Question

answer the following questions.

1. how many molecules are present in 200 grams of ccl₄?
2. how much does 4.5 x 10²² molecules of ba(no₃)₂ weigh?
3. how many molecules are there in 9.34 grams of licl?
4. how many molecules are present in 450 grams of na₂so₄?
5. how many molecules are present in 2.3 grams of nh₄so₂?
6. how many grams do 4.3 x 10²¹ molecules of uf₆ weigh?
7. how many molecules are there in 230 grams of nh₄oh?
8. how many molecules are present in 230 grams of cocl₂?
9. how many grams do 9.4 x 10²⁵ molecules of h₂ weigh?
10. how many grams do 7.5 x 10²³ molecules of h₂so₄ weigh?

Explanation:

Step1: Recall molar - mass and Avogadro's number

The molar mass ($M$) of a compound is the sum of the atomic masses of its constituent atoms. Avogadro's number ($N_A = 6.022\times10^{23}\text{ molecules/mol}$). The number of moles ($n$) is calculated by $n=\frac{m}{M}$, and the number of molecules ($N$) is $N = n\times N_A$. To find the mass ($m$) given the number of molecules, first find the number of moles $n=\frac{N}{N_A}$ and then $m=n\times M$.

Question 1

The molar mass of $CCl_4$:
- Atomic masses: $C = 12.01\text{ g/mol}$, $Cl=35.45\text{ g/mol}$.
- $M_{CCl_4}=12.01 + 4\times35.45=12.01+141.8 = 153.81\text{ g/mol}$
- The number of moles $n=\frac{m}{M}=\frac{200\text{ g}}{153.81\text{ g/mol}}\approx1.30\text{ mol}$
- The number of molecules $N=n\times N_A=1.30\text{ mol}\times6.022\times10^{23}\text{ molecules/mol}\approx7.83\times 10^{23}\text{ molecules}$

Question 2

The molar mass of $Ba(NO_3)_2$:
- Atomic masses: $Ba = 137.33\text{ g/mol}$, $N = 14.01\text{ g/mol}$, $O = 16.00\text{ g/mol}$
- $M_{Ba(NO_3)_2}=137.33+2\times(14.01 + 3\times16.00)=137.33+2\times(14.01 + 48.00)=137.33 + 2\times62.01=137.33+124.02 = 261.35\text{ g/mol}$
- The number of moles $n=\frac{N}{N_A}=\frac{4.5\times 10^{22}\text{ molecules}}{6.022\times10^{23}\text{ molecules/mol}}\approx0.075\text{ mol}$
- The mass $m=n\times M=0.075\text{ mol}\times261.35\text{ g/mol}\approx19.6\text{ g}$

Question 3

The molar mass of $LiCl$:
- Atomic masses: $Li = 6.94\text{ g/mol}$, $Cl = 35.45\text{ g/mol}$
- $M_{LiCl}=6.94 + 35.45=42.39\text{ g/mol}$
- The number of moles $n=\frac{m}{M}=\frac{9.34\text{ g}}{42.39\text{ g/mol}}\approx0.22\text{ mol}$
- The number of molecules $N=n\times N_A=0.22\text{ mol}\times6.022\times10^{23}\text{ molecules/mol}\approx1.32\times 10^{23}\text{ molecules}$

Question 4

The molar mass of $Na_2SO_4$:
- Atomic masses: $Na = 22.99\text{ g/mol}$, $S = 32.07\text{ g/mol}$, $O = 16.00\text{ g/mol}$
- $M_{Na_2SO_4}=2\times22.99+32.07 + 4\times16.00=45.98+32.07+64.00 = 142.05\text{ g/mol}$
- The number of moles $n=\frac{m}{M}=\frac{450\text{ g}}{142.05\text{ g/mol}}\approx3.17\text{ mol}$
- The number of molecules $N=n\times N_A=3.17\text{ mol}\times6.022\times10^{23}\text{ molecules/mol}\approx1.91\times 10^{24}\text{ molecules}$

