Respuesta :
Answer : The new density and new volume of carbon dioxide gas is 0.2281 g/L and [tex]7.2m^3[/tex] respectively.
Explanation :
First we have to calculate the new or final volume of carbon dioxide gas.
Combined gas law is the combination of Boyle's law, Charles's law and Gay-Lussac's law.
The combined gas equation is,
[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]
where,
[tex]P_1[/tex] = initial pressure of gas = 10 kPa
[tex]P_2[/tex] = final pressure of gas = 15 kPa
[tex]V_1[/tex] = initial volume of gas = [tex]10m^3[/tex]
[tex]V_2[/tex] = final volume of gas = ?
[tex]T_1[/tex] = initial temperature of gas = [tex]50^oC=273+50=323K[/tex]
[tex]T_2[/tex] = final temperature of gas = [tex]75^oC=273+75=348K[/tex]
Now put all the given values in the above equation, we get:
[tex]\frac{10kPa\times 10m^3}{323K}=\frac{15kPa\times V_2}{348K}[/tex]
[tex]V_2=7.2m^3[/tex]
The new volume of carbon dioxide gas is [tex]7.2m^3[/tex]
Now we have to calculate the new density of carbon dioxide gas.
[tex]PV=nRT\\\\PV=\frac{m}{M}RT\\\\P=\frac{m}{V}\frac{RT}{M}\\\\P=\rho \frac{RT}{M}\\\\\rho=\frac{PM}{RT}[/tex]
Formula for new density will be:
[tex]\rho_2=\frac{P_2M}{RT_2}[/tex]
where,
[tex]P_2[/tex] = new pressure of gas = 15 kPa
[tex]T_2[/tex] = new temperature of gas = [tex]75^oC=273+75=348K[/tex]
M = molar mass of carbon dioxide gas = 44 g/mole
R = gas constant = 8.314 L.kPa/mol.K
[tex]\rho[/tex] = new density
Now put all the given values in the above equation, we get:
[tex]\rho_2=\frac{(15kPa)\times (44g/mole)}{(8.314L.kPa/mol.K)\times (348K)}[/tex]
[tex]\rho_2=0.2281g/L[/tex]
The new density of carbon dioxide gas is 0.2281 g/L
