[tex]\boxed{\nu=\frac{m}{M}=\frac{V}{V_m}=\frac{n}{N_A}}\\M_{CO_2}=12+16\cdot2=12+32=44\ g/mol;\\V_m=22,42\ l/mol;\\N_A=6,02\cdot10^{23}\ mol^{-1};\\a)\ V_{CO_2}=1\ m^3=1\ 000\ l;\\\Rightarrow n_{CO_2}=\frac{V_{CO_2}\cdot N_A}{V_m}=\frac{1\ 000\ l\cdot6,02\cdot10^{23}\ mol^{-1}}{22,42\ l/mol}\\\Rightarrow \bold{n_{CO_2}=2,685\cdot10^{25}\ molecule};[/tex]
[tex]b)\ m_{CO_2}=1\ kg=1\ 000\ g\\\Rightarrow n_{CO_2}=\frac{m_{CO_2}\cdot N_A}{M_{CO_2}}=\frac{1\ 000\ g \cdot6,02\cdot10^{23}\ mol^{-1}}{44\ g/mol} \\ \Rightarrow \bold{n_{CO_2}=1,368\cdot 10^{25} \ molecule};[/tex]
[tex]c)\ n_{CO_2}=1\ molecul\u{a} \\ \Rightarrow \ m_{CO_2}=\frac{M_{CO_2} \cdot n_{CO_2}}{N_A}=\frac{44 \ g/mol \cdot 1 \ molecul\u{a}}{6,02 \cdot 10^{23} \ mol^{-1}} \\ \Rightarrow \bold{m_{CO_2}=7,3 \cdot 10^{-23}\ g};[/tex]
[tex]d)\ \rho_{CO_2}=\frac{m1_{CO_2}}{V1_{CO_2}} \\ V1_{CO_2} \to pentru \ n1_{CO_2}=1 \ molecul\u{a}; \\ V1_{CO_2}=\frac{V_m \cdot n1_{CO_2}}{N_A}=\frac{22,42\ l/mol \cdot 1 \ molecul\u{a}}{6,02 \cdot 10^{23} \ mol^{-1}} \\ \Rightarrow V1_{CO_2}=3,72 \cdot 10^{-23} \ l; \\ \Rightarrow \rho_{CO_2}=\frac{7,3 \cdot 10^{-23} \ g}{3,72 \cdot 10^{-23} \ l}=\frac{7,3}{3,72} \ g/l; \\ \Rightarrow \bold{\rho_{CO_2}=1,96 \ g/dm^3;}[/tex]
Răspuns:
a)
1 mol de gaz - in conditii normale - contine Numarul lui Avogadro NA de molecule
1 mol = 6,022 x 10 ²³ molecule
1 mol de gaz ocupa 22,4 litri
1 m³ = 1000 litri = 1000 : 22,4 mol = 44,64 mol
numarul de molecule = 44,64 x 6,022 x10²³ = 2,688 x 10²⁵ molecule
b) 1 mol CO₂ = 12 + 16 + 16 = 44 g
intr-un kg sunt 1000 : 44 = 22,72 mol
nr molecule = 22,72 x 6,022 x 10²³ = 1,3686 x 10 ²⁵ molecule
c)
masa unei molecule = masa C + masa O₂ = (12 + 32) x uma
uma = unitate atomica de masa = 1,66 x 10⁻²⁷ kg
masa moleculei CO₂ = 44 x 1,66 x 10⁻²⁷ kg = 7,304 x 10⁻²⁶ kg
d)
densitatea = masa : volum
masa 1 mol = 44 g
volum molar = 22,4 l = 0,0224 m³
densitate = 1,96 kg /m³
