Question

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1. calculate the molar mass for the following compounds.

a. aluminum chloride
b. iron (iii) carbonate

1. convert 20.80g of lithium nitrate to moles.
2. convert 7.00g of na₂s to molecules.
3. what is the mass of 8.33x10²⁴ water molecules?
4. how many chlorine atoms are in 42.5g of sulfur hexachloride?
5. what is the percent mass of oxygen in na₂co₃?

Explanation:

1a. Calculate molar mass of aluminum chloride ($AlCl_3$)

Step1: Identify atomic masses

Atomic mass of $Al = 26.98\ g/mol$, atomic mass of $Cl= 35.45\ g/mol$.

Step2: Calculate molar mass

$M(AlCl_3)=26.98 + 3\times35.45=26.98 + 106.35 = 133.33\ g/mol$

1b. Calculate molar mass of iron(III) carbonate ($Fe_2(CO_3)_3$)

Step1: Identify atomic masses

Atomic mass of $Fe = 55.85\ g/mol$, atomic mass of $C = 12.01\ g/mol$, atomic mass of $O = 16.00\ g/mol$.

Step2: Calculate molar mass

$M(Fe_2(CO_3)_3)=2\times55.85+3\times(12.01 + 3\times16.00)=111.7+3\times(12.01 + 48.00)=111.7+3\times60.01=111.7 + 180.03=291.73\ g/mol$

2. Convert 20.80 g of lithium nitrate ($LiNO_3$) to moles

Step1: Calculate molar mass of $LiNO_3$

Atomic mass of $Li = 6.94\ g/mol$, atomic mass of $N = 14.01\ g/mol$, atomic mass of $O = 16.00\ g/mol$. $M(LiNO_3)=6.94+14.01 + 3\times16.00=6.94+14.01+48.00 = 68.95\ g/mol$.

Step2: Calculate moles

$n=\frac{m}{M}=\frac{20.80\ g}{68.95\ g/mol}\approx0.302\ mol$

3. Convert 7.00 g of $Na_2S$ to molecules

Step1: Calculate molar mass of $Na_2S$

Atomic mass of $Na = 22.99\ g/mol$, atomic mass of $S = 32.07\ g/mol$. $M(Na_2S)=2\times22.99+32.07=45.98 + 32.07=78.05\ g/mol$.

Step2: Calculate moles

$n=\frac{m}{M}=\frac{7.00\ g}{78.05\ g/mol}\approx0.0897\ mol$.

Step3: Calculate number of molecules

Number of molecules $N=n\times N_A$, where $N_A = 6.022\times10^{23}\ mol^{-1}$. $N = 0.0897\ mol\times6.022\times10^{23}\ mol^{-1}\approx5.30\times10^{22}$ molecules.

4. What is the mass of $8.33\times 10^{24}$ water molecules?

Step1: Calculate moles

$n=\frac{N}{N_A}=\frac{8.33\times 10^{24}}{6.022\times10^{23}\ mol^{-1}}\approx13.83\ mol$.

Step2: Calculate molar mass of water ($H_2O$)

Atomic mass of $H = 1.01\ g/mol$, atomic mass of $O = 16.00\ g/mol$. $M(H_2O)=2\times1.01+16.00 = 18.02\ g/mol$.

Step3: Calculate mass

$m=n\times M=13.83\ mol\times18.02\ g/mol\approx249\ g$

5. How many chlorine atoms are in 42.5 g of sulfur hexachloride ($SCl_6$)

Step1: Calculate molar mass of $SCl_6$

Atomic mass of $S = 32.07\ g/mol$, atomic mass of $Cl = 35.45\ g/mol$. $M(SCl_6)=32.07+6\times35.45=32.07 + 212.7=244.77\ g/mol$.

Step2: Calculate moles of $SCl_6$

$n=\frac{m}{M}=\frac{42.5\ g}{244.77\ g/mol}\approx0.1736\ mol$.

Step3: Calculate moles of $Cl$ atoms

In 1 mole of $SCl_6$, there are 6 moles of $Cl$ atoms. So moles of $Cl$ atoms in 0.1736 mol of $SCl_6$ is $n_{Cl}=6\times0.1736\ mol = 1.0416\ mol$.

Step4: Calculate number of $Cl$ atoms

$N_{Cl}=n_{Cl}\times N_A=1.0416\ mol\times6.022\times10^{23}\ mol^{-1}\approx6.27\times10^{23}$ atoms.

6. What is the percent mass of oxygen in $Na_2CO_3$

Step1: Calculate molar mass of $Na_2CO_3$

Atomic mass of $Na = 22.99\ g/mol$, atomic mass of $C = 12.01\ g/mol$, atomic mass of $O = 16.00\ g/mol$. $M(Na_2CO_3)=2\times22.99+12.01+3\times16.00=45.98+12.01 + 48.00=105.99\ g/mol$.

Step2: Calculate mass of oxygen in 1 mole of $Na_2CO_3$

Mass of oxygen in 1 mole of $Na_2CO_3$ is $m_O=3\times16.00\ g = 48.00\ g$.

Step3: Calculate percent mass of oxygen

$\text{Percent mass of }O=\frac{m_O}{M(Na_2CO_3)}\times100\%=\frac{48.00\ g}{105.99\ g}\times100\%\approx45.3\%$

Answer:

1a. $133.33\ g/mol$
1b. $291.73\ g/mol$

1. $0.302\ mol$
2. $\approx5.30\times10^{22}$ molecules
3. $\approx249\ g$
4. $\approx6.27\times10^{23}$ atoms
5. $\approx45.3\%$