5.34\times10^{15}$ particles of $C_2H_6$ ?

$2.66\times 10^{-7}g\hspace{1 mm}C_2H_6$

$6.02\times 10^{-7}g\hspace{1 mm}C_2H_6$

$2.66\times 10^{-15}\hspace{1 mm}g\hspace{1 mm}C_2H_6$

$1.78\times 10^{-7}\hspace{1 mm}g\hspace{1 mm}C_2H_6$

$1.78\times 10^{-15}\hspace{1 mm}g\hspace{1 mm}C_2H_6$

Explanation

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

A container has $4.33\times 10^{24}$ molecules of gas in it. How many moles of the gas are in the container?

moles

Not enough information to solve the problem.

Explanation

Avogadro's number tells us how many molecules of gas are in one mole of the container. We are essentially doing a unit conversion from "number of molecules" to moles -

$4.33\times 10^{24} molecules\left ( \frac{1 mole}{6.022\times 10^{23} molecules} \right )=7.19 moles$

How many atoms are in $\small 50g$ of calcium?

$7.5*10^{23} atoms$

$3.0*10^{25}atoms$

$6.0*10^{23}atoms$

$5.0*10^{24} atoms$

Explanation

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 $\small 40.08$ grams per mole.

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

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

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

Determine the number of sodium atoms in a block of sodium chloride.

$1.55*10^{24}atoms$

$2.05*10^{24}atoms$

$2.27*10^{24}atoms$

Explanation

Use dimensional analysis:

$150gNaCl*\frac{1molNaCl}{58.44gNaCl}*\frac{1 mol Na}{1 mol NaCl}*\frac{6.02*10^{23}atoms}{1 mol}=1.55*10^{24}atoms$

How many hydrogen atoms are present in 500 mL of water at room temperature?

$\rho_{\text{water}}=1\frac{g}{mL}$

$3.35*10^{25}\ \text{atoms}$

$1.67*10^{25}\ \text{atoms}$

$5.96*10^{26}\ \text{atoms}$

$5.01*10^{25}\ \text{atoms}$

Explanation

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.

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

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

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

Finally, multiply by Avogadro's number.

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

How many atoms are there in 47.5g of boron?

$2.65*10^{24} \text{atoms}$

$5.15*10^{24} \text{atoms}$

$2.65*10^{23} \text{atoms}$

$3.65*10^{22} \text{atoms}$

Explanation

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

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

How many atoms of sodium are in three moles of $Na_{2}S$ ?

$3.61*10^{24} \text{atoms Na}$

$3.61*10^{22} \text{atoms Na}$

$1.31*10^{24} \text{atoms Na}$

$3.61*10^{26} \text{atoms Na}$

Explanation

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.

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

How many molecules are in ?

$3.13\cdot10^{24}\text{molecules}$

$3.13\cdot10^{22}\text{molecules}$

$5.14\cdot10^{24}\text{molecules}$

$6.02\cdot10^{23}\text{molecules}$

None of these

Explanation

According to Avogadro's law, each mole of a compound contains $6.02\cdot10^{23}\text{molecules}$ . Use dimensional analysis to find the number of molecules in .

$5.2mol: KCl\cdot \frac{6.02\cdot 10^{23}\text{molecules}}{1mol}=3.13\cdot10^{24}\text{molecules}$

A chemist has $4.37*10^{-3}g$ of $CH_3CH_2OH$ .

How many molecules of $CH_3CH_2OH$ does she have?

$5.72*10^{19}$

$9.50*10^{19}$

$5.72*10^{18}$

$5.73*10^{19}$

$4.73*10^{19}$

Explanation

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

Using Avogadro's Number

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