Question

avogadros number (6.02 x 10²³) was not discovered by him, but named in honor of him. it was dr avogadros original hypothesis about the volume of gas molecules that led to the development of the mole concept many years later. use your newfound molar repertoire to complete the following problems: 1) what is the mass of 5.7 l of nh₃ (g) at stp? 2) how many molecules are in 75.0 g of diphosphorus pentoxide? 3) what is the mass of 2.5 moles of cl₂ (g) at stp? 4) what volume is occupied by 55 g of methane, ch₄ (g) at stp? 5) how many atoms of neon gas would a container with a volume of 67.2 l hold at stp? 6) change 5.20 moles of c₃h₆o₂ to grams 7) change 13.2 g of fe(no₃)₃ to moles. 8) change 13.2 g of sn(co₃)₂ to moles. 9) how many molecules of ammonium chloride are in 54.5 g of ammonium chloride? q. what did avogadro teach his students in math class? a. mole/plicati

Explanation:

Step1: Recall molar - volume relationship at STP

At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 L.

Step2: Calculate moles of $NH_3$ in 5.7 L

$n=\frac{V}{V_m}$, where $V = 5.7$ L and $V_m=22.4$ L/mol. So, $n=\frac{5.7}{22.4}\text{ mol}\approx0.254$ mol.

Step3: Find molar mass of $NH_3$

The molar mass of $NH_3$ ($M$): $M = 14+3\times1=17$ g/mol.

Step4: Calculate mass of $NH_3$

$m = n\times M$. Substituting $n = 0.254$ mol and $M = 17$ g/mol, we get $m=0.254\times17\approx4.32$ g.

Step5: For question 2:

Find molar mass of $P_2O_5$
The molar mass of $P_2O_5$ ($M$): $M = 2\times31 + 5\times16=142$ g/mol.

Step6: Calculate moles of $P_2O_5$

$n=\frac{m}{M}$, where $m = 75.0$ g and $M = 142$ g/mol. So, $n=\frac{75.0}{142}\text{ mol}\approx0.528$ mol.

Step7: Calculate number of molecules

Using Avogadro's number $N_A = 6.02\times10^{23}$ molecules/mol, the number of molecules $N=n\times N_A$. So, $N = 0.528\times6.02\times10^{23}\approx3.18\times10^{23}$ molecules.

Step8: For question 3:

Find molar mass of $Cl_2$
The molar mass of $Cl_2$ ($M$): $M = 2\times35.5 = 71$ g/mol.

Step9: Calculate mass of $Cl_2$

$m=n\times M$, where $n = 2.5$ mol and $M = 71$ g/mol. So, $m=2.5\times71 = 177.5$ g.

Step10: For question 4:

Find molar mass of $CH_4$
The molar mass of $CH_4$ ($M$): $M = 12+4\times1=16$ g/mol.

Step11: Calculate moles of $CH_4$

$n=\frac{m}{M}$, where $m = 55$ g and $M = 16$ g/mol. So, $n=\frac{55}{16}\text{ mol}\approx3.44$ mol.

Step12: Calculate volume at STP

$V=n\times V_m$, where $V_m = 22.4$ L/mol. So, $V=3.44\times22.4\approx76.8$ L.

Step13: For question 5:

Calculate moles of Ne
$n=\frac{V}{V_m}$, where $V = 67.2$ L and $V_m=22.4$ L/mol. So, $n = 3$ mol.

Step14: Calculate number of atoms

Since Ne is a monatomic gas, the number of atoms $N=n\times N_A$. So, $N=3\times6.02\times10^{23}=1.806\times10^{24}$ atoms.

Step15: For question 6:

Find molar mass of $C_3H_6O_2$
$M=(3\times12)+(6\times1)+(2\times16)=74$ g/mol.

Step16: Calculate mass

$m=n\times M$, where $n = 5.20$ mol and $M = 74$ g/mol. So, $m=5.20\times74 = 384.8$ g.

Step17: For question 7:

Find molar mass of $Fe(NO_3)_3$
$M = 56+(3\times(14 + 3\times16))=242$ g/mol.

Step18: Calculate moles

$n=\frac{m}{M}$, where $m = 13.2$ g and $M = 242$ g/mol. So, $n=\frac{13.2}{242}\approx0.0545$ mol.

Step19: For question 8:

Find molar mass of $Sn(CO_3)_2$
$M=119+(2\times(12 + 3\times16))=238$ g/mol.

Step20: Calculate moles

$n=\frac{m}{M}$, where $m = 13.2$ g and $M = 238$ g/mol. So, $n=\frac{13.2}{238}\approx0.0555$ mol.

Step21: For question 9:

Find molar mass of $NH_4Cl$
$M = 14+4\times1+35.5 = 53.5$ g/mol.

Step22: Calculate moles of $NH_4Cl$

$n=\frac{m}{M}$, where $m = 54.5$ g and $M = 53.5$ g/mol. So, $n=\frac{54.5}{53.5}\text{ mol}\approx1.02$ mol.

Step23: Calculate number of molecules

$N=n\times N_A$, so $N = 1.02\times6.02\times10^{23}\approx6.14\times10^{23}$ molecules.

Answer:

1. Approximately $4.32$ g
2. $3.18\times10^{23}$ molecules
3. $177.5$ g
4. $76.8$ L
5. $1.806\times10^{24}$ atoms
6. $384.8$ g
7. Approximately $0.0545$ mol
8. Approximately $0.0555$ mol
9. Approximately $6.14\times10^{23}$ molecules