[tex]\displaystyle{ \nu = 2 \ moli }[/tex]
[tex]\displaystyle{ \mu = 28 \ kg/kmol = 28 \cdot 10^{-3} \ kg/mol }[/tex]
t₁ = 27°C ⇒ T₁ = 27 + 273 = 300 K
[tex]\displaystyle{ V = 10 \ l = 10 \cdot 10^{-3} \ m^{3} }[/tex]
[tex]\displaystyle{ p_{2} = 2 \cdot p_{1} }[/tex]
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a) [tex]\displaystyle{ \rho = ? }[/tex]
b) [tex]\displaystyle{ T_{2} = \ ? }[/tex]
c) [tex]\displaystyle{ \Delta N = \ ? \ (p_{2}=p_{1}) }[/tex]
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a)
[tex]\displaystyle{ \nu = \frac{m}{\mu}} \rightarrow m = \nu \cdot \mu }[/tex]
[tex]\displaystyle{ m = 2 \cdot 28 \cdot 10^{-3} = 56 \cdot 10^{-3} \ kg }[/tex]
[tex]\displaystyle{ \rho = \frac{m}{V} = \frac{56 \cdot 10^{-3}}{10 \cdot 10^{-3} }[/tex]
[tex]\displaystyle{ \rho = \frac{56}{10} = 5,6 \ kg/m^{3} }[/tex]
b)
[tex]\displaystyle{ \nu }[/tex] rămâne constant, V rămâne constant ⇒ transformare izocoră
[tex]\displaystyle{ \frac{p_{1}}{T_{1}} = \frac{p_{2}}{T_{2}} }[/tex]
[tex]\displaystyle{ p_{1} \cdot T_{2} = 2 \cdot p_{1} \cdot T_{1} }[/tex]
[tex]\displaystyle{ T_{2} = 2 \cdot T_{1} }[/tex]
[tex]\displaystyle{ T_{2} = 2 \cdot 300 }[/tex]
[tex]\displaystyle{ T_{2} = 600 \ K }[/tex]
c)
[tex]\displaystyle{ \nu = \frac{N}{N_{A}} \rightarrow p_{1} \cdot V = \frac{N}{N_{A}} \cdot R \cdot T }[/tex]
[tex]\displaystyle{ p_{2} \cdot V = \frac{N - \Delta N}{N_{A}} \cdot R \cdot 2T }[/tex]
[tex]\displaystyle{ p_{1} = p_{2} \rightarrow din \ cele \ doua \ relatii \rightarrow \Delta N = \frac{\nu \cdot N_{A}}{2} }[/tex]
[tex]\displaystyle{ \Delta N = N_{A} }[/tex]
[tex]\displaystyle{ \Delta N = 6,023 \cdot 10^{23} \ molecule }[/tex]
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Matei.