Question 5

The molar mass of $NH_4SO_2$ is not a common compound. Assuming it is a mis - write and you mean $(NH_4)_2SO_4$:
- Atomic masses: $N = 14.01\text{ g/mol}$, $H = 1.01\text{ g/mol}$, $S = 32.07\text{ g/mol}$, $O = 16.00\text{ g/mol}$
- $M_{(NH_4)_2SO_4}=2\times(14.01 + 4\times1.01)+32.07+4\times16.00=2\times(14.01 + 4.04)+32.07 + 64.00=2\times18.05+32.07+64.00=36.10+32.07+64.00 = 132.17\text{ g/mol}$
- The number of moles $n=\frac{m}{M}=\frac{2.3\text{ g}}{132.17\text{ g/mol}}\approx0.0174\text{ mol}$
- The number of molecules $N=n\times N_A=0.0174\text{ mol}\times6.022\times10^{23}\text{ molecules/mol}\approx1.05\times 10^{22}\text{ molecules}$

Question 6

The molar mass of $UF_6$:
- Atomic masses: $U = 238.03\text{ g/mol}$, $F = 19.00\text{ g/mol}$
- $M_{UF_6}=238.03+6\times19.00=238.03 + 114.00=352.03\text{ g/mol}$
- The number of moles $n=\frac{N}{N_A}=\frac{4.3\times 10^{21}\text{ molecules}}{6.022\times10^{23}\text{ molecules/mol}}\approx0.00714\text{ mol}$
- The mass $m=n\times M=0.00714\text{ mol}\times352.03\text{ g/mol}\approx2.51\text{ g}$

Question 7

The molar mass of $NH_4OH$:
- Atomic masses: $N = 14.01\text{ g/mol}$, $H = 1.01\text{ g/mol}$, $O = 16.00\text{ g/mol}$
- $M_{NH_4OH}=14.01+5\times1.01 + 16.00=14.01+5.05+16.00 = 35.06\text{ g/mol}$
- The number of moles $n=\frac{m}{M}=\frac{230\text{ g}}{35.06\text{ g/mol}}\approx6.56\text{ mol}$
- The number of molecules $N=n\times N_A=6.56\text{ mol}\times6.022\times10^{23}\text{ molecules/mol}\approx3.95\times 10^{24}\text{ molecules}$

Question 8

The molar mass of $CoCl_2$:
- Atomic masses: $Co = 58.93\text{ g/mol}$, $Cl = 35.45\text{ g/mol}$
- $M_{CoCl_2}=58.93+2\times35.45=58.93 + 70.90=129.83\text{ g/mol}$
- The number of moles $n=\frac{m}{M}=\frac{230\text{ g}}{129.83\text{ g/mol}}\approx1.77\text{ mol}$
- The number of molecules $N=n\times N_A=1.77\text{ mol}\times6.022\times10^{23}\text{ molecules/mol}\approx1.06\times 10^{24}\text{ molecules}$

Question 9

The molar mass of $H_2$: $M_{H_2}=2\times1.01\text{ g/mol}=2.02\text{ g/mol}$
- The number of moles $n=\frac{N}{N_A}=\frac{9.4\times 10^{25}\text{ molecules}}{6.022\times10^{23}\text{ molecules/mol}}\approx156\text{ mol}$
- The mass $m=n\times M=156\text{ mol}\times2.02\text{ g/mol}\approx315\text{ g}$

Question 10

The molar mass of $H_2SO_4$:
- Atomic masses: $H = 1.01\text{ g/mol}$, $S = 32.07\text{ g/mol}$, $O = 16.00\text{ g/mol}$
- $M_{H_2SO_4}=2\times1.01+32.07+4\times16.00=2.02+32.07+64.00 = 98.09\text{ g/mol}$
- The number of moles $n=\frac{N}{N_A}=\frac{7.5\times 10^{23}\text{ molecules}}{6.022\times10^{23}\text{ molecules/mol}}\approx1.25\text{ mol}$
- The mass $m=n\times M=1.25\text{ mol}\times98.09\text{ g/mol}\approx123\text{ g}$

Answer:

1. Approximately $7.83\times 10^{23}$ molecules
2. Approximately $19.6$ g
3. Approximately $1.32\times 10^{23}$ molecules
4. Approximately $1.91\times 10^{24}$ molecules
5. Approximately $1.05\times 10^{22}$ molecules
6. Approximately $2.51$ g
7. Approximately $3.95\times 10^{24}$ molecules
8. Approximately $1.06\times 10^{24}$ molecules
9. Approximately $315$ g
10. Approximately $123$ g