Respuesta :
Answer : The ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon is, 0.5735
Explanation :
First we have to calculate the original number of moles of air in the balloon.
Using ideal gas equation:
PV = nRT
or,
[tex]n_1=\frac{PV_1}{RT_1}[/tex]
where,
[tex]n_1[/tex] = original number of moles of air in the balloon = ?
P = pressure of gas = 745 torr = 99308.5 Pa (conversion used : 1 torr = 133.3 Pa)
[tex]V_1[/tex] = volume of gas = [tex]4.00\times 10^3m^3[/tex]
[tex]T_1[/tex] = temperature of gas = [tex]218^oC=273+218=491K[/tex]
R = gas constant = [tex]8.314Pa.m^3/mol.K[/tex]
Now put all the given values in the above equation, we get:
[tex]n_1=\frac{(99308.5 Pa)\times (4.00\times 10^3m^3)}{(8.314Pa.m^3/mol.K)\times (491K)}[/tex]
[tex]n_1=97309.4mol[/tex]
Now we have to calculate the number of moles of air in heated balloon.
Using ideal gas equation:
PV = nRT
or,
[tex]n_2=\frac{PV_2}{RT_2}[/tex]
where,
[tex]n_2[/tex] = number of moles of air in heated balloon = ?
P = pressure of gas = 745 torr = 99308.5 Pa (conversion used : 1 torr = 133.3 Pa)
[tex]V_2[/tex] = volume of gas = [tex]4.20\times 10^3m^3[/tex]
[tex]T_2[/tex] = temperature of gas = [tex]626^oC=273+626=899K[/tex]
R = gas constant = [tex]8.314Pa.m^3/mol.K[/tex]
Now put all the given values in the above equation, we get:
[tex]n_2=\frac{(99308.5 Pa)\times (4.20\times 10^3m^3)}{(8.314Pa.m^3/mol.K)\times (899K)}[/tex]
[tex]n_2=55804.1mol[/tex]
Now we have to calculate the ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon.
[tex]\frac{n_2}{n_1}=\frac{55804.1mol}{97309.4mol}=0.5735[/tex]
Thus, the ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon is, 0.5735
