Respuesta :
Answer:
See explanation.
Explanation:
Hello
(a) In this case, one uses the following formulas, which allow to compute the mass fraction of each component:[tex]\% O_2=\frac{m_{O_2}}{m_{O_2}+m_{N_2}+m_{CO_2}}*100\%=\frac{4kg}{4kg+5kg+7kg}*100\%=25\%O_2\\\% N_2=\frac{m_{N_2}}{m_{O_2}+m_{N_2}+m_{CO_2}}*100\%=\frac{5kg}{4kg+5kg+7kg}*100\%=31.25\%N_2\\\% CO_2=\frac{m_{CO_2}}{m_{O_2}+m_{N_2}+m_{CO_2}}*100\%=\frac{7kg}{4kg+5kg+7kg}*100\%=43.75\%CO_2[/tex]
(b) For the mole fractions, it is necessary to find all the components' moles by using their molar mass as shown below:
[tex]n_{O_2}=4kgO_2*\frac{1kmolO_2}{32kgO_2} =0.125kmolO_2\\n_{N_2}=5kgN_2*\frac{1kmolN_2}{28kgN_2} =0.179kmolN_2\\n_{CO_2}=7kgCO_2*\frac{1kmolCO_2}{44kgCO_2} =0.159kmolCO_2[/tex]
Now, the mole fractions:
[tex]x_{O_2}=\frac{n_{O_2}}{n_{O_2}+n_{N_2}+n_{CO_2}}*100\%=\frac{0.125kmolO_2}{0.125kmolO_2+0.179kmolN_2+0.159kmolCO_2}*100\%=27\%O_2\\x_{N_2}=\frac{n_{N_2}}{n_{O_2}+n_{N_2}+n_{CO_2}}*100\%=\frac{0.179kmolN_2}{0.125kmolO_2+0.179kmolN_2+0.159kmolCO_2}*100\%=38.7\%N_2\\ x_{CO_2}=\frac{n_{CO_2}}{n_{O_2}+n_{N_2}+n_{CO_2}}*100\%=\frac{0.159kmolCO_2}{0.125kmolO_2+0.179kmolN_2+0.159kmolCO_2}*100\%=34.3\%CO_2[/tex]
(c) Finally the average molar mass is computed considering the molar fractions and each component's molar mass:
[tex]M_{average}=0.27*32g/mol+0.387*28g/mol+0.343*44g/mol=34.57g/mol[/tex]
And the gas constant:
[tex]Rg=0.082\frac{atm*L}{mol*K}*\frac{1mol}{34.57g}=0.00237\frac{atm*L}{g*K}[/tex]
Best regards.
The mass fraction of the Oxygen, Nitrogen and Carbon dioxide is 25%, 31.25% and 43.75%.
(A)Mass fraction of components
[tex]\bold {Oxygen = \dfrac {m O_2 }{mN_2 +mH_2 +m CO_2} \times 100}\\\bold {Oxygen = \dfrac {4 }{4 + 7} \times 100}\\\\\bold {Oxygen = 25 \%}[/tex]
So, mass fraction of Nitrogen and Carbon dioxide can be calculated by this formula.
Mass fraction of Oxygen = 25%
Mass fraction of Nitrogen = 31.25%
Mass fraction of Carbon dioxide = 43.75%
(B) mole fraction of each component,
First calculate number of moles,
[tex]\bold {nO_2 = \dfrac {4000g}{32 g/mol} = 125\ moles}[/tex]
[tex]\bold {nN_2 = \dfrac {5000g}{28 g/mol} = 179\ moles}\\\bold {nCO_2 = \dfrac {7000g}{44 g/mol} = 159\ moles}\\[/tex]
Mole fraction of Oxygen,
[tex]\bold {xO_2 = \dfrac {nO_2}{nO_2 + nN_2+ nCO_2}\times 100}\\\bold {xO_2 = \dfrac {125}{125 + 179+ 159}\times 100}\\\\\bold {xO_2 = 27\%}[/tex]
[tex]\bold {xN_2 = 38.7\%}\\\\\bold {xCO_2 = 34.3\%}[/tex]
(C) The average molar mass of components
[tex]\bold {Mavr = 0.27 \times 32 + 0.387 \times 28 +0.343\times 44 = 34.57\ g /mol }[/tex]
The gas constant,
[tex]\bold {Rgas = 0.082 \times 34.57 = 0.00237 }[/tex]
Therefore, the gas constant of the gas is 0.00237.
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